{"id":19414,"date":"2024-08-01T19:16:28","date_gmt":"2024-08-01T14:46:28","guid":{"rendered":"https:\/\/cafetadris.com\/blog\/?p=19414"},"modified":"2024-08-04T11:04:56","modified_gmt":"2024-08-04T06:34:56","slug":"%d9%86%d8%ad%d9%88%d9%87-%db%8c%d8%a7%d9%81%d8%aa%d9%86-%da%a9%d9%88%d8%aa%d8%a7%d9%87%d8%aa%d8%b1%db%8c%d9%86-%d9%85%d8%b3%db%8c%d8%b1-%d8%af%d8%b1-%da%af%d8%b1%d8%a7%d9%81-%d8%a8%d8%b1","status":"publish","type":"post","link":"https:\/\/cafetadris.com\/blog\/%d9%86%d8%ad%d9%88%d9%87-%db%8c%d8%a7%d9%81%d8%aa%d9%86-%da%a9%d9%88%d8%aa%d8%a7%d9%87%d8%aa%d8%b1%db%8c%d9%86-%d9%85%d8%b3%db%8c%d8%b1-%d8%af%d8%b1-%da%af%d8%b1%d8%a7%d9%81-%d8%a8%d8%b1\/","title":{"rendered":"\u0645\u0633\u0626\u0644\u0647 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 &#8211; \u0628\u0631\u0631\u0633\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627\u060c \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u0641\u0644\u0648\u06cc\u062f"},"content":{"rendered":"\n<p>\u0645\u0633\u0626\u0644\u0647 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Shortest_path_problem\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Shortest path problem<\/mark><\/a>)\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0627\u0633\u0627\u0633\u06cc \u0648 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u0639\u0644\u0648\u0645 \u0631\u0627\u06cc\u0627\u0646\u0647 \u0648 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u062f\u0631 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627 \u0627\u0632 \u062c\u0645\u0644\u0647 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u062d\u0645\u0644\u200c\u0648\u0646\u0642\u0644\u060c \u0637\u0631\u0627\u062d\u06cc \u0645\u062f\u0627\u0631\u0647\u0627\u06cc \u0627\u0644\u06a9\u062a\u0631\u06cc\u06a9\u06cc \u0648 \u062d\u062a\u06cc \u062f\u0631 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc \u0648\u06cc\u062f\u0626\u0648\u06cc\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0628\u0627 \u0627\u0646\u0648\u0627\u0639 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u0622\u0634\u0646\u0627 \u0645\u06cc\u200c\u0634\u0648\u06cc\u0645.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06af\u0631\u0627\u0641 \u0686\u06cc\u0633\u062a\u061f<\/h2>\n\n\n\n<p><a href=\"https:\/\/cafetadris.com\/blog\/%d9%86%d8%b8%d8%b1%db%8c%d9%87-%da%af%d8%b1%d8%a7%d9%81-%d9%be%d9%84%db%8c-%d8%a8%db%8c%d9%86-%d8%b1%db%8c%d8%a7%d8%b6%db%8c%d8%a7%d8%aa-%d9%88-%d8%af%d9%86%db%8c%d8%a7%db%8c-%d9%88%d8%a7%d9%82%d8%b9\/\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u06af\u0631\u0627\u0641<\/mark><\/a> (Graph) \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u062f\u0644\u200c\u0633\u0627\u0632\u06cc \u0631\u0648\u0627\u0628\u0637 \u0628\u06cc\u0646 \u0627\u0634\u06cc\u0627\u0621 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0633\u0627\u062e\u062a\u0627\u0631 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u0646\u0642\u0627\u0637 \u0628\u0647 \u0646\u0627\u0645 \u0631\u0627\u0633 (Nodes) \u06cc\u0627 \u0631\u0627\u0633 (Vertices) \u0648 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u062e\u0637\u0648\u0637 \u0628\u0647 \u0646\u0627\u0645 \u06cc\u0627\u0644 \u06cc\u0627 \u06cc\u0627\u0644 (Edges) \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0645\u062a\u0635\u0644 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0631\u0627\u0633\u200c\u0647\u0627 \u0646\u0642\u0627\u0637\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0645\u0648\u062c\u0648\u062f\u06cc\u062a\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0646\u0645\u0627\u06cc\u0646\u062f\u06af\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f. \u0645\u062b\u0644\u0627\u064b \u062f\u0631 \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0627\u062c\u062a\u0645\u0627\u0639\u06cc\u060c \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0646\u0645\u0627\u06cc\u0627\u0646\u06af\u0631 \u0627\u0641\u0631\u0627\u062f \u0628\u0627\u0634\u0646\u062f. \u06cc\u0627\u0644\u200c\u0647\u0627 \u062e\u0637\u0648\u0637\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0645\u062a\u0635\u0644 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0648 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0631\u0648\u0627\u0628\u0637 \u06cc\u0627 \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0628\u06cc\u0646 \u0622\u0646\u200c\u0647\u0627 \u0647\u0633\u062a\u0646\u062f. \u0645\u062b\u0644\u0627\u064b \u062f\u0631 \u0647\u0645\u0627\u0646 \u0634\u0628\u06a9\u0647 \u0627\u062c\u062a\u0645\u0627\u0639\u06cc\u060c \u06cc\u0627\u0644\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u062f\u0648\u0633\u062a\u06cc \u0628\u06cc\u0646 \u0627\u0641\u0631\u0627\u062f \u0628\u0627\u0634\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0646\u0648\u0627\u0639 \u06af\u0631\u0627\u0641<\/h3>\n\n\n\n<p>\u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0633\u062a\u0647 \u0628\u0647 \u0646\u0648\u0639 \u0648 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc\u0634\u0627\u0646 \u0628\u0647 \u0686\u0646\u062f\u06cc\u0646 \u062f\u0633\u062a\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0634\u0648\u0646\u062f\u060c \u0627\u0635\u0644\u06cc\u200c\u062a\u0631\u06cc\u0646 \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647\u200c\u0628\u0646\u062f\u06cc\u200c\u0647\u0627 \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u062c\u0647\u062a\u200c\u062f\u0627\u0631 (Directed Graphs):<\/strong> \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0647\u0631 \u06cc\u0627\u0644 \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u062c\u0647\u062a \u0645\u0634\u062e\u0635 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u0627\u0631\u062a\u0628\u0627\u0637 \u0627\u0632 \u06a9\u062f\u0627\u0645 \u0631\u0627\u0633 \u0628\u0647 \u06a9\u062f\u0627\u0645 \u0631\u0627\u0633 \u062f\u06cc\u06af\u0631 \u0628\u0631\u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n\n\n\n<li><strong>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u062c\u0647\u062a (Undirected Graphs):<\/strong> \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u06cc\u0627\u0644\u200c\u0647\u0627 \u062c\u0647\u062a \u0646\u062f\u0627\u0631\u0646\u062f \u0648 \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0648 \u0637\u0631\u0641\u0647 \u0627\u0633\u062a.<\/li>\n\n\n\n<li><strong>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 (Weighted Graphs):<\/strong> \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0647\u0631 \u06cc\u0627\u0644 \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0648\u0632\u0646 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0647\u0632\u06cc\u0646\u0647\u060c \u0641\u0627\u0635\u0644\u0647 \u06cc\u0627 \u0647\u0631 \u0645\u0639\u06cc\u0627\u0631 \u062f\u06cc\u06af\u0631\u06cc \u0627\u0632 \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0633 \u0627\u0633\u062a.<\/li>\n\n\n\n<li><strong>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 (Unweighted Graphs):<\/strong> \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u06cc\u0627\u0644\u200c\u0647\u0627 \u0648\u0632\u0646 \u0646\u062f\u0627\u0631\u0646\u062f \u0648 \u062a\u0646\u0647\u0627 \u0648\u062c\u0648\u062f \u06cc\u0627 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u0647\u0645 \u0627\u0633\u062a.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647 \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0645\u0648\u0631\u062f \u06af\u0631\u0627\u0641 \u0648 \u0627\u0646\u0648\u0627\u0639 \u0622\u0646 \u0645\u0642\u0627\u0644\u0647<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"> <\/mark><a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%d9%86%d8%b8%d8%b1%db%8c%d9%87-%da%af%d8%b1%d8%a7%d9%81-%d9%be%d9%84%db%8c-%d8%a8%db%8c%d9%86-%d8%b1%db%8c%d8%a7%d8%b6%db%8c%d8%a7%d8%aa-%d9%88-%d8%af%d9%86%db%8c%d8%a7%db%8c-%d9%88%d8%a7%d9%82%d8%b9\/\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0646\u0638\u0631\u06cc\u0647 \u06af\u0631\u0627\u0641: \u067e\u0644\u06cc \u0628\u06cc\u0646 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u0648 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc<\/mark><\/a> \u0631\u0627 \u0628\u062e\u0648\u0627\u0646\u06cc\u062f.<\/p>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u062f \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u06cc \u062f\u0627\u0631\u0646\u062f\u060c \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0646\u062a\u0638\u0627\u0631 \u062f\u0627\u0634\u062a \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0648\u0627\u062d\u062f \u0628\u062a\u0648\u0627\u0646\u062f \u062a\u0645\u0627\u0645\u06cc \u0645\u0633\u0627\u0626\u0644 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u062d\u0644 \u06a9\u0646\u062f. \u067e\u06cc\u0634 \u0627\u0632 \u0628\u0631\u0631\u0633\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647\u060c \u0644\u0627\u0632\u0645 \u0627\u0633\u062a \u062f\u0648 \u062f\u0633\u062a\u0647 \u06a9\u0644\u06cc \u0645\u0633\u0627\u0626\u0644 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0645\u0639\u0631\u0641\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0645\u0633\u0626\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u0627 \u06cc\u06a9 \u0645\u0628\u062f\u0627<\/h2>\n\n\n\n<p>\u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0627 \u06cc\u06a9 \u0645\u0628\u062f\u0627 (Single Source Shortest Path)\u060c \u0647\u062f\u0641 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a. \u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u062f\u0631 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062f\u0627\u0631\u06cc\u0645 \u0648 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u0628\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u06af\u0631\u0627\u0641 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0645\u062e\u062a\u0644\u0641\u06cc \u0645\u0627\u0646\u0646\u062f \u0645\u0633\u06cc\u0631\u06cc\u0627\u0628\u06cc \u062f\u0631 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u0646\u0642\u0634\u0647\u200c\u0647\u0627\u06cc \u0634\u0647\u0631\u06cc \u0648 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631\u0647\u0627 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645\u200c\u0647\u0627\u06cc \u062d\u0645\u0644\u200c\u0648\u0646\u0642\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0645\u0633\u0626\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u062c\u0641\u062a\u200c \u0631\u0627\u0633\u200c\u0647\u0627<\/h2>\n\n\n\n<p>\u0628\u0631\u062e\u0644\u0627\u0641 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0627 \u06cc\u06a9 \u0645\u0628\u062f\u0627 \u06a9\u0647 \u062a\u0646\u0647\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627 (All Pairs Shortest Path) \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062c\u0641\u062a \u0645\u0645\u06a9\u0646 \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0647\u0633\u062a\u0646\u062f.<\/p>\n\n\n\n<p>\u0627\u06cc\u0646 \u0646\u0648\u0639 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0646\u06cc\u0632 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u0633\u06cc\u0633\u062a\u0645\u200c\u0647\u0627\u06cc \u062d\u0645\u0644\u200c\u0648\u0646\u0642\u0644 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u062f\u0627\u0631\u0646\u062f.<\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0646\u0627\u0633\u0628 \u062d\u0644 \u0647\u0631 \u062f\u0633\u062a\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0633\u0627\u0626\u0644 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641<\/h2>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u060c \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0635 \u0628\u0647 \u062e\u0648\u062f \u0631\u0627 \u062f\u0627\u0631\u062f. \u0627\u0645\u0627 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u0633\u0627\u0633 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641 \u0628\u0647 \u062f\u0648 \u0632\u06cc\u0631 \u0645\u0633\u0626\u0644\u0647 \u062f\u06cc\u06af\u0631 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631<\/h2>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f\u06cc \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u0646\u062f \u06a9\u0647 \u0645\u0647\u0645\u200c\u062a\u0631\u06cc\u0646 \u0622\u0646\u200c\u0647\u0627 \u0639\u0628\u0627\u0631\u062a\u200c\u0627\u0646\u062f \u0627\u0632:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h2>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Dijkstra%27s_algorithm\" target=\"_blank\" rel=\"noopener\">Dijkstra&#8217;s Algorithm<\/a>) \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Greedy_algorithm\" target=\"_blank\" rel=\"noopener\">Greedy algorithm<\/a>) \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0634\u0631\u0648\u0639 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0628\u0647 \u062a\u062f\u0631\u06cc\u062c \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u06cc\u0627\u0644 \u0645\u0646\u0641\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f \u062f\u0631\u0633\u062a \u06a9\u0627\u0631 \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u062a\u0648\u0633\u0637 \u06cc\u06a9 \u062f\u0627\u0646\u0634\u0645\u0646\u062f \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0647\u0644\u0646\u062f\u06cc \u0628\u0647 \u0646\u0627\u0645 \u0627\u062f\u0633\u062e\u0631 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Edsger_W._Dijkstra\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Edsger Dijkstra<\/mark><\/a>) \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f5\u06f6 \u0627\u0628\u062f\u0627\u0639 \u0634\u062f \u0648 \u0627\u0648\u0644\u06cc\u0646 \u0628\u0627\u0631 \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f5\u06f9 \u0645\u0646\u062a\u0634\u0631 \u0634\u062f. \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u062d\u0645\u0644 \u0648 \u0646\u0642\u0644 \u062a\u0648\u0633\u0639\u0647 \u062f\u0627\u062f\u060c \u0627\u0645\u0627 \u0628\u0647 \u0633\u0631\u0639\u062a \u0645\u0634\u062e\u0635 \u0634\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0631 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u06af\u0631\u0627\u0641 \u0646\u06cc\u0632 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0633\u0627\u062f\u06af\u06cc \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc\u200c\u0627\u0634 \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0647\u0645\u200c\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u062f\u0631 \u0646\u0638\u0631\u06cc\u0647 \u06af\u0631\u0627\u0641 \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0686\u0637\u0648\u0631 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u0627\u062d\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0628\u062a\u062f\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062a\u0627 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0628\u0647 \u0635\u0641\u0631 \u0648 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a (\u221e) \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0633\u067e\u0633 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062e\u0627\u0644\u06cc \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 (\u0631\u0627\u0633\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646\u200c\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647)\u060c \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u06cc \u0631\u0627\u0633\u200c\u0627\u06cc \u06a9\u0647 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062f\u0627\u0631\u062f \u0648 \u0647\u0646\u0648\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647\u060c \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0631\u0627\u0633 \u0627\u0646\u062a\u062e\u0627\u0628\u200c\u0634\u062f\u0647 \u0631\u0627 \u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0627\u0646\u062a\u062e\u0627\u0628\u200c\u0634\u062f\u0647 \u062a\u0627 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0628\u0648\u062f\u0646 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0645\u0631\u0627\u062d\u0644 \u06f3 \u062a\u0627 \u06f5 \u0631\u0627 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u0648\u0646\u062f\u060c \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n<\/ul>\n\n\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/storage.cafetadris.com\/blog\/dijk.gif\"><\/p>\n\n\n<h3 class=\"wp-block-heading\">\u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0686\u06cc\u0633\u062a\u061f<\/h3>\n\n\n\n<p>\u0628\u0627 \u06a9\u0645\u06cc \u062f\u0642\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0641\u0647\u0645\u06cc\u062f \u06a9\u0647 \u0646\u062a\u06cc\u062c\u0647 \u062d\u0627\u0635\u0644 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0648\u06cc \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 (\u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc) \u06cc\u06a9 \u062f\u0631\u062e\u062a \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0631\u0627 \u0628\u06cc\u0646 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0648 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062f\u0631\u062e\u062a\u060c \u062f\u0631\u062e\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Shortest-path_tree\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Shortest Path Tree &#8211; SPT<\/mark><\/a>) \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0631\u062e\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u06af\u0631\u0627\u0641 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image.png\" alt=\"\" class=\"wp-image-19429\" width=\"591\" height=\"324\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image.png 775w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-300x165.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-768x421.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-585x321.png 585w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647<\/h4>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0631\u062e\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641\u060c \u0631\u0627\u0633 A \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0631\u0627\u062d\u062a\u200c\u062a\u0631 \u062f\u0646\u0628\u0627\u0644 \u06a9\u0646\u06cc\u0645\u060c \u06cc\u06a9 \u062c\u062f\u0648\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. \u062f\u0631 \u0633\u062a\u0648\u0646 \u0627\u0648\u0644 \u0627\u06cc\u0646 \u062c\u062f\u0648\u0644 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 (Visited) \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u06cc\u0645. \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u06cc\u0645\u060c \u0648\u0642\u062a\u06cc \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u0631\u0627\u0633\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0622\u0646 \u0627\u0632 \u0631\u0627\u0633 A \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0627\u0634\u062f.<\/p>\n\n\n\n<p>\u0633\u062a\u0648\u0646 \u062f\u0648\u0645 \u0627\u06cc\u0646 \u062c\u062f\u0648\u0644\u060c \u0641\u0627\u0635\u0644\u0647 (Distance) \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u062a\u0627 \u0631\u0627\u0633 A \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0631\u0627 \u0627\u0628\u062a\u062f\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u06cc\u0646 \u0633\u062a\u0648\u0646 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u0642\u062a\u06cc \u067e\u0631 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0627 \u067e\u06cc\u0634\u0631\u0641\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u063a\u06cc\u06cc\u0631 \u06a9\u0646\u0646\u062f. \u0648\u0642\u062a\u06cc \u0631\u0627\u0633\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0622\u0646 \u0645\u0634\u062e\u0635 \u062e\u0648\u0627\u0647\u062f \u0634\u062f. \u0633\u062a\u0648\u0646 \u0622\u062e\u0631 \u0627\u06cc\u0646 \u062c\u062f\u0648\u0644 \u0631\u0627\u0633 \u0642\u0628\u0644\u06cc (Previous) \u062f\u0631 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0648\u06cc \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641\u060c \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 \u0631\u0627 \u0628\u0627 \u0631\u0646\u06af \u0642\u0631\u0645\u0632\u060c \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06a9\u0647 \u0647\u0645\u0686\u0646\u0627\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646\u200c\u0647\u0627 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0628\u0627 \u0631\u0646\u06af \u062e\u0627\u06a9\u0633\u062a\u0631\u06cc \u0648 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 &#8211; 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\u0645\u0631\u062d\u0644\u0647\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 A \u0631\u0627 \u0628\u0647 \u0635\u0641\u0631 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0627\u062f\u0647 \u0648 \u0686\u0648\u0646 \u0645\u0633\u06cc\u0631 \u062f\u06cc\u06af\u0631\u06cc \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646 \u0646\u062f\u0627\u0631\u06cc\u0645\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 \u062f\u0631 \u062c\u062f\u0648\u0644 \u062b\u0628\u062a \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u0628\u0627\u06cc\u062f \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647 A (\u0631\u0627\u0633\u200c\u0647\u0627 B \u0648 E) \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0648 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class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-2.png\" alt=\"\" class=\"wp-image-19431\" width=\"802\" height=\"336\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-2-300x126.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-2-768x323.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-2-585x246.png 585w\" sizes=\"(max-width: 802px) 100vw, 802px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0627\u0632\u062f\u06cc\u062f \u0631\u0627\u0633 E<\/h4>\n\n\n\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f \u0628\u0627\u06cc\u062f \u0627\u0632 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647\u060c \u0631\u0627\u0633\u06cc \u0631\u0627 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646 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\u0627\u0633\u062a (\u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 B\u060c \u06f7 \u0648 \u0628\u0642\u06cc\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0647\u0633\u062a\u0646\u062f). \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0631\u0627\u0633 E \u0631\u0627 \u0645\u0644\u0627\u0642\u0627\u062a \u06a9\u0631\u062f\u0647 \u0648 \u0627\u06cc\u0646 \u06cc\u0639\u0646\u06cc \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 A \u0628\u0647 E \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1 \u0627\u0633\u062a.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0686\u0631\u0627 \u0631\u0627\u0633 E \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u06cc\u0645\u061f<\/h4>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u062a\u0648\u0636\u06cc\u062d 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\u0641\u0627\u0635\u0644\u0647 A \u0628\u0647 B \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 A \u0628\u0647 E \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0647\u0631 \u0645\u0633\u06cc\u0631\u06cc \u06a9\u0647 \u0627\u0632 B \u0645\u06cc\u200c\u06af\u0630\u0631\u062f\u060c \u0628\u0627\u06cc\u062f \u0637\u0648\u0644\u0627\u0646\u06cc\u200c\u062a\u0631 \u0627\u0632 A \u0628\u0647 E \u0628\u0627\u0634\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 AE \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 A \u0628\u0647 E \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0645\u0627 \u0647\u0646\u0648\u0632 \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u06cc \u0631\u0627 \u06a9\u0647 \u0627\u0632 A \u0628\u0647 B \u0645\u06cc\u200c\u0631\u0648\u062f\u060c \u0646\u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645. \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0633\u06cc\u0631 \u0645\u0633\u062a\u0642\u06cc\u0645 AB \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u06f8 \u0628\u0627\u0634\u062f. \u0627\u0645\u0627 \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 AE \u0628\u0631\u0627\u0628\u0631 \u06f1 \u0627\u0633\u062a\u060c \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0633\u06cc\u0631 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc \u0628\u0647 B \u0627\u0632 \u0637\u0631\u06cc\u0642 E \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0642\u0639\u06cc\u062a\u060c \u0645\u0627 \u0647\u0646\u0648\u0632 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 B \u0631\u0627 \u0646\u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u0648 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0645\u0648\u0642\u062a\u06cc \u0645\u06cc\u200c\u0646\u0627\u0645\u06cc\u0645.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0628\u0627\u06cc\u062f \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647 E \u06cc\u0639\u0646\u06cc B\u060c C \u0648 D \u0631\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0628\u0627 \u0647\u0632\u06cc\u0646\u0647 \u06a9\u0645\u062a\u0631\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 E \u0628\u0647 \u0622\u0646\u200c\u0647\u0627 \u0631\u0633\u06cc\u062f\u060c \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0645\u0648\u0631\u062f \u0631\u0627\u0633 B\u060c \u0641\u0627\u0635\u0644\u0647 AEB \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f8 + \u06f1 = \u06f9 \u0627\u0633\u062a \u0648 \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc B \u06a9\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f8 \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u062a\u0627 \u0627\u06cc\u0646 \u0644\u062d\u0638\u0647\u060c \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a\u06cc C \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u067e\u0633 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u0627\u0632 \u0637\u0631\u06cc\u0642 E \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0645\u0627\u0646 AEC \u0627\u0633\u062a. \u0641\u0627\u0635\u0644\u0647 \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1 + \u06f2 = \u06f3 \u0627\u0633\u062a. \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a\u06cc D \u0628\u0627 AED \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1 + \u06f7 = \u06f8 \u0627\u0633\u062a. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u062c\u062f\u0648\u0644 \u0645\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062f\u0631\u0645\u06cc\u200c\u0622\u06cc\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-3.png\" alt=\"\" class=\"wp-image-19432\" width=\"808\" height=\"340\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-3.png 935w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-3-300x126.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-3-768x324.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-3-585x247.png 585w\" sizes=\"(max-width: 808px) 100vw, 808px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0627\u0632\u062f\u06cc\u062f \u0631\u0627\u0633 C<\/h4>\n\n\n\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627\u0633\u06cc \u06a9\u0647 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a \u0631\u0627 \u062f\u0627\u0631\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0646\u0642\u0637\u0647 \u0634\u0631\u0648\u0639 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u0632 \u062c\u062f\u0648\u0644 \u0645\u0631\u062d\u0644\u0647 \u0642\u0628\u0644\u060c \u0631\u0627\u0633\u200c\u0647\u0627 B\u060c C \u0648 D \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647\u200c\u0627\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0628\u06cc\u0646 \u0622\u0646\u200c\u0647\u0627 C \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 (\u06f3) \u0631\u0627 \u062f\u0627\u0631\u062f. \u067e\u0633 C \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 \u0639\u0644\u0627\u0645\u062a \u0645\u06cc\u200c\u0632\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647 C \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 B \u0648 D \u0647\u0633\u062a\u0646\u062f. \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a\u06cc B \u0627\u0632 \u0637\u0631\u06cc\u0642 C \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f3 + \u06f3 = \u06f6 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0641\u0627\u0635\u0644\u0647 \u0627\u0635\u0644\u06cc C \u0648 \u0648\u0632\u0646 \u06cc\u0627\u0644 BC \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f3 \u0647\u0633\u062a\u0646\u062f\u060c \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u062c\u062f\u06cc\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0642\u0628\u0644\u06cc B (\u06f7) \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644 \u0645\u0648\u0642\u062a B \u0631\u0627 \u0628\u0647 \u06f6 \u0648 \u0631\u0627\u0633 \u0642\u0628\u0644\u06cc\u200c\u0627\u0634 \u0631\u0627 \u0647\u0645 \u0628\u0647 C \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a\u06cc D \u0627\u0632 \u0637\u0631\u06cc\u0642 C \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f3 + \u06f6 = \u06f9 \u0627\u0633\u062a. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0633\u062a\u060c \u0622\u0646 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-4.png\" alt=\"\" class=\"wp-image-19433\" width=\"770\" height=\"324\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-4.png 918w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-4-300x126.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-4-768x324.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-4-585x247.png 585w\" sizes=\"(max-width: 770px) 100vw, 770px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0627\u0632\u062f\u06cc\u062f \u0631\u0627\u0633 B<\/h4>\n\n\n\n<p>\u06a9\u0627\u0631 \u0645\u0627 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u062a\u0645\u0627\u0645 \u0634\u062f\u0647\u200c \u0627\u0633\u062a. \u062f\u0631 \u0648\u0627\u0642\u0639 \u0627\u06a9\u0646\u0648\u0646 \u062a\u0646\u0647\u0627 \u0631\u0627\u0633\u200c\u0647\u0627 B \u0648 D \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647\u200c\u0627\u0646\u062f \u0648 B \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0645\u0648\u0642\u062a\u06cc \u0631\u0627 \u062f\u0627\u0631\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u06f6 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u0639\u0644\u0627\u0645\u062a \u0645\u06cc\u200c\u0632\u0646\u06cc\u0645. B \u0647\u06cc\u0686 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647\u200c\u0627\u06cc \u0646\u062f\u0627\u0631\u062f \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u06a9\u0627\u0631 \u062f\u06cc\u06af\u0631\u06cc \u0646\u0628\u0627\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-5.png\" alt=\"\" class=\"wp-image-19434\" width=\"759\" height=\"320\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-5.png 911w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-5-300x126.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-5-768x324.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-5-585x247.png 585w\" sizes=\"(max-width: 759px) 100vw, 759px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0627\u0632\u062f\u06cc\u062f \u0631\u0627\u0633 D<\/h4>\n\n\n\n<p>\u0627\u06a9\u0646\u0648\u0646 \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0627\u0632\u062f\u06cc\u062f\u0646\u0634\u062f\u0647 \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f\u0647 \u06a9\u0647 D \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u06f8 (\u0686\u0648\u0646 \u0631\u0627\u0647 \u0628\u0647\u062a\u0631\u06cc \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646 \u0646\u06cc\u0633\u062a) \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u0639\u0644\u0627\u0645\u062a \u0645\u06cc\u200c\u0632\u0646\u06cc\u0645. \u0686\u0648\u0646 \u0647\u06cc\u0686 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647\u200c\u0627\u06cc \u0627\u0632 D \u0646\u06cc\u0632 \u0628\u0627\u0642\u06cc \u0646\u0645\u0627\u0646\u062f\u0647\u060c \u06a9\u0627\u0631 \u0645\u0627 \u062a\u0645\u0627\u0645 \u0627\u0633\u062a:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-6.png\" alt=\"\" class=\"wp-image-19435\" width=\"782\" height=\"330\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-6.png 923w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-6-300x126.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-6-768x324.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-6-585x247.png 585w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u062f\u0631\u062e\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631<\/h4>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0627\u0633\u062a \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0633\u06cc\u0631 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627\u060c \u06cc\u0639\u0646\u06cc A \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 D \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 AED \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u06f8 \u0627\u0633\u062a \u0648 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 B \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 AECB \u0628\u0627 \u0637\u0648\u0644 \u06f6 \u0627\u0633\u062a:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-7.png\" alt=\"\" class=\"wp-image-19436\" width=\"626\" height=\"347\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-7.png 792w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-7-300x166.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-7-768x426.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-7-585x324.png 585w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/><\/figure><\/div>\n\n\n<p>\u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u062f\u0631\u062e\u062a \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u0632 A \u0634\u0631\u0648\u0639 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a. \u0627\u06af\u0631 \u0627\u0632 \u0631\u0627\u0633 \u062f\u06cc\u06af\u0631\u06cc \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645\u060c \u0645\u0633\u06cc\u0631\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u062f\u0631\u062e\u062a \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0646\u0628\u0627\u0634\u062f. \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 C \u0628\u0647 D \u0628\u0631\u0648\u06cc\u0645\u060c \u0637\u0628\u0642 \u0627\u06cc\u0646 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u062f \u0627\u0632 \u0637\u0631\u06cc\u0642 E \u0628\u0631\u0648\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0627\u06cc \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f9 \u062f\u0627\u0631\u062f. \u0627\u0645\u0627 \u0628\u0627 \u0646\u06af\u0627\u0647 \u0628\u0647 \u06a9\u0644 \u06af\u0631\u0627\u0641\u060c \u0645\u06cc\u200c\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0631\u0641\u062a\u0646 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0627\u0632 C \u0628\u0647 D \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u06f6 \u0627\u0645\u06a9\u0627\u0646\u200c\u067e\u0630\u06cc\u0631 \u0627\u0633\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h3>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u06cc\u067e \u062f\u0648\u062f\u0648\u06cc\u06cc<\/h4>\n\n\n\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0627\u0632 <a rel=\"noreferrer noopener\" href=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%87%D8%B1%D9%85_%D8%AF%D9%88%D8%AF%D9%88%DB%8C%DB%8C\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0647\u06cc\u067e \u062f\u0648\u062f\u0648\u06cc\u06cc<\/mark><\/a> (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Binary_heap\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Binary Heap<\/mark><\/a>) \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0635\u0641 \u0627\u0648\u0644\u0648\u06cc\u062a \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0645\u0631\u062d\u0644\u0647\u200c\u06cc \u0627\u0628\u062a\u062f\u0627\u06cc\u06cc<\/strong>: \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u0635\u0641 \u0627\u0648\u0644\u0648\u06cc\u062a \u0628\u0627 V \u0631\u0627\u0633 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 O(V).<\/li>\n\n\n\n<li><strong>\u0639\u0645\u0644\u06cc\u0627\u062a \u062d\u0630\u0641 \u0631\u0627\u0633 \u0628\u0627 \u062d\u062f\u0627\u0642\u0644 \u0641\u0627\u0635\u0644\u0647<\/strong>: \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0631 \u062d\u0630\u0641 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(logV) \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u06a9\u0644 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(VlogV) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/li>\n\n\n\n<li><strong>\u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0641\u0648\u0627\u0635\u0644<\/strong>: \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u0627\u0644 \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0631 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(logV) \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u06a9\u0644 \u0628\u0631\u0627\u06cc E \u06cc\u0627\u0644\u060c \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(ElogV) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0627 \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0627\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u06cc\u067e \u062f\u0648\u062f\u0648\u06cc\u06cc \u0628\u0631\u0627\u0628\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u0628\u0627:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O((V + E) \\log V) = O(E \\log V)<\/span><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc \u0647\u06cc\u067e<\/h4>\n\n\n\n<p>\u0627\u06af\u0631 \u0627\u0632 <a href=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%87%D8%B1%D9%85_%D9%81%DB%8C%D8%A8%D9%88%D9%86%D8%A7%DA%86%DB%8C\" data-type=\"URL\" data-id=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%87%D8%B1%D9%85_%D9%81%DB%8C%D8%A8%D9%88%D9%86%D8%A7%DA%86%DB%8C\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0647\u06cc\u067e \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc<\/mark><\/a> (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fibonacci_heap\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Fibonacci Heap<\/mark><\/a>) \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0635\u0641 \u0627\u0648\u0644\u0648\u06cc\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647\u0628\u0648\u062f \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0645\u0631\u062d\u0644\u0647\u200c\u06cc \u0627\u0628\u062a\u062f\u0627\u06cc\u06cc<\/strong>: \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u0635\u0641 \u0627\u0648\u0644\u0648\u06cc\u062a \u0628\u0627 V \u0631\u0627\u0633 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 O(V).<\/li>\n\n\n\n<li><strong>\u0639\u0645\u0644\u06cc\u0627\u062a \u062d\u0630\u0641 \u0631\u0627\u0633 \u0628\u0627 \u062d\u062f\u0627\u0642\u0644 \u0641\u0627\u0635\u0644\u0647<\/strong>: \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0631 \u062d\u0630\u0641 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(logV) \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u06a9\u0644 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(VlogV) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/li>\n\n\n\n<li><strong>\u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0641\u0648\u0627\u0635\u0644<\/strong>: \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u0627\u0644 E \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0631 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(1) \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u06a9\u0644 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(E) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0627 \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0627\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u06cc\u067e \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc \u0628\u0631\u0627\u0628\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u0628\u0627:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O(V \\log V + E)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0647 \u0646\u0627\u0645&nbsp;<code>dijkstra<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0628\u062a\u062f\u0627\u060c \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0631\u062f\u0647 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u0633\u067e\u0633 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 <code>sptSet<\/code> \u0628\u0631\u0627\u06cc \u0646\u06af\u0647\u062f\u0627\u0631\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f\u0634\u062f\u0647 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0648 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062d\u0644\u0642\u0647 <code>for<\/code>\u060c \u0631\u0627\u0633\u06cc \u0631\u0627 \u06a9\u0647 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062f\u0627\u0631\u062f \u0648 \u0647\u0646\u0648\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647\u060c \u0627\u0646\u062a\u062e\u0627\u0628 \u0648 \u0628\u0647 <code>sptSet<\/code> \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0647\u0631 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0627\u06cc\u0646 \u0631\u0627\u0633\u060c \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u062c\u062f\u06cc\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0642\u0628\u0644\u06cc\u200c\u0627\u0634 \u0628\u0627\u0634\u062f\u060c \u0645\u0642\u062f\u0627\u0631 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647\u200c\u0631\u0648\u0632 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u0648\u0646\u062f \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627\u0632\u06af\u0631\u062f\u0627\u0646\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def dijkstra(graph, source):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances from the source to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># except the source itself which is set to zero<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist[source] = 0<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Set to keep track of vertices included in the shortest path tree<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;sptSet = set()<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Loop until all vertices are processed<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;while len(sptSet) &lt; len(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Select the vertex with the minimum distance value<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;u = min((vertex for vertex in dist if vertex not in sptSet), key=dist.get)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Add the selected vertex to the set<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sptSet.add(u)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Update distance value of the adjacent vertices<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[u].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># If the vertex is not in the shortest path tree<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if neighbor not in sptSet:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Update the distance if the new distance is shorter<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[u] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[neighbor] = dist[u] + weight<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Print the current state of distances<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(f'{u} as minimum', ': ', dist)<\/code><\/p>\n\n\n\n<p>\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u06cc\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'A': {'B': 7, 'E': 1},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'B': {'A': 7, 'C': 3, 'E': 8},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'C': {'B': 3, 'E': 2, 'D': 6},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'D': {'C': 6, 'E': 7},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'E': {'A': 1, 'B': 8, 'C': 2, 'D': 7}<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>dijkstra(graph, 'A')<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>A as minimum:<\/strong><br \/>\n{&#8216;A&#8217;: 0, &#8216;B&#8217;: 7, &#8216;C&#8217;: inf, &#8216;D&#8217;: inf, &#8216;E&#8217;: 1}<br \/>\n<strong>E as minimum:<\/strong><br \/>\n{&#8216;A&#8217;: 0, &#8216;B&#8217;: 7, &#8216;C&#8217;: 3, &#8216;D&#8217;: 8, &#8216;E&#8217;: 1}<br \/>\n<strong>C as minimum:<\/strong><br \/>\n{&#8216;A&#8217;: 0, &#8216;B&#8217;: 6, &#8216;C&#8217;: 3, &#8216;D&#8217;: 8, &#8216;E&#8217;: 1}<br \/>\n<strong>B as minimum:<\/strong><br \/>\n{&#8216;A&#8217;: 0, &#8216;B&#8217;: 6, &#8216;C&#8217;: 3, &#8216;D&#8217;: 8, &#8216;E&#8217;: 1}<br \/>\n<strong>D as minimum:<\/strong><br \/>\n{&#8216;A&#8217;: 0, &#8216;B&#8217;: 6, &#8216;C&#8217;: 3, &#8216;D&#8217;: 8, &#8216;E&#8217;: 1}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h2>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bellman%E2%80%93Ford_algorithm\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Bellman-Ford Algorithm<\/mark><\/a>) \u0646\u06cc\u0632 \u0645\u0627\u0646\u0646\u062f \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0628\u0627 \u0627\u06cc\u0646 \u062a\u0641\u0627\u0648\u062a \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0631\u0627 \u0646\u06cc\u0632 \u0645\u062f\u06cc\u0631\u06cc\u062a \u06a9\u0646\u062f. \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0648\u062c\u0648\u062f \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc (\u062f\u0648\u0631\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc) \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062a\u0634\u062e\u06cc\u0635 \u062f\u0627\u062f\u0647 \u0648 \u0622\u0646 \u0631\u0627 \u0627\u0639\u0644\u0627\u0645 \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Dynamic_programming\" target=\"_blank\" rel=\"noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Dynamic Programming<\/mark><\/a>) \u0627\u0633\u062a \u06a9\u0647 \u0686\u0646\u062f\u06cc\u0646 \u0628\u0627\u0631 \u0627\u0632 \u0631\u0648\u06cc \u062a\u0645\u0627\u0645 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0639\u0628\u0648\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0628\u0647 \u0637\u0648\u0631 \u0645\u0633\u062a\u0642\u0644 \u062a\u0648\u0633\u0637 \u062f\u0648 \u062f\u0627\u0646\u0634\u0645\u0646\u062f \u0628\u0647 \u0646\u0627\u0645\u200c\u0647\u0627\u06cc \u0631\u06cc\u0686\u0627\u0631\u062f \u0628\u0644\u0645\u0646 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Richard_E._Bellman\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Richard Bellman<\/mark><\/a>) \u0648 \u0644\u0633\u062a\u0631 \u0641\u0648\u0631\u062f (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Lester_R._Ford\" target=\"_blank\" rel=\"noopener\">Lester Ford<\/a>) \u062f\u0631 \u062f\u0647\u0647 \u06f1\u06f9\u06f5\u06f0 \u062a\u0648\u0633\u0639\u0647 \u06cc\u0627\u0641\u062a. \u0628\u0644\u0645\u0646 \u0648 \u0641\u0648\u0631\u062f \u0647\u0631 \u062f\u0648 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0633\u062a\u0642\u0644 \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u0648 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0631\u062f\u0646\u062f \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0646\u062a\u06cc\u062c\u0647 \u062a\u0644\u0627\u0634\u200c\u0647\u0627\u06cc \u0622\u0646\u200c\u0647\u0627 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0628\u0648\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0642\u0627\u0628\u0644\u06cc\u062a \u0645\u062f\u06cc\u0631\u06cc\u062a \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0628\u0647 \u0633\u0631\u0639\u062a \u062c\u0627\u06cc\u06af\u0627\u0647 \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0686\u0637\u0648\u0631 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u067e\u06cc\u0634 \u0627\u0632 \u062a\u0648\u0636\u06cc\u062d \u0631\u0648\u0646\u062f \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u0645\u0641\u0647\u0648\u0645 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0622\u0634\u0646\u0627 \u0634\u0648\u06cc\u0645:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062f\u0648\u0631 \u0645\u0646\u0641\u06cc<\/h4>\n\n\n\n<p>\u062f\u0648\u0631 \u0645\u0646\u0641\u06cc (Negative Cycle) \u06cc\u06a9 \u0686\u0631\u062e\u0647 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a \u06a9\u0647 \u0648\u0642\u062a\u06cc \u0648\u0632\u0646 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u0622\u0646 \u062c\u0645\u0639 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0646\u062a\u06cc\u062c\u0647 \u0645\u0646\u0641\u06cc \u0627\u0633\u062a. \u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u0627\u06af\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0634\u0631\u0648\u0639 \u06a9\u0631\u062f\u0647 \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0628\u0647 \u0647\u0645\u0627\u0646 \u0631\u0627\u0633 \u0628\u0627\u0632\u06af\u0631\u062f\u06cc\u0645 \u0648 \u0645\u062c\u0645\u0648\u0639 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u0637\u06cc \u0634\u062f\u0647 \u0645\u0646\u0641\u06cc \u0628\u0627\u0634\u062f\u060c \u0622\u0646 \u0631\u0627 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0645\u06cc\u200c\u0646\u0627\u0645\u06cc\u0645.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0623\u062b\u06cc\u0631 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0628\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0633\u06cc\u0631\u06cc\u0627\u0628\u06cc<\/h4>\n\n\n\n<p>\u062f\u0631 \u062d\u0636\u0648\u0631 \u062f\u0648\u0631\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc\u060c \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0631\u062f\u060c \u0632\u06cc\u0631\u0627 \u0647\u0631 \u0628\u0627\u0631 \u06a9\u0647 \u0627\u0632 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0639\u0628\u0648\u0631 \u06a9\u0646\u06cc\u0645\u060c \u0645\u062c\u0645\u0648\u0639 \u0648\u0632\u0646 \u0645\u0633\u06cc\u0631 \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f \u0648 \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0645\u0646\u0641\u06cc \u0627\u062f\u0627\u0645\u0647 \u06cc\u0627\u0628\u062f. \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0631\u0627 \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062a\u0634\u062e\u06cc\u0635 \u062f\u0627\u062f \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u06af\u0631\u0627\u0641 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u062c\u0648\u0627\u0628 \u0646\u0645\u06cc\u200c\u062f\u0647\u062f \u0627\u0645\u0627 \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u06af\u0641\u062a\u06cc\u0645\u060c \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0631\u0627 \u062a\u0634\u062e\u06cc\u0635 \u062f\u0627\u062f\u0647 \u0648 \u0627\u0639\u0644\u0627\u0645 \u06a9\u0646\u062f.<\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0645\u0631\u0627\u062d\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0628\u062a\u062f\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062a\u0627 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0628\u0647 \u0635\u0641\u0631 \u0648 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a (\u221e) \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0633\u067e\u0633 \u062a\u0645\u0627\u0645\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0631\u0627 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u06af\u0631\u0627\u0641 \u0645\u0646\u0647\u0627\u06cc \u06cc\u06a9 (n-1) \u0628\u0627\u0631 \u0645\u0631\u0648\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u062f\u0631 \u0647\u0631 \u0628\u0627\u0631\u060c \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u0627\u0644 (u, v) \u0628\u0627 \u0648\u0632\u0646 w\u060c \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0645\u0628\u062f\u0627 \u0628\u0647 u \u0628\u0647 \u0639\u0644\u0627\u0648\u0647 \u0648\u0632\u0646 w \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 \u0645\u0628\u062f\u0627 \u0628\u0647 v \u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0645\u0628\u062f\u0627 \u0628\u0647 v \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0647 \u0627\u06cc\u0646 \u0639\u0645\u0644 relax \u06a9\u0631\u062f\u0646 \u06cc\u0627 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 n-1 \u0628\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n\n\n\n<li>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0628\u0631\u0627\u06cc n\u0627\u0645\u06cc\u0646 \u0628\u0627\u0631\u060c \u062a\u0645\u0627\u0645\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u0645\u0631\u0648\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u0622\u06cc\u0627 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631. \u0627\u06af\u0631 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u06a9\u0646\u0646\u062f\u060c \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0648\u062c\u0648\u062f \u06cc\u06a9 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a.<\/li>\n<\/ul>\n\n\n\n<p>\u062f\u0642\u062a \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u062f\u0631 \u0647\u0631 \u0628\u0627\u0631 \u0627\u062c\u0631\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 (\u0628\u0627 \u06cc\u06a9 \u062a\u0631\u062a\u06cc\u0628 \u062b\u0627\u0628\u062a) \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/p>\n\n\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/storage.cafetadris.com\/blog\/bellmn.gif\" width=\"656\" height=\"474\"><\/p>\n\n\n<h3 class=\"wp-block-heading\">\u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0686\u06cc\u0633\u062a\u061f<\/h3>\n\n\n\n<p>\u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0634\u0627\u0645\u0644 \u062f\u0648 \u0628\u062e\u0634 \u0627\u0633\u062a:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627<\/strong>: \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u06cc\u06af\u0631 \u06af\u0631\u0627\u0641 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u06cc\u06a9 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u06cc\u0627 \u0644\u06cc\u0633\u062a \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u06a9\u0644\u06cc\u062f\u0647\u0627 \u0631\u0627\u0633\u200c\u0647\u0627 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u0634\u062f\u0647 \u0647\u0633\u062a\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u062a\u0634\u062e\u06cc\u0635 \u062f\u0648\u0631\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc<\/strong>: \u0627\u06af\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u06cc\u06a9 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0622\u0646 \u0631\u0627 \u062a\u0634\u062e\u06cc\u0635 \u062f\u0647\u062f. \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0628\u0627 \u0645\u0631\u0648\u0631 \u062f\u0648\u0628\u0627\u0631\u0647 \u062a\u0645\u0627\u0645\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0628\u0639\u062f \u0627\u0632 n-1 \u062a\u06a9\u0631\u0627\u0631 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06af\u0631 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u0648\u0631 \u0646\u0647\u0627\u06cc\u06cc\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0647\u0645\u0686\u0646\u0627\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u06a9\u0646\u0646\u062f\u060c \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0648\u062c\u0648\u062f \u06cc\u06a9 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 P \u0631\u0627 \u062f\u0631 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"806\" height=\"466\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-8.png\" alt=\"\" class=\"wp-image-19437\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-8.png 806w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-8-300x173.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-8-768x444.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-8-585x338.png 585w\" sizes=\"(max-width: 806px) 100vw, 806px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647<\/h4>\n\n\n\n<p>\u0627\u0628\u062a\u062f\u0627 \u0631\u0627\u0633 P \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0646\u0642\u0637\u0647 \u0634\u0631\u0648\u0639 \u06cc\u0627 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 P \u062a\u0627 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u062a\u0627 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0628\u0647 \u0635\u0641\u0631 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc \u067e\u06cc\u06af\u06cc\u0631\u06cc \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u062f\u0631 \u0637\u0648\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0627\u0632 \u06cc\u06a9 \u062c\u062f\u0648\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u0634\u0627\u0628\u0647 \u062c\u062f\u0648\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u062c\u062f\u0648\u0644\u060c \u0641\u0648\u0627\u0635\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0648\u0642\u062a \u062b\u0628\u062a \u0634\u062f\u0647 \u0648 \u062f\u0631 \u0637\u06cc \u0641\u0631\u0622\u06cc\u0646\u062f \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u060c \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"918\" height=\"371\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-9.png\" alt=\"\" class=\"wp-image-19438\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-9.png 918w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-9-300x121.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-9-768x310.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-9-585x236.png 585w\" sizes=\"(max-width: 918px) 100vw, 918px\" \/><\/figure><\/div>\n\n\n<p>\u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u062a\u0631\u062a\u06cc\u0628 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">1. (Q, S)<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">2. (T, S)<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">3. (R, S)<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">4. (R, T)<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">5. (P, Q)<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">6. (P, R)<\/span><\/p>\n\n\n\n<p>\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0647\u0631 \u062f\u0648\u0631 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0622\u0631\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u0627\u0648\u0644<\/h4>\n\n\n\n<p>\u062d\u0627\u0644\u0627 \u0634\u0631\u0648\u0639 \u0628\u0647 \u0628\u0631\u0631\u0633\u06cc \u0648 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627 \u0628\u0647 \u0647\u0645\u0627\u0646 \u062a\u0631\u062a\u06cc\u0628 \u06af\u0641\u062a\u0647\u200c\u0634\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (Q, S)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 Q \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (T, S)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 T \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, S)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, T)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 T \u0646\u06cc\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 T \u0627\u0632 P \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, Q)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 P \u062a\u0627 \u062e\u0648\u062f\u0634 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0635\u0641\u0631 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc P \u062a\u0627 Q \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0633 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0627\u06af\u0631 \u0627\u0632 P \u0628\u0647 Q \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f0 + \u06f2 = \u06f2 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 Q \u0627\u0632 P \u0628\u0647 \u06f2 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, R)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 P \u062a\u0627 \u062e\u0648\u062f\u0634 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0635\u0641\u0631 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc P \u062a\u0627 R \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0633 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0627\u06af\u0631 \u0627\u0632 P \u0628\u0647 R \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f0 + \u06f4 = \u06f4 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 R \u0627\u0632 P \u0628\u0647 \u06f4 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"976\" height=\"422\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-10.png\" alt=\"\" class=\"wp-image-19442\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-10.png 976w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-10-300x130.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-10-768x332.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-10-585x253.png 585w\" sizes=\"(max-width: 976px) 100vw, 976px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u062f\u0648\u0645<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0628\u0627 \u0627\u062a\u0645\u0627\u0645 \u062f\u0648\u0631 \u0627\u0648\u0644 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc\u060c \u06cc\u06a9 \u062f\u0648\u0631 \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 relax \u0634\u062f\u0646\u062f \u0648 \u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u062f\u0648\u0645\u06cc\u0646 \u0628\u0627\u0631 \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (Q, S)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 Q \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f2 \u0648\u0627\u062d\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc P \u062a\u0627 S \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 Q \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0627\u06af\u0631 \u0627\u0632 P \u0628\u0647 Q \u0648 \u0633\u067e\u0633 \u0628\u0647 S \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f2 + \u06f2 = \u06f4 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u0628\u0647 \u06f4 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (T, S)<\/strong>: \u062f\u0631 \u0627\u06cc\u0646 \u0644\u062d\u0638\u0647 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 T \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 T \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f5- \u0627\u0633\u062a. \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 \u0637\u0631\u06cc\u0642 T \u0628\u0647 S \u0628\u0631\u0648\u06cc\u0645 \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 T \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0627\u06cc\u0646 \u0639\u062f\u062f \u0628\u0627 \u06f5- \u062c\u0645\u0639 \u0634\u062f\u0647 \u0648 \u062d\u0627\u0635\u0644 \u0628\u0627\u0632 \u0647\u0645 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u06f4 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0644\u0630\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u062f\u06cc\u06af\u0631 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, S)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0627\u0633\u062a\u060c \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 \u0637\u0631\u06cc\u0642 R \u0628\u0647 S \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f4 + \u06f4 = \u06f8 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u06a9\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u06f4 \u0627\u0633\u062a\u0648 \u0644\u0630\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 S \u0627\u0632 P \u062f\u06cc\u06af\u0631 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, T)<\/strong>: \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u062a\u0627 T \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 T \u0628\u0631\u0627\u0628\u0631 \u06f3 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 \u0637\u0631\u06cc\u0642 R \u0628\u0647 T \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f3 + \u06f4 = \u06f7 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 T \u0627\u0632 P \u0628\u0647 \u06f7 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, Q)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 &nbsp;Q\u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 Q \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, R)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"987\" height=\"388\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-11.png\" alt=\"\" class=\"wp-image-19443\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-11.png 987w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-11-300x118.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-11-768x302.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-11-585x230.png 585w\" sizes=\"(max-width: 987px) 100vw, 987px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u0633\u0648\u0645<\/h4>\n\n\n\n<p>\u062f\u0631 \u062f\u0648\u0631 \u0633\u0648\u0645\u060c \u062f\u0648\u0628\u0627\u0631\u0647 \u062a\u0645\u0627\u0645 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (Q, S)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 P \u062a\u0627 Q \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 Q \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0627\u06af\u0631 \u0627\u0632 P \u0628\u0647 Q \u0648 \u0633\u067e\u0633 \u0628\u0647 S \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f2 + \u06f2 = \u06f4 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 S \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (T, S)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 P \u062a\u0627 T \u0628\u0631\u0627\u0628\u0631 \u06f7 \u0648\u0627\u062d\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 T \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f5- \u0627\u0633\u062a. \u0627\u06af\u0631 \u0627\u0632 P \u0628\u0647 T \u0648 \u0633\u067e\u0633 \u0628\u0647 S \u0628\u0631\u0648\u06cc\u0645\u060c \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0686\u0648\u0646 \u06f2 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u06f4 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 S \u0627\u0632 P \u0628\u0647 \u06f2 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, S)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc P \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647\u200c S \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, T)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 T \u0628\u0631\u0627\u0628\u0631 \u06f3 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062c\u0645\u0639 \u0627\u06cc\u0646 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u06f7 \u0627\u0633\u062a \u0648 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647\u200c \u0641\u0639\u0644\u06cc T \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647\u200c T \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, Q)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 Q \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647\u200c \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 Q \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, R)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647\u200c \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647\u200c P \u062a\u0627 R \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"999\" height=\"386\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-12.png\" alt=\"\" class=\"wp-image-19444\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-12.png 999w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-12-300x116.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-12-768x297.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-12-585x226.png 585w\" sizes=\"(max-width: 999px) 100vw, 999px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u0686\u0647\u0627\u0631\u0645<\/h4>\n\n\n\n<p>\u062f\u0631 \u062f\u0648\u0631 \u0686\u0647\u0627\u0631\u0645\u060c \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (Q, S)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 Q \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 Q \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627 \u0645\u0633\u06cc\u0631 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 S \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (T, S):<\/strong> \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 T \u0628\u0631\u0627\u0628\u0631 \u06f7 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 T \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f5- \u0627\u0633\u062a. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627 \u0645\u0633\u06cc\u0631 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 S \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, S)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 S \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 S \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 S \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (R, T)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 R \u062a\u0627 T \u0628\u0631\u0627\u0628\u0631 \u06f3 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627 \u0645\u0633\u06cc\u0631 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 T \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, Q)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 Q \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 Q \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644 (P, R)<\/strong>: \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u0632 P \u062a\u0627 R \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0646\u06cc\u0632 \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 P \u062a\u0627 R \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"985\" height=\"431\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-13.png\" alt=\"\" class=\"wp-image-19445\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-13.png 985w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-13-300x131.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-13-768x336.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-13-585x256.png 585w\" sizes=\"(max-width: 985px) 100vw, 985px\" \/><\/figure><\/div>\n\n\n<p>\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0628\u0639\u062f \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0631\u0627\u062d\u0644\u060c \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0641\u0631\u0622\u06cc\u0646\u062f \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u062a\u06a9\u0631\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u0634\u062f \u062a\u0627 \u0645\u0637\u0645\u0626\u0646 \u0634\u0648\u06cc\u0645 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0646\u062f\u0627\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0686\u0648\u0646 \u0628\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u0631\u062d\u0644\u0647 \u0622\u062e\u0631\u060c \u0641\u0627\u0635\u0644\u0647 \u0647\u06cc\u0686 \u0645\u0633\u06cc\u0631\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u0646\u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f\u060c \u0645\u06cc\u200c\u0641\u0647\u0645\u06cc\u0645 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0646\u062f\u0627\u0631\u06cc\u0645 \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0631\u0633\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h3>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0648 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647<\/strong>: \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0628\u0631\u0627\u06cc V \u0631\u0627\u0633\u060c \u0628\u0647 \u0632\u0645\u0627\u0646 O(V) \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627<\/strong>: \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0628\u0631\u0627\u06cc V\u22121 \u0628\u0627\u0631 (\u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u0646\u0647\u0627\u06cc \u06cc\u06a9) \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u06cc \u0628\u0627 E \u06cc\u0627\u0644\u060c \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 O(E) \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u06a9\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f O(V\u22c5E).<\/li>\n\n\n\n<li><strong>\u0628\u0631\u0631\u0633\u06cc \u0648\u062c\u0648\u062f \u0686\u0631\u062e\u0647\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc<\/strong><strong>: <\/strong>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u06cc\u06a9 \u0628\u0627\u0631 \u062a\u0645\u0627\u0645 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u0628\u0647 O(E) \u0632\u0645\u0627\u0646 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0627 \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0645\u0631\u0627\u062d\u0644 \u0641\u0648\u0642\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O(V \\cdot E)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0647 \u0646\u0627\u0645 <code>bellman_ford<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0628\u062a\u062f\u0627\u060c \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062e\u0648\u062f\u0634 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062d\u0644\u0642\u0647 <code>for<\/code> \u06a9\u0647 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 (n) \u0645\u0646\u0647\u0627\u06cc \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0648 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc\u0634 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u0628\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631\u061b \u0627\u06af\u0631 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0639\u062f\u062f \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0628\u0639\u062f \u0627\u0632 n-1 \u0628\u0627\u0631 \u0627\u062c\u0631\u0627\u06cc \u0641\u0631\u0622\u06cc\u0646\u062f \u0622\u0631\u0627\u0645\u200c\u0633\u0627\u0632\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u060c \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 (\u0628\u0631\u0627\u06cc \u0628\u0627\u0631 n\u0645) \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0622\u06cc\u0627 \u0647\u0646\u0648\u0632 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0631\u0627 \u06a9\u0627\u0647\u0634 \u062f\u0627\u062f \u06cc\u0627 \u062e\u06cc\u0631\u061b \u0627\u06af\u0631 \u0686\u0646\u06cc\u0646 \u0628\u0627\u0634\u062f\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u0627\u0633\u062a \u06a9\u0647 \u06af\u0631\u0627\u0641 \u062f\u0627\u0631\u0627\u06cc \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0627\u0633\u062a \u0648 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def bellman_ford(graph, source):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp; <span style=\"color:green\">#Initialize distances from the source to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp; <span style=\"color:green\">#except the source itself which is set to zero.<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist[source] = 0<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp; <span style=\"color:green\">#Define the order of vertices<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;vertices = sorted(graph.keys())<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp; <span style=\"color:green\">#Relax edges repeatedly<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for i in range(len(graph) - 1):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for vertex in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[vertex].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[vertex] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[neighbor] = dist[vertex] + weight<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(i, 'round of relaxation: ', {v: dist[v] for v in vertices})<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp; <span style=\"color:green\">#Check for negative weight cycles<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for vertex in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[vertex].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[vertex] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(\"Graph contains a negative weight cycle\")<\/code><\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u06cc\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'Q': {'S': 2},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'T': {'S': -5},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'S': {},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'R': {'S': 4, 'T': 3},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'P': {'Q': 2, 'R': 4}<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>bellman_ford(graph, 'P')<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>0 round of relaxation:<\/strong><br \/>\n{&#8216;P&#8217;: 0, &#8216;Q&#8217;: 2, &#8216;R&#8217;: 4, &#8216;S&#8217;: inf, &#8216;T&#8217;: inf}<br \/>\n<strong>1 round of relaxation:<\/strong><br \/>\n{&#8216;P&#8217;: 0, &#8216;Q&#8217;: 2, &#8216;R&#8217;: 4, &#8216;S&#8217;: 4, &#8216;T&#8217;: 7}<br \/>\n<strong>2 round of relaxation:<\/strong><br \/>\n{&#8216;P&#8217;: 0, &#8216;Q&#8217;: 2, &#8216;R&#8217;: 4, &#8216;S&#8217;: 2, &#8216;T&#8217;: 7}<br \/>\n<strong>3 round of relaxation:<\/strong><br \/>\n{&#8216;P&#8217;: 0, &#8216;Q&#8217;: 2, &#8216;R&#8217;: 4, &#8216;S&#8217;: 2, &#8216;T&#8217;: 7}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG<\/h2>\n\n\n\n<p>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Directed_acyclic_graph\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Directed Acyclic Graphs &#8211; DAGs<\/mark><\/a>) \u0646\u0648\u0639 \u062e\u0627\u0635\u06cc \u0627\u0632 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646\u200c\u0647\u0627 \u0686\u0631\u062e\u0647\u200c\u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062e\u0627\u0635\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u062f\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0647\u0645\u200c\u062a\u0631\u06cc\u0646 \u0622\u0646\u200c\u0647\u0627 \u0627\u0628\u062a\u062f\u0627 \u06af\u0631\u0627\u0641 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%D8%A8%D8%B1%D8%B1%D8%B3%DB%8C-%D8%AC%D8%A7%D9%85%D8%B9-%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85%D9%87%D8%A7%DB%8C-%D9%BE%DB%8C%D9%85%D8%A7%DB%8C%D8%B4-%DA%AF%D8%B1%D8%A7%D9%81\/#lwptoc27\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc<\/mark><\/a> (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Topological_sorting\" data-type=\"URL\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Topological_sorting\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Topological Sort<\/mark><\/a>) \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0633\u067e\u0633 \u062a\u06a9\u200c\u062a\u06a9 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u06a9\u0647 \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0622\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0641\u0639\u0644\u06cc \u0628\u0647\u200c\u0631\u0648\u0632 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631 (DAG) \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u062e\u0627\u0635 \u062f\u0631 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%D9%86%D8%B8%D8%B1%DB%8C%D9%87-%DA%AF%D8%B1%D8%A7%D9%81-%D9%BE%D9%84%DB%8C-%D8%A8%DB%8C%D9%86-%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA-%D9%88-%D8%AF%D9%86%DB%8C%D8%A7%DB%8C-%D9%88%D8%A7%D9%82%D8%B9\/\" target=\"_blank\">\u0646\u0638\u0631\u06cc\u0647 \u06af\u0631\u0627\u0641\u200c\u0647\u0627<\/a> <\/mark>\u0634\u0646\u0627\u062e\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc (Topological Sort) \u0628\u0646\u0627 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0628\u0627\u0631 \u062a\u0648\u0633\u0637 \u0631\u0627\u0628\u0631\u062a \u062a\u0627\u0631\u0698\u0627\u0646 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Robert_Tarjan\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Robert Tarjan<\/mark><\/a>) \u062f\u0631 \u062f\u0647\u0647 \u06f1\u06f9\u06f7\u06f0 \u0645\u0639\u0631\u0641\u06cc \u0634\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 DAG \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0633\u0627\u062e\u062a\u0627\u0631 \u062e\u0627\u0635 \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0628\u0627\u0644\u0627\u06cc\u0634\u0627\u0646 \u062f\u0631 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631\u060c \u0645\u0648\u0631\u062f \u062a\u0648\u062c\u0647 \u0645\u062d\u0642\u0642\u0627\u0646 \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647\u200c\u0627\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG \u0631\u0627 \u0686\u0637\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u061f<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u0627\u062d\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0628\u062a\u062f\u0627 \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f \u0631\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a (infinity) \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/li>\n\n\n\n<li>\u062f\u0631 \u06af\u0627\u0645 \u0628\u0639\u062f\u06cc\u060c \u06cc\u06a9 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u062a\u0627 \u06cc\u06a9 \u062a\u0631\u062a\u06cc\u0628 \u062e\u0637\u06cc \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645. \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0642\u0628\u0644 \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631\u0634 \u0628\u0627\u0632\u062f\u06cc\u062f \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n\n\n\n<li>\u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u06cc\u06a9\u06cc \u06cc\u06a9\u06cc \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u067e\u0631\u062f\u0627\u0632\u0634\u200c\u0634\u062f\u0647\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627\u0633 \u0628\u0647\u200c\u0631\u0648\u0632 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u062c\u062f\u06cc\u062f \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0642\u0628\u0644\u06cc \u0628\u0627\u0634\u062f\u060c \u0645\u0642\u062f\u0627\u0631 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0639\u062f\u062f \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631 \u0632\u06cc\u0631 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-14.png\" alt=\"\" class=\"wp-image-19446\" width=\"694\" height=\"322\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-14.png 949w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-14-300x139.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-14-768x357.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-14-585x272.png 585w\" sizes=\"(max-width: 694px) 100vw, 694px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0646\u0638\u06cc\u0645 \u0627\u0648\u0644\u06cc\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0648 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u060c \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062a\u0627 \u062e\u0648\u062f\u0634 \u0628\u0647 \u0635\u0641\u0631 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0631\u0627\u0633 s \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. \u0633\u067e\u0633 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0622\u0646 \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u062a\u0631\u062a\u06cc\u0628\u200c\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">r \\rightarrow s \\rightarrow t \\rightarrow x \\rightarrow y \\rightarrow z<\/span><\/p>\n\n\n\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc \u0648 \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631 \u0631\u0648\u0646\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0634\u06a9\u0644 \u06af\u0631\u0627\u0641 \u0631\u0627 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0631\u0633\u0645 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062a\u0627 \u0647\u0631 \u0631\u0627\u0633 \u0631\u0627 \u0631\u0648\u06cc \u0622\u0646 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-15.png\" alt=\"\" class=\"wp-image-19448\" width=\"710\" height=\"302\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-15.png 896w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-15-300x128.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-15-768x327.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-15-585x249.png 585w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc r \u0648 s<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0628\u0627\u06cc\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0628\u062a\u062f\u0627 \u0631\u0627\u0633 r \u0631\u0627 \u06a9\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0631\u0627\u0633 \u062f\u0631 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0627\u0633\u062a\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 s \u062a\u0627 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a (\u06a9\u0644\u0627 \u0647\u0645 \u0631\u0627\u0647\u06cc \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 s \u0628\u0647 r \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u0648 \u0627\u06cc\u0646 \u0639\u062f\u062f \u062a\u0627 \u067e\u0627\u06cc\u0627\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062e\u0648\u0627\u0647\u062f \u0645\u0627\u0646\u062f)\u060c \u0645\u062c\u0645\u0648\u0639 \u0627\u06cc\u0646 \u0639\u062f\u062f \u0628\u0647 \u0639\u0644\u0627\u0648\u0647 \u0648\u0632\u0646 \u06cc\u0627\u0644 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u062a\u0627 \u0631\u0626\u0648\u0633 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0627\u0634\u060c \u0628\u0627\u0632 \u0647\u0645 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062e\u0648\u0627\u0647\u062f \u0634\u062f. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0641\u0627\u0635\u0644\u0647 \u0647\u06cc\u0686 \u0631\u0627\u0633\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 r \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0646\u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u0633\u067e\u0633 \u0631\u0627\u0633 s \u0631\u0627 \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 s \u062a\u0627 \u062e\u0648\u062f\u0634 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0648 \u0648\u0632\u0646 \u06cc\u0627\u0644 st \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u062a\u0627 \u0631\u0627\u0633 t \u0628\u0631\u0627\u0628\u0631 \u06f0 + \u06f2 = \u06f2 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc s \u062a\u0627 t (\u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a) \u0627\u0633\u062a \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u06f2 \u062a\u063a\u06cc\u06cc\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0686\u0648\u0646 \u0648\u0632\u0646 \u06cc\u0627\u0644 sx \u0628\u0631\u0627\u0628\u0631 \u06f6 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u062a\u0627 \u0631\u0627\u0633 x \u0628\u0631\u0627\u0628\u0631 \u06f0 + \u06f6 = \u06f6 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0627\u06cc\u0646 \u0639\u062f\u062f \u0647\u0645 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc s \u062a\u0627 x (\u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a) \u0627\u0633\u062a \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u0639\u062f\u062f \u06f6 \u062a\u063a\u06cc\u06cc\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-16.png\" alt=\"\" class=\"wp-image-19449\" width=\"739\" height=\"277\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-16.png 839w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-16-300x113.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-16-768x288.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-16-585x220.png 585w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633 t<\/h4>\n\n\n\n<p>\u062d\u0627\u0644 \u0631\u0627\u0633 t \u0631\u0627 \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 t \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0627\u0633\u062a \u0648 \u0648\u0632\u0646 \u06cc\u0627\u0644 t \u0628\u0647 x \u0628\u0631\u0627\u0628\u0631 \u06f7 \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 s \u062a\u0627 x \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 t \u0628\u0631\u0627\u0628\u0631\u06f2 + \u06f7 = \u06f9 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc x (\u06f6) \u0646\u06cc\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062a\u063a\u06cc\u06cc\u0631\u06cc \u062f\u0631 \u0641\u0627\u0635\u0644\u0647 s \u0628\u0647 x \u0627\u06cc\u062c\u0627\u062f \u0646\u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u0627\u0645\u0627 \u0648\u0632\u0646 \u06cc\u0627\u0644 t \u0628\u0647 y \u0628\u0631\u0627\u0628\u0631 \u06f4 \u0627\u0633\u062a \u0648 \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 t \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 y \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 t \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f2 + \u06f4 = \u06f6 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc y (\u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a) \u0627\u0633\u062a. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u0639\u062f\u062f \u06f6 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0648\u0632\u0646 \u06cc\u0627\u0644 t \u0628\u0647 z \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0627\u0633\u062a \u0648 \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 s \u062a\u0627 z \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 z \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 t \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f2 + \u06f2 = \u06f4 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc z (\u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a) \u0627\u0633\u062a. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u0639\u062f\u062f \u06f4 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-17.png\" alt=\"\" class=\"wp-image-19450\" width=\"728\" height=\"257\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-17.png 840w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-17-300x106.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-17-768x271.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-17-585x206.png 585w\" sizes=\"(max-width: 728px) 100vw, 728px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633 x<\/h4>\n\n\n\n<p>\u062d\u0627\u0644 \u0631\u0627\u0633 x \u0631\u0627 \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 x \u0628\u0631\u0627\u0628\u0631 \u06f6 \u0648 \u0648\u0632\u0646 \u06cc\u0627\u0644 x \u0628\u0647 y \u0628\u0631\u0627\u0628\u0631 \u06f1- \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 s \u062a\u0627 y \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 x \u0628\u0631\u0627\u0628\u0631 \u06f1 &#8211; \u06f6 = \u06f5 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc y (\u06f6) \u0627\u0633\u062a \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u06f5 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p>\u0627\u0645\u0627 \u0648\u0632\u0646 \u06cc\u0627\u0644 x \u0628\u0647 z \u0628\u0631\u0627\u0628\u0631 \u06f1 \u0627\u0633\u062a \u0648 \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 x \u0628\u0631\u0627\u0628\u0631 \u06f6 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 z \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 x \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1 + \u06f6 = \u06f7 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc z (\u06f4) \u0646\u06cc\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062a\u063a\u06cc\u06cc\u0631\u06cc \u062f\u0631 \u0641\u0627\u0635\u0644\u0647 s \u0628\u0647 z \u0627\u06cc\u062c\u0627\u062f \u0646\u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-18.png\" alt=\"\" class=\"wp-image-19451\" width=\"736\" height=\"267\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-18.png 875w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-18-300x109.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-18-768x279.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-18-585x213.png 585w\" sizes=\"(max-width: 736px) 100vw, 736px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633 y<\/h4>\n\n\n\n<p>\u062d\u0627\u0644 \u0631\u0627\u0633 y \u0631\u0627 \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0686\u0648\u0646 \u0641\u0627\u0635\u0644\u0647 s \u062a\u0627 y \u0628\u0631\u0627\u0628\u0631 \u06f5 \u0648 \u0648\u0632\u0646 \u06cc\u0627\u0644 y \u0628\u0647 z \u0628\u0631\u0627\u0628\u0631 \u06f2- \u0627\u0633\u062a\u060c \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 s \u062a\u0627 z \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 y \u0628\u0631\u0627\u0628\u0631 \u06f2 &#8211; \u06f5 = \u06f3 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc z (\u06f4) \u0627\u0633\u062a \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0647 \u06f3 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-19.png\" alt=\"\" class=\"wp-image-19452\" width=\"710\" height=\"267\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-19.png 878w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-19-300x113.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-19-768x290.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-19-585x221.png 585w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633 z<\/h4>\n\n\n\n<p>\u0645\u0631\u062d\u0644\u0647 \u0622\u062e\u0631 \u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627\u0633 z \u0627\u0633\u062a \u06a9\u0647 \u0686\u0648\u0646 \u0647\u06cc\u0686 \u06cc\u0627\u0644\u06cc \u0627\u0632 \u0622\u0646 \u062e\u0627\u0631\u062c \u0646\u0634\u062f\u0647\u060c \u062a\u063a\u06cc\u06cc\u0631\u06cc \u062f\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 s \u062a\u0627 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0627\u06cc\u062c\u0627\u062f \u0646\u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-20.png\" alt=\"\" class=\"wp-image-19453\" width=\"720\" height=\"253\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-20.png 870w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-20-300x106.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-20-768x270.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-20-585x206.png 585w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure><\/div>\n\n\n<p>\u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 s \u062a\u0627 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG<\/h3>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u062f\u06cc\u062f\u06cc\u062f\u060c \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0632 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0628\u0627\u0639\u062b \u0645\u06cc\u200c\u0634\u0648\u062f \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0622\u0646 \u062e\u0637\u06cc \u0628\u0627\u0634\u062f:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u06cc\u0627\u0641\u062a\u0646 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc: <\/strong>\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u06a9\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0639\u0645\u0642 \u0627\u0648\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u06cc \u0628\u0627 V \u0631\u0627\u0633 \u0648 E \u06cc\u0627\u0644 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 O(V+E) \u0627\u0633\u062a.<\/li>\n\n\n\n<li><strong>\u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647: \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627<\/strong>: \u062f\u0631 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645&nbsp;\u0628\u0647 O(V) \u0632\u0645\u0627\u0646 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/li>\n\n\n\n<li><strong>\u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627: <\/strong>\u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0646\u06cc\u0632 \u062f\u0631 \u0632\u0645\u0627\u0646 \u062e\u0637\u06cc&nbsp;O(V+E) \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0627 \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0645\u0631\u0627\u062d\u0644 \u0641\u0648\u0642\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O(V + E)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 DAG\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0647 \u0646\u0627\u0645 <code>dag_shortest_path<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0628\u062a\u062f\u0627\u060c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%D8%A8%D8%B1%D8%B1%D8%B3%DB%8C-%D8%AC%D8%A7%D9%85%D8%B9-%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85%D9%87%D8%A7%DB%8C-%D9%BE%DB%8C%D9%85%D8%A7%DB%8C%D8%B4-%DA%AF%D8%B1%D8%A7%D9%81\/#lwptoc29\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u062a\u0627\u0628\u0639 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u06cc \u0628\u0627 \u06a9\u0645\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 DFS \u0622\u0646 \u0631\u0627 \u0633\u0627\u062e\u062a\u06cc\u0645<\/mark><\/a>\u060c \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u0648\u0631\u06cc\u0645. \u0633\u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u06a9\u0647 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u06cc\u0645\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u061b \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0648 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc\u0634 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u0628\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631 \u0648 \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u06af\u0641\u062a\u06cc\u0645\u060c \u0627\u06af\u0631 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0639\u062f\u062f \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0648 \u062f\u0631 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0627\u0632 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0686\u0627\u067e \u0645\u06cc\u200c\u0634\u0648\u062f \u062a\u0627 \u0631\u0648\u0646\u062f \u06a9\u0627\u0631 \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def dfs(graph, start, visited=None, stack=None):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize visited and stack if not provided<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;if visited is None:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;visited = []<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;if stack is None:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;stack = []<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Mark the current node as visited<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;visited.append(start)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Recur for all the vertices adjacent to this vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for neighbor in graph[start]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if neighbor not in visited:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dfs(graph, neighbor, visited, stack)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Push current vertex to stack which stores the result<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;stack.append(start)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def topological_sort(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;visited = []<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;stack = []<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Call the recursive helper function to store<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Topological Sort starting from all vertices one by one<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for node in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if node not in visited:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dfs(graph, node, visited, stack)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;return stack[::-1]<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def dag_shortest_path(graph, source):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Perform topological sort using DFS<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;topological_order = topological_sort(graph)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;print(f'Topological sort: {topological_order}\\n')<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances to all vertices as infinite<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = {vertex: float('infinity') for vertex in topological_order}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist[source] = 0<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Process vertices in topological order<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for vertex in topological_order:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[vertex].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[vertex] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[neighbor] = dist[vertex] + weight<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(f'Process node {vertex}: {dist}')<\/code><\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 DAG \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u06cc\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'s': {'t': 2, 'x': 6},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'r': {'s': 5, 't': 3},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'t': {'x': 7, 'y': 4},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'x': {'y': -1, 'z': 1},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'y': {'z': -2},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'z': {},<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>dag_shortest_path(graph, 's')<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>Topological sort:<\/strong><br \/>\n[&#8216;r&#8217;, &#8216;s&#8217;, &#8216;t&#8217;, &#8216;x&#8217;, &#8216;y&#8217;, &#8216;z&#8217;]\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>Process node r:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: inf, &#8216;x&#8217;: inf, &#8216;y&#8217;: inf, &#8216;z&#8217;: inf}<br \/>\n<strong>Process node s:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: 2, &#8216;x&#8217;: 6, &#8216;y&#8217;: inf, &#8216;z&#8217;: inf}<br \/>\n<strong>Process node t:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: 2, &#8216;x&#8217;: 6, &#8216;y&#8217;: 6, &#8216;z&#8217;: inf}<br \/>\n<strong>Process node x:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: 2, &#8216;x&#8217;: 6, &#8216;y&#8217;: 5, &#8216;z&#8217;: 7}<br \/>\n<strong>Process node y:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: 2, &#8216;x&#8217;: 6, &#8216;y&#8217;: 5, &#8216;z&#8217;: 3}<br \/>\n<strong>Process node z:<\/strong><br \/>\n{&#8216;r&#8217;: inf, &#8216;s&#8217;: 0, &#8216;t&#8217;: 2, &#8216;x&#8217;: 6, &#8216;y&#8217;: 5, &#8216;z&#8217;: 3}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646<\/h2>\n\n\n\n<p>\u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u060c \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0648\u0632\u0646 \u06cc\u06a9\u0633\u0627\u0646\u06cc \u062f\u0627\u0631\u0646\u062f \u0648 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u0648\u0646\u062f. \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0633\u0627\u062f\u0647\u200c\u062a\u0631\u06cc \u0627\u0632 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0648 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644<\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Breadth-first_search\" data-type=\"URL\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Breadth-first_search\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Breadth First Search &#8211; BFS<\/mark><\/a>) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u06cc\u06a9 <a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%d8%a8%d8%b1%d8%b1%d8%b3%db%8c-%d8%ac%d8%a7%d9%85%d8%b9-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85%d9%87%d8%a7%db%8c-%d9%be%db%8c%d9%85%d8%a7%db%8c%d8%b4-%da%af%d8%b1%d8%a7%d9%81\/\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u06af\u0631\u0627\u0641<\/mark><\/a> \u0633\u0627\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u0634\u0631\u0648\u0639 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627\u060c \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u0647 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0647\u0645\u200c\u0645\u0628\u062f\u0627 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0686\u0637\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u061f<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u0645\u0631\u0627\u062d\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0637\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0648 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0646\u06af\u0647\u200c\u062f\u0627\u0631\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0647\u0631 \u06af\u0631\u0647 \u0627\u0632 \u0645\u0646\u0628\u0639 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u06af\u0631\u0647\u200c\u06cc \u0634\u0631\u0648\u0639 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/li>\n\n\n\n<li>\u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0646\u0634\u062f\u0647:\n<ul class=\"wp-block-list\">\n<li>\u06af\u0631\u0647 \u0627\u0648\u0644 \u0635\u0641 \u0631\u0627 \u0627\u0632 \u0635\u0641 \u062e\u0627\u0631\u062c \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u062a\u0645\u0627\u0645\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06af\u0631\u0647\u200c\u06cc \u062e\u0627\u0631\u062c \u0634\u062f\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u0627\u06cc\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627 \u0647\u0646\u0648\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0622\u0646\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u06af\u0631\u0647\u200c\u06cc \u0641\u0639\u0644\u06cc \u0628\u0647 \u0627\u0636\u0627\u0641\u0647\u200c\u06cc \u06cc\u06a9 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u067e\u0633 \u0627\u0632 \u0627\u062a\u0645\u0627\u0645 \u06a9\u0627\u0631\u060c \u0622\u0631\u0627\u06cc\u0647\u200c\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0628\u0647 \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0686\u0642\u062f\u0631 \u0627\u0633\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u06cc\u200c\u0648\u0632\u0646<\/h3>\n\n\n\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0628\u0631\u0631\u0633\u06cc \u0633\u0637\u062d \u0628\u0647 \u0633\u0637\u062d \u0648 \u0639\u062f\u0645 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0631\u0627\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u060c \u0642\u0627\u062f\u0631 \u0627\u0633\u062a \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0627\u0632 \u06cc\u06a9 \u0645\u0646\u0628\u0639 \u0648\u0627\u062d\u062f \u0628\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0626\u0648\u0633 \u062f\u06cc\u06af\u0631 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0631\u0627 \u0628\u0627 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc O(V+E) \u06a9\u0647 \u062f\u0631 \u0622\u0646 V \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0648 E \u062a\u0639\u062f\u0627\u062f \u06cc\u0627\u0644\u200c\u0647\u0627 \u0627\u0633\u062a\u060c \u067e\u06cc\u062f\u0627 \u06a9\u0646\u062f. \u062f\u0631\u0648\u0627\u0642\u0639 \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0645\u0627\u0646 <a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%d8%a8%d8%b1%d8%b1%d8%b3%db%8c-%d8%ac%d8%a7%d9%85%d8%b9-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85%d9%87%d8%a7%db%8c-%d9%be%db%8c%d9%85%d8%a7%db%8c%d8%b4-%da%af%d8%b1%d8%a7%d9%81\/#lwptoc54\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS<\/mark><\/a> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u062a\u0627\u0628\u0639\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>bfs_shortest_paths<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639\u060c \u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>distances<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0647\u0631 \u0631\u0627\u0633 (\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06a9\u0644\u06cc\u062f \u06cc\u0627 \u0647\u0645\u0627\u0646 keys) \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f \u0648 \u062a\u0645\u0627\u0645\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 (values) \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0641\u0631 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0631\u062f\u0647 \u0648 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0646\u0634\u062f\u0647\u060c \u06af\u0631\u0647 \u0627\u0648\u0644 \u0635\u0641 \u0631\u0627 \u0627\u0632 \u0635\u0641 \u062e\u0627\u0631\u062c \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u062a\u0645\u0627\u0645\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06af\u0631\u0647 \u062e\u0627\u0631\u062c \u0634\u062f\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u0627\u06cc\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627 \u0647\u0646\u0648\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0622\u0646\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u06af\u0631\u0647 \u0641\u0639\u0644\u06cc \u0628\u0647 \u0627\u0636\u0627\u0641\u0647\u200c\u06cc \u06cc\u06a9 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0634\u0648\u062f \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc <code>distances<\/code> \u062d\u0627\u0648\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>from collections import deque<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def bfs_shortest_paths(graph, start):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;distances = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Distance to the start vertex is set to 0<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;distances[start] = 0<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize the queue with the start vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;queue = deque([start])<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Process the queue until it is empty<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;while queue:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;node = queue.popleft()<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Iterate through neighbors of the current node<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor in graph[node]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># If the neighbor has not been visited, update the distance<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if distances[neighbor] == float('infinity'):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;queue.append(neighbor)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;distances[neighbor] = distances[node] + 1<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(distances)<\/code><\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0627 \u0631\u0627\u0633 \u0634\u0631\u0648\u0639 A \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-21.png\" alt=\"\" class=\"wp-image-19454\" width=\"700\" height=\"421\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-21.png 878w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-21-300x180.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-21-768x462.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-21-585x352.png 585w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><\/figure><\/div>\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'A': ['B', 'C', 'D'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'B': ['A', 'D'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'C': ['A', 'E'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'D': ['A', 'B'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'E': ['C', 'F'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'F': ['E']<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>bfs_shortest_paths(graph, 'A')<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: inf, &#8216;D&#8217;: inf, &#8216;E&#8217;: inf, &#8216;F&#8217;: inf}<\/strong><br \/>\n<strong>{&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: inf, &#8216;E&#8217;: inf, &#8216;F&#8217;: inf}<\/strong><br \/>\n<strong>{&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: inf, &#8216;F&#8217;: inf}<\/strong><br \/>\n<strong>{&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2, &#8216;F&#8217;: inf}<\/strong><br \/>\n<strong>{&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2, &#8216;F&#8217;: 3}<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641<\/h2>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u060c \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0635 \u0628\u0647 \u062e\u0648\u062f \u0631\u0627 \u062f\u0627\u0631\u062f. \u0627\u0645\u0627 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u0633\u0627\u0633 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641 \u0628\u0647 \u062f\u0648 \u0632\u06cc\u0631 \u0645\u0633\u0626\u0644\u0647 \u062f\u06cc\u06af\u0631 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631<\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0648 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u062f\u0627\u0631\u06cc\u0645\u060c \u0647\u0631\u0686\u0646\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0631\u0627 V \u0628\u0627\u0631 \u06cc\u0639\u0646\u06cc \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u06a9\u0644 \u0631\u0627\u0633\u200c\u0647\u0627 \u06af\u0631\u0627\u0641 (\u0647\u0631 \u0628\u0627\u0631 \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0634\u0631\u0648\u0639) \u0627\u062c\u0631\u0627 \u06a9\u0631\u062f \u0648 \u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0633\u062a \u06cc\u0627\u0641\u062a \u0627\u0645\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0631\u0627 V \u0628\u0631\u0627\u0628\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0686\u0646\u062f\u0627\u0646 \u0628\u0647\u06cc\u0646\u0647 \u0646\u06cc\u0633\u062a. \u062f\u0631 \u0639\u0648\u0636 \u0631\u0627\u0647 \u062d\u0644 \u0628\u0647\u06cc\u0646\u0647\u200c\u062a\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0628\u0647 \u0622\u0646\u200c\u0647\u0627 \u0627\u0634\u0627\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/h2>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Floyd%E2%80%93Warshall_algorithm\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Floyd-Warshall Algorithm<\/mark><\/a>) \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0639\u0631\u0648\u0641\u200c\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0632 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647\u060c \u0628\u0647 \u062a\u062f\u0631\u06cc\u062c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0645\u0647 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0642\u0627\u062f\u0631 \u0628\u0647 \u0645\u062f\u06cc\u0631\u06cc\u062a \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc \u0646\u06cc\u0632 \u0647\u0633\u062a.<\/p>\n\n\n\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0628\u0627 \u0646\u0627\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0634\u0646\u0627\u062e\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0627\u0632 \u062c\u0645\u0644\u0647:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f&nbsp;(Floyd&#8217;s Algorithm)<\/li>\n\n\n\n<li>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0648\u06cc-\u0641\u0644\u0648\u06cc\u062f&nbsp;(Roy-Floyd Algorithm)<\/li>\n\n\n\n<li>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0648\u06cc-\u0648\u0627\u0631\u0634\u0627\u0644&nbsp;(Roy-Warshall Algorithm)<\/li>\n\n\n\n<li>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644&nbsp;(Floyd-Warshall Algorithm)<\/li>\n\n\n\n<li>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 WFI (\u0645\u062e\u0641\u0641 \u0646\u0627\u0645 \u0633\u0647 \u062f\u0627\u0646\u0634\u0645\u0646\u062f\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u062a\u0648\u0633\u0639\u0647 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0645\u06a9 \u06a9\u0631\u062f\u0647\u200c\u0627\u0646\u062f)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u062a\u0648\u0633\u0637 \u0631\u0627\u0628\u0631\u062a \u0641\u0644\u0648\u06cc\u062f (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Robert_W._Floyd\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Robert Floyd<\/mark><\/a>) \u0648 \u0627\u0633\u062a\u06cc\u0648\u0646 \u0648\u0627\u0631\u0634\u0627\u0644 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Stephen_Warshall\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Stephen Warshall<\/mark><\/a>) \u0628\u0647 \u0637\u0648\u0631 \u0645\u0633\u062a\u0642\u0644 \u062f\u0631 \u062f\u0647\u0647 \u06f1\u06f9\u06f6\u06f0 \u062a\u0648\u0633\u0639\u0647 \u06cc\u0627\u0641\u062a. \u0631\u0627\u0628\u0631\u062a \u0641\u0644\u0648\u06cc\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f6\u06f2 \u0648 \u0627\u0633\u062a\u06cc\u0648\u0646 \u0648\u0627\u0631\u0634\u0627\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0634\u0627\u0628\u0647\u06cc \u0631\u0627 \u062f\u0631 \u0647\u0645\u0627\u0646 \u0633\u0627\u0644 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u06af\u0631\u0627\u0641 \u0627\u0631\u0627\u0626\u0647 \u062f\u0627\u062f\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0627\u0632 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0645\u0647 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0648 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0628\u0627\u0644\u0627\u06cc\u0634\u0627\u0646 \u0628\u0647 \u0633\u0631\u0639\u062a \u0645\u062d\u0628\u0648\u0628\u06cc\u062a \u06cc\u0627\u0641\u062a\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0686\u0637\u0648\u0631 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 (Distance Matrix) \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645\u06cc \u0632\u0648\u062c\u200c \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633\u060c \u0647\u0631 \u0639\u0646\u0635\u0631 (i, j) \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0645\u0633\u062a\u0642\u06cc\u0645 \u06cc\u0627 \u063a\u06cc\u0631\u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u06cc\u0646 \u0631\u0626\u0648\u0633 i \u0648 j \u0627\u0633\u062a.<\/li>\n\n\n\n<li>\u0633\u067e\u0633 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0648\u0644\u06cc\u0647 \u067e\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u06cc\u06a9 \u06cc\u0627\u0644 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u06cc\u0646 \u0631\u0626\u0648\u0633 i \u0648 j \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0648\u0632\u0646 \u0622\u0646 \u06cc\u0627\u0644 \u0631\u0627 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a\u060c \u0645\u0642\u062f\u0627\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0641\u0627\u0635\u0644\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0628\u0627 \u062e\u0648\u062f\u0634 \u0631\u0627 \u0646\u06cc\u0632 \u0635\u0641\u0631 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645\u060c \u06cc\u0639\u0646\u06cc \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0631\u0648\u06cc \u0642\u0637\u0631 \u0627\u0635\u0644\u06cc \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0645\u0627\u0645 \u0635\u0641\u0631 \u0627\u0633\u062a.<\/li>\n\n\n\n<li>\u062f\u0631 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0633\u0647 \u062d\u0644\u0642\u0647 \u062a\u0648 \u062f\u0631 \u062a\u0648 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0622\u0646\u200c\u0647\u0627 \u0628\u0631 \u0631\u0648\u06cc \u062a\u0645\u0627\u0645 \u0631\u0626\u0648\u0633 \u06af\u0631\u0627\u0641 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u0628\u0627 \u062d\u0644\u0642\u0647 \u0628\u06cc\u0631\u0648\u0646\u06cc \u0631\u0627\u0633 \u0645\u06cc\u0627\u0646\u06cc k \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0627 \u062d\u0644\u0642\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u0648\u0646\u06cc \u062f\u0648 \u0631\u0627\u0633 i \u0648 j \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u062a\u0645\u0627\u0645\u06cc \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u06cc\u0646 i \u0648 j \u0627\u0632 \u0637\u0631\u06cc\u0642 k \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0628\u0631\u0627\u06cc \u0647\u0631 \u062c\u0641\u062a \u0631\u0627\u0633 (i, j) \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0633\u06cc\u0631 \u0639\u0628\u0648\u0631 \u0627\u0632 k \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u06cc\u0646 &nbsp;i \u0648 j \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631. \u0627\u06af\u0631 \u0686\u0646\u06cc\u0646 \u0628\u0627\u0634\u062f\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/li>\n<\/ul>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">\\text{distance}[i][j] = \\min(\\text{distance}[i][j], \\text{distance}[i][k] + \\text{distance}[k][j])<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u06cc\u0646 \u0641\u0631\u0627\u06cc\u0646\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645\u06cc \u0631\u0626\u0648\u0633 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0645\u06cc\u0627\u0646\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062a\u0645\u0627\u0645\u06cc \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u0631\u0631\u0633\u06cc \u0634\u0648\u0646\u062f \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0647\u200c\u0631\u0648\u0632 \u0634\u0648\u062f.<\/li>\n<\/ul>\n\n\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/storage.cafetadris.com\/blog\/floyd.gif\"><\/p>\n\n\n<h3 class=\"wp-block-heading\">\u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/h3>\n\n\n\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u06cc\u0646 \u0647\u0645\u0647 \u0632\u0648\u062c\u200c \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f\u060c \u0645\u0627\u0646\u0646\u062f \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u060c \u0628\u0631\u0631\u0633\u06cc \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0628\u06cc\u0646 \u0631\u0626\u0648\u0633 \u0648 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u0647 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062f\u0642\u06cc\u0642 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u062f\u0627\u0631\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/h3>\n\n\n\n<p>\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0631\u0648\u0646\u062f \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u0632\u06cc\u0631 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"759\" height=\"427\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-22.png\" alt=\"\" class=\"wp-image-19455\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-22.png 759w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-22-300x169.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-22-585x329.png 585w\" sizes=\"(max-width: 759px) 100vw, 759px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0627\u06cc\u062c\u0627\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0627\u0648\u0644\u06cc\u0647<\/h4>\n\n\n\n<p>\u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 D<sub>0<\/sub> \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0631 \u0639\u0646\u0635\u0631 D[i][j] \u0622\u0646 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u06cc\u0646 \u0631\u0627\u0633 i \u0648 j \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f2 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627\u06f5\u06f2 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f1,\u06f2) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f1 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f5\u06f0 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f2,\u06f1) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f5\u06f0 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f3 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1\u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f2,\u06f3) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f1\u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f4 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f2,\u06f4) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f1 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f3\u06f0 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f3,\u06f1) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f3\u06f0 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f4 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1\u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f4,\u06f1) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f1\u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f1 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1\u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f3,\u06f4) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f1\u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f3 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u062f\u0631 \u062f\u0631\u0627\u06cc\u0647 (\u06f4,\u06f3) \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u062f\u062f \u06f5 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0631\u0648\u06cc \u0642\u0637\u0631 \u0627\u0635\u0644\u06cc \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u06af\u0641\u062a\u06cc\u0645 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0648 \u0633\u0627\u06cc\u0631 \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u0646\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"872\" height=\"300\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-23.png\" alt=\"\" class=\"wp-image-19456\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-23.png 872w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-23-300x103.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-23-768x264.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-23-585x201.png 585w\" sizes=\"(max-width: 872px) 100vw, 872px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0627 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u06cc\u06a9<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>1<\/sub> \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0641\u0631\u0645\u0648\u0644 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0627\u0633\u062a:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{1}[i,j]=\\min(D_{0}[i,j],D_{0}[i,1]+D_{0}[1,j])<\/span><\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062a\u0646\u0647\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06f3 \u0648 \u06f4 \u0628\u0647 \u0631\u0627\u0633 \u06f2 (\u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 &nbsp;\u06f1) \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0632\u06cc\u0631\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u0631\u0627\u0633 \u06f2 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f1 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f2 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f3\u06f5 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f2 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{1}[3,2]=\\min(D_{0}[3,2],D_{0}[3,1]+D_{0}[1,2]) \\rightarrow D_{1}[3,2]=\\min( \\infty, 30 + 5) = 35<\/span><\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f2 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f1 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f2 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f2\u06f0 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f2 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{1}[4,2]=\\min(D_{0}[4,2],D_{0}[4,1]+D_{0}[1,2]) \\rightarrow D_{1}[4,2]=\\min( \\infty, 15 + 5) = 20<\/span><\/p>\n\n\n\n<p>\u0633\u0627\u06cc\u0631 \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062f\u0633\u062a\u062e\u0648\u0634 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0632\u06cc\u0631\u0627 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc\u200c\u0634\u0627\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u06af\u0630\u0631\u062f\u061b \u0645\u062b\u0644\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f2 \u062a\u0627 \u06f4 \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0628\u0631\u0627\u0628\u0631 \u06f5 \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 \u06f2 \u0628\u0647 \u06f1 \u0628\u0631\u0648\u06cc\u0645 \u0641\u0627\u0635\u0644\u0647\u200c\u0627\u06cc \u0628\u0631\u0627\u0628\u0631 \u06f5\u06f0 \u062f\u0627\u0631\u062f \u0648 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u06f1 \u0628\u0647 \u06f4 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0631\u0627\u06cc \u0631\u0641\u062a\u0646 \u0627\u0632 \u06f2 \u0628\u0647 \u06f4 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 \u06f1 \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0633 \u062e\u0648\u0627\u0647\u062f \u0634\u062f \u0648 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{1}[2,4]=\\min(D_{0}[2,4],D_{0}[2,1]+D_{0}[1,4]) \\rightarrow D_{1}[2,4]=\\min( 5, 50 + \\infty) = 5<\/span><\/p>\n\n\n\n<p>\u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>1<\/sub> \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"898\" height=\"311\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-24.png\" alt=\"\" class=\"wp-image-19457\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-24.png 898w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-24-300x104.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-24-768x266.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-24-585x203.png 585w\" sizes=\"(max-width: 898px) 100vw, 898px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0627 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u062f\u0648<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>2<\/sub> \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0633 \u062f\u0648 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0641\u0631\u0645\u0648\u0644 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0627\u0633\u062a:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{2}[i,j]=\\min(D_{1}[i,j],D_{1}[i,2]+D_{1}[2,j])<\/span><\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062a\u0646\u0647\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06f3 \u0648 \u06f4 (\u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 \u06f2) \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0632\u06cc\u0631\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u0631\u0627\u0633 \u06f3 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f2 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f3 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f2\u06f0 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f3 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{2}[1,3]=\\min(D_{1}[1,3],D_{1}[1,2]+D_{1}[2,3]) \\rightarrow D_{2}[1,3]=\\min(\\infty, 5 + 15) = 20<\/span><\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f4 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f2 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f4 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f1\u06f0 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f4 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{2}[1,4]=\\min(D_{1}[1,4],D_{1}[1,2]+D_{1}[2,4]) \\rightarrow D_{2}[1,4]=\\min(\\infty, 5+ 5) = 10<\/span><\/p>\n\n\n\n<p>\u0633\u0627\u06cc\u0631 \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062f\u0633\u062a\u062e\u0648\u0634 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0632\u06cc\u0631\u0627 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc\u200c\u0634\u0627\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u06af\u0630\u0631\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>2<\/sub> \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"930\" height=\"343\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-25.png\" alt=\"\" class=\"wp-image-19458\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-25.png 930w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-25-300x111.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-25-768x283.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-25-585x216.png 585w\" sizes=\"(max-width: 930px) 100vw, 930px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0627 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0633\u0647<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>3<\/sub> \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0633 \u0633\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0641\u0631\u0645\u0648\u0644 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0627\u0633\u062a:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{3}[i,j]=\\min(D_{2}[i,j],D_{2}[i,3]+D_{2}[3,j])<\/span><\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062a\u0646\u0647\u0627 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u0631\u0627\u0633\u200c \u06f1 (\u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 \u06f3) \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0632\u06cc\u0631\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u0631\u0627\u0633 \u06f1 \u0628\u0631\u0627\u0628\u0631 \u06f5\u06f0 \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f3 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f3 \u0628\u0647 \u06f1 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f4\u06f5 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u06f5\u06f0 \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f1 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{3}[2,1]=\\min(D_{2}[2,1],D_{2}[2,3]+D_{2}[3,1]) \\rightarrow D_{3}[2,1]=\\min(50, 15+ 30) = 45<\/span><\/p>\n\n\n\n<p>\u0633\u0627\u06cc\u0631 \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062f\u0633\u062a\u062e\u0648\u0634 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0632\u06cc\u0631\u0627 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc\u200c\u0634\u0627\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u06af\u0630\u0631\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>3<\/sub> \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"945\" height=\"342\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-26.png\" alt=\"\" class=\"wp-image-19459\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-26.png 945w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-26-300x109.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-26-768x278.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-26-585x212.png 585w\" sizes=\"(max-width: 945px) 100vw, 945px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0627 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0686\u0647\u0627\u0631<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>4<\/sub> \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0633 \u0686\u0647\u0627\u0631 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0641\u0631\u0645\u0648\u0644 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0627\u0633\u062a:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{4}[i,j]=\\min(D_{3}[i,j],D_{3}[i,4]+D_{3}[4,j])<\/span><\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u0631\u0627\u0633\u200c \u06f1 \u0648 \u0646\u06cc\u0632 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06f1 \u0648 \u06f2 \u0628\u0647 \u06f3 (\u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 \u06f4) \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0632\u06cc\u0631\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u0631\u0627\u0633 \u06f1 \u0628\u0631\u0627\u0628\u0631 \u06f4\u06f5 \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f4 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f1 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f2\u06f0 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u06f4\u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f1 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{4}[2,1]=\\min(D_{3}[2,1],D_{3}[2,4]+D_{3}[4,1]) \\rightarrow D_{4}[2,1]=\\min(45, 5 + 15) = 20<\/span><\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f3 \u0628\u0631\u0627\u0628\u0631 \u06f2\u06f0 \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f4 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f3 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f1\u06f5 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u06f2\u06f0 \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f1 \u0628\u0647 \u06f3 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{4}[1,3]=\\min(D_{3}[1,3],D_{3}[1,4]+D_{3}[4,3]) \\rightarrow D_{4}[1,3]=\\min(20, 10 + 5) = 15<\/span><\/p>\n\n\n\n<p>\u0627\u0632 \u0637\u0631\u0641\u06cc \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f3 \u0628\u0631\u0627\u0628\u0631 \u06f1\u06f5 \u0627\u0633\u062a \u0627\u0645\u0627 \u0627\u06af\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f4 \u0628\u0631\u0648\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0627\u0633 \u06f4 \u0628\u0647 \u06f3 \u0628\u0631\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u06f1\u06f0 \u062e\u0648\u0627\u0647\u062f \u0631\u0633\u06cc\u062f. \u0686\u0648\u0646 \u0627\u06cc\u0646 \u0639\u062f\u062f \u06a9\u0645\u062a\u0631 \u0627\u0632 \u06f1\u06f5 \u0627\u0633\u062a\u060c \u067e\u0633 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u06f2 \u0628\u0647 \u06f3 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">D_{4}[2,3]=\\min(D_{3}[2,3],D_{3}[2,4]+D_{3}[4,3]) \\rightarrow D_{4}[2,3]=\\min(15, 5 + 5) = 10<\/span><\/p>\n\n\n\n<p>\u0633\u0627\u06cc\u0631 \u062f\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062f\u0633\u062a\u062e\u0648\u0634 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0632\u06cc\u0631\u0627 \u0641\u0627\u0635\u0644\u0647 \u0641\u0639\u0644\u06cc\u200c\u0634\u0627\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0631\u0627\u0633 \u06cc\u06a9 \u0628\u06af\u0630\u0631\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 D<sub>4<\/sub> \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"933\" height=\"352\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-27.png\" alt=\"\" class=\"wp-image-19460\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-27.png 933w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-27-300x113.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-27-768x290.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-27-585x221.png 585w\" sizes=\"(max-width: 933px) 100vw, 933px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/h3>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0633\u0647 \u062d\u0644\u0642\u0647 \u062a\u0648\u062f\u0631\u062a\u0648 \u0628\u0631\u0627\u06cc \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 &nbsp;O(V<sup>3<\/sup>) \u0627\u0633\u062a\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 V \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0633\u062a. \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u0627 \u06a9\u0647 \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u06a9\u0639\u0628\u06cc \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644\u060c \u0627\u0628\u062a\u062f\u0627 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 <code>numpy<\/code> \u0631\u0627 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u062a\u0627\u0628\u0639\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>floyd_warshall<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 graph \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a <a rel=\"noreferrer noopener\" href=\"https:\/\/cafetadris.com\/blog\/%D9%85%D8%B9%D8%B1%D9%81%DB%8C-%D8%AC%D8%A7%D9%85%D8%B9-%D8%B1%D9%88%D8%B4%D9%87%D8%A7%DB%8C-%D9%86%D9%85%D8%A7%DB%8C%D8%B4-%DA%AF%D8%B1%D8%A7%D9%81-%D8%A7%D8%B2-%D9%85%D8%A7%D8%AA%D8%B1\/#lwptoc2\" data-type=\"URL\" data-id=\"https:\/\/cafetadris.com\/blog\/%D9%85%D8%B9%D8%B1%D9%81%DB%8C-%D8%AC%D8%A7%D9%85%D8%B9-%D8%B1%D9%88%D8%B4%D9%87%D8%A7%DB%8C-%D9%86%D9%85%D8%A7%DB%8C%D8%B4-%DA%AF%D8%B1%D8%A7%D9%81-%D8%A7%D8%B2-%D9%85%D8%A7%D8%AA%D8%B1\/#lwptoc2\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062c\u0627\u0648\u0631\u062a<\/mark><\/a> \u0648 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0622\u0631\u06af\u0648\u0645\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639\u060c \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0632 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0648 \u06cc\u06a9 \u06a9\u067e\u06cc \u0627\u0632 \u0645\u0627\u062a\u0631\u06cc\u0633 \u06af\u0631\u0627\u0641 \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u0634\u0648\u062f. \u0633\u067e\u0633 \u0633\u0647 \u062d\u0644\u0642\u0647 \u062a\u0648 \u062f\u0631 \u062a\u0648 \u0647\u0631 \u062c\u0641\u062a \u0631\u0627\u0633 <code>(i, j)<\/code> \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0631 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647 (<code>k<\/code>) \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f. \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u0631\u0633\u06cc\u062f\u0646 \u0627\u0632 \u0631\u0627\u0633 <code>i<\/code> \u0628\u0647 <code>j<\/code> \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 <code>k<\/code> \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0645\u0633\u06cc\u0631 \u0641\u0639\u0644\u06cc <code>i<\/code> \u0628\u0647 <code>j<\/code> \u0628\u0627\u0634\u062f\u060c \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u0631\u0626\u0648\u0633 <code>i<\/code> \u0648 <code>j<\/code> \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0631\u0627\u0633 <code>k<\/code> \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>import numpy as np<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def floyd_warshall(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Number of vertices in the graph<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;num_vertices = graph.shape[0]<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Create a copy of the graph to store distances<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = graph.copy()<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Apply Floyd-Warshall algorithm<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for k in range(num_vertices):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for i in range(num_vertices):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for j in range(num_vertices):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># If the path through vertex k is shorter, update the distance<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[i, j] &gt; dist[i, k] + dist[k, j]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[i, j] = dist[i, k] + dist[k, j]<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Print the distance matrix after each intermediate vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(f'node {k+1} as intermediate node:\\n', dist, '\\n')<\/code><\/p>\n\n\n\n<p>\u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062c\u0627\u0648\u0631\u062a \u06af\u0631\u0627\u0641 \u0634\u0627\u0645\u0644 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 <code>np.inf<\/code> \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0646\u0628\u0648\u062f \u0645\u0633\u06cc\u0631 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0628\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0633 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641 \u0647\u0645\u0627\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0627\u0648\u0644\u06cc\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0627\u0644\u0627 \u0628\u0627 D<sub>0<\/sub> \u0622\u0646 \u0631\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u06cc\u0645 \u0648 \u0628\u0647 \u0645\u0631\u0648\u0631 \u0622\u0646 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u06a9\u0631\u062f\u06cc\u0645.<\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u06cc\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = np.array([<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;[0, 5, np.inf, np.inf],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;[50, 0, 15, 5],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;[30, np.inf, 0, 15],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;[15, np.inf, 5, 0]<\/code><br \/>\n<code>])<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>floyd_warshall(graph)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>node1 as intermediate node:<\/strong><br \/>\n[[ 0.  5. inf inf]<br \/>\n [50.  0. 15.  5.]<br \/>\n [30. 35.  0. 15.]<br \/>\n [15. 20.  5.  0.]]\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>node2 as intermediate node:<\/strong><br \/>\n[[ 0.  5. 20. 10.]<br \/>\n [50.  0. 15.  5.]<br \/>\n [30. 35.  0. 15.]<br \/>\n [15. 20.  5.  0.]]\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>node3 as intermediate node:<\/strong><br \/>\n[[ 0.  5. 20. 10.]<br \/>\n [45.  0. 15.  5.]<br \/>\n [30. 35.  0. 15.]<br \/>\n [15. 20.  5.  0.]]\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>node4 as intermediate node:<\/strong><br \/>\n[[ 0.  5. 15. 10.]<br \/>\n [20.  0. 10.  5.]<br \/>\n [30. 35.  0. 15.]<br \/>\n [15. 20.  5.  0.]]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646<\/h2>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Johnson%27s_algorithm\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Johnson&#8217;s Algorithm<\/mark><\/a>) \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0633\u062a \u0648 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0634\u0627\u0645\u0644 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0647\u0633\u062a\u0646\u062f \u0646\u06cc\u0632 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u062f\u0627\u0631\u062f\u060c \u0628\u0647 \u0634\u0631\u0637\u06cc \u06a9\u0647 \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u062a\u0648\u0633\u0637 \u062f\u0648\u0646\u0627\u0644\u062f \u0628\u06cc. \u062c\u0627\u0646\u0633\u0648\u0646 (<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Donald_B._Johnson\" target=\"_blank\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Donald B. Johnson<\/mark><\/a>) \u062f\u0631 \u0633\u0627\u0644 \u06f1\u06f9\u06f7\u06f7 \u0645\u0639\u0631\u0641\u06cc \u0634\u062f. \u062c\u0627\u0646\u0633\u0648\u0646 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0631\u0648\u0634 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0648 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0645\u0647 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 (Sparse graph) \u062a\u0648\u0633\u0639\u0647 \u062f\u0627\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0628\u0647\u06cc\u0646\u0647\u200c\u062a\u0631 \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0628\u0627\u0644\u0627\u06cc\u0634 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af\u060c \u0628\u0647 \u0633\u0631\u0639\u062a \u062f\u0631 \u062c\u0648\u0627\u0645\u0639 \u0639\u0644\u0645\u06cc \u0648 \u0635\u0646\u0639\u062a\u06cc \u0645\u0648\u0631\u062f \u062a\u0648\u062c\u0647 \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0686\u0637\u0648\u0631 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u06af\u0631\u0627\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0635\u0641\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u06af\u0631\u0627\u0641 \u0645\u062a\u0635\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0633\u067e\u0633 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0627\u0636\u0627\u0641\u0647\u200c\u0634\u062f\u0647 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645. \u0627\u06af\u0631 \u06af\u0631\u0627\u0641 \u062f\u0627\u0631\u0627\u06cc \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0622\u0646 \u0631\u0627 \u062a\u0634\u062e\u06cc\u0635 \u0645\u06cc\u200c\u062f\u0647\u062f \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u062e\u0627\u062a\u0645\u0647 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f.<\/li>\n\n\n\n<li>\u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0647\u200c\u062f\u0633\u062a\u200c\u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 (h) \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0648\u0632\u0646\u200c \u06cc\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647\u200c\u062f\u0633\u062a\u200c\u0622\u0645\u062f\u0647 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f (&#8216;w) \u0647\u0631 \u06cc\u0627\u0644 (u, v) \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0631\u0645\u0648\u0644 \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/li>\n<\/ul>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(u, v) = w(u, v) + h(u) - h(v)<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0628\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0648\u0632\u0646\u200c \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u063a\u06cc\u0631\u0645\u0646\u0641\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f (\u0634\u0631\u0637\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a).<\/li>\n\n\n\n<li>\u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0627 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0628\u0647\u200c\u062f\u0633\u062a\u200c\u0622\u0645\u062f\u0647 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647 \u062d\u0627\u0644\u062a \u0627\u0635\u0644\u06cc \u0628\u0631\u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u06cc\u0645. \u0641\u0627\u0635\u0644\u0647 \u0646\u0647\u0627\u06cc\u06cc \u0628\u06cc\u0646 \u0647\u0631 \u062c\u0641\u062a \u0631\u0627\u0633 (u, v) \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/li>\n<\/ul>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(u, v) = d'(u, v) + h(v) - h(u)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0628\u0631\u0631\u0633\u06cc \u06af\u0627\u0645\u200c\u0628\u0647\u200c\u06af\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646<\/h3>\n\n\n\n<p>\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0631\u0648\u0646\u062f \u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u0632\u06cc\u0631 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28-1024x597.png\" alt=\"\" class=\"wp-image-19461\" width=\"788\" height=\"459\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28-1024x597.png 1024w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28-300x175.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28-768x448.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28-585x341.png 585w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-28.png 1109w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0627\u0641\u0632\u0648\u062f\u0646 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f<\/h4>\n\n\n\n<p>\u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u0646\u0627\u0645 q \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0648\u0632\u0646 \u06cc\u0627\u0644 \u0635\u0641\u0631 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u062a\u0635\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29-1024x597.png\" alt=\"\" class=\"wp-image-19462\" width=\"799\" height=\"465\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29-1024x597.png 1024w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29-300x175.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29-768x448.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29-585x341.png 585w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-29.png 1112w\" sizes=\"(max-width: 799px) 100vw, 799px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h4>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 q \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0641\u0648\u0627\u0635\u0644 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0627\u0632 \u0631\u0627\u0633 q \u062a\u0627 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645. \u062e\u0631\u0648\u062c\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644h &nbsp;\u0631\u0627 \u0628\u0647 \u0645\u0627 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0637\u0628\u0642 \u0641\u0631\u0645\u0648\u0644 \u06af\u0641\u062a\u0647\u200c\u0634\u062f\u0647\u060c \u0628\u0631\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0647\u06cc \u0645\u062c\u062f\u062f \u06cc\u0627\u0644\u200c\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0645\u062b\u0628\u062a \u0628\u0627\u0634\u0646\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 q \u062a\u0627 \u0647\u0645\u0647 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0645\u0627 \u06cc\u0627 \u0647\u0645\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 h \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">h(A) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">h(B) = -5<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">h(C) = -3<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">h(D) = -4<\/span><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0648\u0632\u0646\u200c\u062f\u0647\u06cc \u0645\u062c\u062f\u062f \u06cc\u0627\u0644\u200c\u0647\u0627<\/h4>\n\n\n\n<p>\u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0631\u0645\u0648\u0644\u06cc \u06a9\u0647 \u062f\u0631 \u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0627\u0631\u0627\u0626\u0647 \u06a9\u0631\u062f\u06cc\u0645\u060c \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f (&#8216;w) \u0647\u0631 \u06cc\u0627\u0644 (u, v) \u06af\u0631\u0627\u0641 \u0628\u0627 \u06a9\u0645\u06a9 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(A, B) = w(A, B) + h(A) - h(B) \\rightarrow w'(A, B) = -5 + 0 - (-5) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(A, C) = w(A, C) + h(A) - h(C) \\rightarrow w'(A, C) = 2 + 0 - (-3) = 5<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(B, C) = w(B, C) + h(B) - h(C) \\rightarrow w'(B, C) = 2 + (-5) - (-3) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(B, D) = w(B, D) + h(B) - h(D) \\rightarrow w'(B, D) = 1 + (-5) - (-4) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">w'(C, D) = w(C, D) + h(C) - h(D) \\rightarrow w'(C, D) = 2 + (-3) - (-4) = 3<\/span><\/p>\n\n\n\n<p>\u0646\u0647\u0627\u06cc\u062a\u0627 \u0648\u0632\u0646 \u0647\u0631 \u06cc\u0627\u0644 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0639\u062f\u0627\u062f\u06cc \u06a9\u0647 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u06cc\u0645 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u0648 \u0631\u0627\u0633 q \u0631\u0627 \u0627\u0632 \u06af\u0631\u0627\u0641 \u062d\u0630\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062f\u0631 \u0645\u06cc\u200c\u0622\u06cc\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30-1024x597.png\" alt=\"\" class=\"wp-image-19463\" width=\"775\" height=\"451\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30-1024x597.png 1024w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30-300x175.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30-768x448.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30-585x341.png 585w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-30.png 1120w\" sizes=\"(max-width: 775px) 100vw, 775px\" \/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">\u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h4>\n\n\n\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f \u0628\u0627\u06cc\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0627 \u0627\u0632 \u0647\u0631 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f\u060c \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u0631\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(A, B) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(A, C) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(A, D) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(B, A) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(B, C) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(B, D) = 0<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(C, A) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(C, B) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(C, D) = 3<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(D, A) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(D, B) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d'(D, C) = \\infty<\/span><\/p>\n\n\n\n<p>\u062f\u0631 \u067e\u0627\u06cc\u0627\u0646 \u0641\u0648\u0627\u0635\u0644 \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f\u060c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0627\u0635\u0644\u06cc \u0628\u0627\u0632 \u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(A, B) = d'(A, B) + h(B) - h(A) = 0 + (-5) - 0 = -5<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(A, C) = d'(A, C) + h(C) - h(A) = 0 + (-3) - 0 = -3<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(A, D) = d'(A, D) + h(D) - h(A) = 0 + (-4) - 0 = -4<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(B, A) = d'(B, A) + h(A) - h(B) = \\infty + 0 - (-5) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(B, C) = d'(B, C) + h(C) - h(B) = 0 + (-3) - (-5) = 2<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(B, D) = d'(B, D) + h(D) - h(B) = 0 + (-4) - (-5) = 1<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(C, A) = d'(C, A) + h(A) - h(C) = \\infty + 0 - (-3) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(C, B) = d'(C, B) + h(B) - h(C) = \\infty + (-5) - (-3) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(C, D) = d'(C, D) + h(D) - h(C) = 3 + (-4) - (-3) = 2<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(D, A) = d'(D, A) + h(A) - h(D) = \\infty + 0 - (-4) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(D, B) = d'(D, B) + h(B) - h(D) = \\infty + (-5) - (-4) = \\infty<\/span>\n<\/p>\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">d(D, C) = d'(D, C) + h(C) - h(D) = \\infty + (-3) - (-4) = \\infty<\/span><\/p>\n\n\n\n<p>\u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0628\u06cc\u0646 \u0647\u0645\u0647 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0635\u0644\u06cc \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646<\/h3>\n\n\n\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0632 \u062a\u0631\u06a9\u06cc\u0628 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc\u200c\u0627\u0634 \u0647\u0645 \u0631\u0627\u0628\u0637\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645\u06cc \u0628\u0627 \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u06cc\u0646 \u062f\u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u0627 V \u0631\u0627\u0633 \u0648 E \u06cc\u0627\u0644:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u0627\u0641\u0632\u0648\u062f\u0646 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f<\/strong><strong>: <\/strong>\u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 \u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u06af\u0631\u0627\u0641 \u0648 \u0627\u062a\u0635\u0627\u0644 \u0622\u0646 \u0628\u0627 \u0648\u0632\u0646 \u06cc\u0627\u0644 \u0635\u0641\u0631 \u0628\u0647 \u0647\u0631 \u0631\u0627\u0633 \u062f\u06cc\u06af\u0631 \u0632\u0645\u0627\u0646 O(V) \u0631\u0627 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<strong><\/strong><\/li>\n\n\n\n<li><strong>\u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/strong><strong>:<\/strong> \u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0627\u0632 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u0641\u0648\u0627\u0635\u0644 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u0632\u0645\u0627\u0646 O(V\u22c5E) &nbsp;\u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<strong><\/strong><\/li>\n\n\n\n<li><strong>\u0648\u0632\u0646\u200c\u06af\u0630\u0627\u0631\u06cc \u0645\u062c\u062f\u062f \u06cc\u0627\u0644\u200c\u0647\u0627<\/strong><strong>: <\/strong>\u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u0627\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647 \u0632\u0645\u0627\u0646 O(E) \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<strong><\/strong><\/li>\n\n\n\n<li><strong>\u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/strong>: \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0632 \u0647\u0631 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0628\u0627 \u0647\u06cc\u067e \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc \u0628\u0647 \u0632\u0645\u0627\u0646 O((V+E)logV) \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u060c \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0628\u0647O(V\u22c5(V+E)logV) &nbsp;\u0632\u0645\u0627\u0646 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<strong><\/strong><\/li>\n\n\n\n<li><strong>\u062a\u0646\u0638\u06cc\u0645 \u0641\u0648\u0627\u0635\u0644 \u0646\u0647\u0627\u06cc\u06cc: \u062a\u0628\u062f\u06cc\u0644 <\/strong>\u0641\u0648\u0627\u0635\u0644 \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0647 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0627\u0635\u0644\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0647 \u0632\u0645\u0627\u0646 O(V<sup>2<\/sup>) \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/li>\n<\/ul>\n\n\n\n<p>\u0628\u0627 \u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0645\u0631\u0627\u062d\u0644 \u0641\u0648\u0642\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O(V \\cdot E + V^2 \\log V)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u06af\u0641\u062a\u0647 \u0634\u062f\u060c \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u0632\u0648\u062c \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062f\u0627\u0631\u0627\u06cc \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0628\u0627\u0634\u062f\u060c \u0627\u0632 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/h4>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0646\u0646\u062f \u0642\u0633\u0645\u062a\u200c\u0647\u0627\u06cc \u0642\u0628\u0644\u060c \u062a\u0627\u0628\u0639\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>bellman_ford<\/code> \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def bellman_ford(graph, source):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances from the source to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># except the source itself which is set to zero<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist[source] = 0<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Define the order of vertices<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;vertices = sorted(graph.keys())<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Relax edges repeatedly<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for _ in range(len(graph) - 1):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for vertex in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[vertex].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[vertex] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[neighbor] = dist[vertex] + weight<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Check for negative weight cycles<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for vertex in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[vertex].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[vertex] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(\"Graph contains a negative weight cycle\")<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;return dist<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/h4>\n\n\n\n<p>\u0633\u067e\u0633\u060c \u062a\u0627\u0628\u0639 <code>dijkstra<\/code> \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 (\u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def dijkstra(graph, source):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances from the source to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;dist[source] = 0<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Set to keep track of vertices included in the shortest path tree<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;sptSet = set()<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;while len(sptSet) &lt; len(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Select the vertex with the minimum distance value<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;u = min((vertex for vertex in dist if vertex not in sptSet), key=dist.get)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Add the selected vertex to the set<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sptSet.add(u)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor, weight in graph[u].items():<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if neighbor not in sptSet:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if dist[u] + weight &lt; dist[neighbor]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist[neighbor] = dist[u] + weight<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;return dist<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u062c\u0627\u0646\u0633\u0648\u0646<\/h4>\n\n\n\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u062a\u0627\u0628\u0639 <code>johnson<\/code> \u0631\u0627 \u06a9\u0647 \u0627\u0632 \u062f\u0648 \u062a\u0627\u0628\u0639 <code>bellman_ford<\/code> \u0648 <code>dijkstra<\/code> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f (<code>new_vertex<\/code>) \u0628\u0647 \u0646\u0627\u0645 <code>q<\/code> \u0628\u0647 \u06af\u0631\u0627\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0628\u0627 \u06cc\u0627\u0644\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0635\u0641\u0631 \u0628\u0647 \u0647\u0645\u0647 \u0631\u0626\u0648\u0633 \u06af\u0631\u0627\u0641 \u0648\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f (<code>v: 0 for v in graph<\/code>). \u0633\u067e\u0633 \u062a\u0627\u0628\u0639 <code>bellman_ford<\/code> \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u060c \u0628\u0627 \u0631\u0627\u0633 \u0634\u0631\u0648\u0639 <code>q<\/code> \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0633\u067e\u0633 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0628\u0647 \u0646\u0627\u0645 <code>reweighted_graph<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 <code>u<\/code> \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0635\u0644\u06cc\u060c \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f \u06cc\u0627\u0644\u06cc \u06a9\u0647 \u0627\u0632 \u0631\u0627\u0633 <code>u<\/code> \u0628\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0645\u06cc\u200c\u0631\u0648\u062f \u0631\u0627 \u062f\u0631 \u062e\u0648\u062f \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u062a\u0648\u0636\u06cc\u062d \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u06af\u0641\u062a\u06cc\u0645\u060c \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0631\u0645\u0648\u0644 <code>w + h[u] - h[v]<\/code> \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>w<\/code> \u0648\u0632\u0646 \u0627\u0635\u0644\u06cc \u06cc\u0627\u0644 \u0628\u06cc\u0646 <code>u<\/code> \u0648 <code>v<\/code> \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0635\u0644\u06cc \u0627\u0633\u062a.<\/li>\n\n\n\n<li><code>h[u]<\/code> \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0631\u0627\u0633 <code>u<\/code> \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 <code>q<\/code> (\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f) \u0627\u0633\u062a.<\/li>\n\n\n\n<li><code>h[v]<\/code> \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0631\u0627\u0633 <code>v<\/code> (\u06cc\u06a9\u06cc \u0627\u0632 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0631\u0627\u0633 <code>u<\/code> \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0635\u0644\u06cc) \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 <code>q<\/code> (\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f) \u0627\u0633\u062a.<\/li>\n<\/ul>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def johnson(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Add a new vertex 'q' with zero-weight edges to all other vertices<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;new_vertex = 'q'<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;new_graph = {new_vertex: {v: 0 for v in graph}}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;new_graph.update(graph)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Run Bellman-Ford with 'q' as source node<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;h = bellman_ford(new_graph, new_vertex)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Reweight the edges<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;reweighted_graph = {u : {v: w + h[u] - h[v] for v, w in edges.items()} for u, edges in graph.items()}<\/code><\/p>\n\n\n\n<p>\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u06cc\u06a9 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u062e\u0627\u0644\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>all_pairs_shortest_paths<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0634\u0627\u0645\u0644 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645\u06cc \u0632\u0648\u062c \u0631\u0627\u0633\u200c\u0647\u0627 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u06a9\u0644\u06cc\u062f\u0647\u0627\u06cc (keys) \u0627\u06cc\u0646 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 (values) \u0622\u0646\u200c\u0647\u0627 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0627\u0632 \u0647\u0631 \u0631\u0627\u0633 \u0628\u0647 \u0647\u0645\u0647 \u062f\u06cc\u06af\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u0633\u067e\u0633\u060c \u062a\u0627\u0628\u0639 <code>dijkstra<\/code> \u0631\u0627 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0631\u0626\u0648\u0633 \u06af\u0631\u0627\u0641 \u0627\u0635\u0644\u06cc \u0648 \u0647\u0631 \u0628\u0627\u0631 \u0628\u0627 \u06cc\u06a9 \u0631\u0627\u0633 \u0634\u0631\u0648\u0639 \u0645\u062a\u0641\u0627\u0648\u062a (<code>u<\/code>)\u060c \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u06cc\u0627 \u0647\u0645\u0627\u0646 <code>reweighted_graph<\/code> \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0647\u0645\u0627\u0646\u200c\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0628\u062e\u0634 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u062f\u06cc\u062f\u06cc\u062f\u060c \u062e\u0631\u0648\u062c\u06cc \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u062f\u0631 \u0647\u0631 \u0628\u0627\u0631\u060c \u06cc\u06a9 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0631\u0626\u0648\u0633 \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0628\u0647 \u0645\u0627 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n\n\n\n<p>\u0646\u0647\u0627\u06cc\u062a\u0627 \u0628\u0627 \u06a9\u0645\u06a9 \u062e\u0631\u0648\u062c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627\u060c \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc <code>all_pairs_shortest_paths<\/code> \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0631\u0645\u0648\u0644 <code>d + h[v] - h[v]<\/code> \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u06a9\u0647 \u062f\u0631 \u0622\u0646:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>u<\/code> \u0631\u0627\u0633\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/li>\n\n\n\n<li><code>v<\/code> \u0631\u0627\u0633\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 u \u062a\u0627 \u0622\u0646 \u0628\u0627 \u06a9\u0645\u06a9 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/li>\n\n\n\n<li>d \u0641\u0627\u0635\u0644\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 <code>u<\/code> \u0628\u0647 <code>v<\/code> \u062f\u0631 \u06af\u0631\u0627\u0641 \u062c\u062f\u06cc\u062f \u0627\u0633\u062a.<\/li>\n\n\n\n<li><code>h[v]<\/code> \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0631\u0627\u0633 <code>v<\/code> \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 <code>u<\/code> (\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627) \u0627\u0633\u062a.<\/li>\n<\/ul>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Run Dijkstra's algorithm for each vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;all_pairs_shortest_paths = {}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for u in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dist = dijkstra(reweighted_graph, u)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;all_pairs_shortest_paths[u] = {v: d + h[v] - h[u] for v, d in dist.items()}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(f'{u} as source', ': ', all_pairs_shortest_paths,'\\n')<\/code><\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0631\u0627 \u0631\u0648\u06cc \u06af\u0631\u0627\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u06cc\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'A': {'B': -5, 'C': 2},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'B': {'C': 2, 'D': 1},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'C': {'D': 2},<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'D': {}<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>johnson(graph)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>A as source:<\/strong><br \/>\n{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: -5, &#8216;C&#8217;: -3, &#8216;D&#8217;: -4}}<br \/>\n<strong>B as source:<\/strong><br \/>\n{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: -5, &#8216;C&#8217;: -3, &#8216;D&#8217;: -4}, &#8216;B&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1}}<br \/>\n<strong>C as source:<\/strong><br \/>\n{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: -5, &#8216;C&#8217;: -3, &#8216;D&#8217;: -4}, &#8216;B&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1}, &#8216;C&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: inf, &#8216;C&#8217;: 0, &#8216;D&#8217;: 2}}<br \/>\n<strong>D as source:<\/strong><br \/>\n{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: -5, &#8216;C&#8217;: -3, &#8216;D&#8217;: -4}, &#8216;B&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1}, &#8216;C&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: inf, &#8216;C&#8217;: 0, &#8216;D&#8217;: 2}, &#8216;D&#8217;: {&#8216;A&#8217;: inf, &#8216;B&#8217;: inf, &#8216;C&#8217;: inf, &#8216;D&#8217;: 0}}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646<\/h2>\n\n\n\n<p>\u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u060c \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0633\u0627\u062f\u0647\u200c\u062a\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u0634\u0648\u062f. \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0647\u0645 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (BFS) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0635\u0641\u060c \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0645\u0627\u0645 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0628\u06cc\u0646 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0647\u0645\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u06cc\u200c\u0648\u0632\u0646 \u0631\u0627 \u0686\u0637\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u061f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (BFS) \u0628\u0647 \u0637\u0648\u0631 \u0645\u0639\u0645\u0648\u0644 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 BFS \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0646\u06cc\u0632 \u0628\u0647\u0631\u0647 \u0628\u0631\u062f.<\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0627\u0628\u0639\u0627\u062f n\u00d7n \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u06a9\u0647 n \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0627\u0633\u062a.<\/li>\n\n\n\n<li>\u0633\u067e\u0633 \u062a\u0645\u0627\u0645\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0628\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0628\u062c\u0632 \u0642\u0637\u0631 \u0627\u0635\u0644\u06cc \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0635\u0641\u0631 \u0627\u0633\u062a (\u0641\u0627\u0635\u0644\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0628\u0627 \u062e\u0648\u062f\u0634).<\/li>\n\n\n\n<li>\u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0631\u0627 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u06cc\u06a9 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0648 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0646\u06af\u0647\u062f\u0627\u0631\u06cc \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0647\u0631 \u06af\u0631\u0647 \u0627\u0632 \u0645\u0628\u062f\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n\n\n\n<li>\u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u062e\u0648\u062f\u0634 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/li>\n\n\n\n<li>\u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0646\u0634\u062f\u0647:<ul><li>\u06af\u0631\u0647 \u0627\u0648\u0644 \u0635\u0641 \u0631\u0627 \u0627\u0632 \u0635\u0641 \u062e\u0627\u0631\u062c \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li><\/ul>\n<ul class=\"wp-block-list\">\n<li>\u062a\u0645\u0627\u0645\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06af\u0631\u0647\u200c\u06cc \u062e\u0627\u0631\u062c \u0634\u062f\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u0627\u06cc\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627 \u0647\u0646\u0648\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u0622\u0646\u200c\u0647\u0627 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647\u200c\u06cc \u06af\u0631\u0647\u200c\u06cc \u0641\u0639\u0644\u06cc \u0628\u0647 \u0627\u0636\u0627\u0641\u0647\u200c\u06cc \u06cc\u06a9 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u0646\u062a\u0627\u06cc\u062c \u0627\u062c\u0631\u0627\u06cc BFS \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u0631\u0627 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 n\u00d7n &nbsp;\u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/li>\n<\/ul>\n\n\n\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c \u0631\u0627\u0633\u200c\u0647\u0627 \u0686\u0642\u062f\u0631 \u0627\u0633\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u0647\u0645\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u06cc\u200c\u0648\u0632\u0646<\/h3>\n\n\n\n<p>\u0647\u0631 \u0628\u0627\u0631 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u062f\u0627\u0631\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc O(V+E) \u0627\u0633\u062a. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0627\u0632 V \u0631\u0627\u0633 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n\n\n<p style=\"direction:ltr;text-align:center!important\">\n<span class=\"wp-katex-eq\" data-display=\"false\">O(V^2 + V \\cdot E)<\/span><\/p>\n\n\n\n<p>\u0627\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0632\u06cc\u0627\u062f\u06cc \u0631\u0627\u0633 \u0648 \u06cc\u0627\u0644\u060c \u0632\u0645\u0627\u0646 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0627\u0641\u0632\u0627\u06cc\u0634 \u06cc\u0627\u0628\u062f\u060c \u0648 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0647\u06cc\u0646\u0647\u200c\u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0628\u0631\u0627\u06cc \u0686\u0646\u06cc\u0646 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc\u06cc \u0646\u06cc\u0633\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h3>\n\n\n\n<p>\u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0628\u0627 \u062f\u0648 \u062a\u0627\u0628\u0639 &nbsp;<code>bfs_shortest_paths<\/code> \u0648 <code>all_pairs_shortest_paths<\/code> \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u062a\u0627\u0628\u0639 \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u062a\u0627\u0628\u0639 \u062f\u0648\u0645 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0628\u0647 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0627\u0628\u0639 bfs_shortest_paths<\/h4>\n\n\n\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc <code>distances<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647 \u0647\u0631 \u0631\u0627\u0633 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f. \u0627\u0628\u062a\u062f\u0627 \u062a\u0645\u0627\u0645\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u06cc\u0646 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0631\u0627 \u0628\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0639\u062f \u0641\u0627\u0635\u0644\u0647 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0627\u0632 \u062e\u0648\u062f\u0634 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u06cc\u06a9 \u0635\u0641 (<code>queue<\/code>) \u0627\u0632 \u0631\u0627\u0633\u200c\u0647\u0627\u06cc \u062f\u0631 \u062d\u0627\u0644 \u067e\u0631\u062f\u0627\u0632\u0634 \u0627\u06cc\u062c\u0627\u062f \u0648 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0635\u0641 \u062e\u0627\u0644\u06cc \u0646\u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u06af\u0631\u0647 \u0627\u0648\u0644 \u0635\u0641 \u0627\u0632 \u0635\u0641 \u062e\u0627\u0631\u062c \u0648 \u062a\u0645\u0627\u0645\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06af\u0631\u0647 \u062e\u0627\u0631\u062c \u0634\u062f\u0647 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0628\u0627\u0634\u062f\u060c \u0627\u06cc\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0647 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u06af\u0631\u0647 \u0641\u0639\u0644\u06cc \u0628\u0647 \u0627\u0636\u0627\u0641\u0647 \u06cc\u06a9 \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc <code>distances<\/code> \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f\u060c \u0628\u0627\u0632 \u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>from collections import deque<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def bfs_shortest_paths(graph, start):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize distances to all vertices as infinity<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;distances = {vertex: float('infinity') for vertex in graph}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Distance to the start vertex is set to 0<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;distances[start] = 0<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize the queue with the start vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;queue = deque([start])<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Process the queue until it is empty<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;while queue:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;node = queue.popleft()<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Iterate through neighbors of the current node<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for neighbor in graph[node]:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># If the neighbor has not been visited, update the distance<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if distances[neighbor] == float('infinity'):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;queue.append(neighbor)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;distances[neighbor] = distances[node] + 1<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;return distances<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u062a\u0627\u0628\u0639 &nbsp;all_pairs_shortest_paths<\/h4>\n\n\n\n<p>\u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639\u060c \u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0628\u0647 \u0646\u0627\u0645 <code>all_distances<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f. \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u062f\u0631 \u06af\u0631\u0627\u0641\u060c \u062a\u0627\u0628\u0639 <code>bfs_shortest_paths<\/code> \u0631\u0627 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0622\u0646 \u0631\u0627\u0633 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u0648\u062f. \u0646\u062a\u0627\u06cc\u062c \u0647\u0631 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0631\u0627 \u062f\u0631 \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc <code>all_distances<\/code> \u0630\u062e\u06cc\u0631\u0647 \u06a9\u0631\u062f\u0647 \u0648 \u067e\u0633 \u0627\u0632 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0647\u0631 \u0631\u0627\u0633\u060c \u0645\u062d\u062a\u0648\u06cc\u0627\u062a \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0631\u0627 \u0686\u0627\u067e \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>def all_pairs_shortest_paths(graph):<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Initialize a dictionary to store distances for all pairs<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;all_distances = {}<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"color:green\"># Calculate shortest paths for each vertex<\/span><\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;for vertex in graph:<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;all_distances[vertex] = bfs_shortest_paths(graph, vertex)<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(all_distances)<\/code><\/p>\n\n\n\n<p>\u0646\u062a\u06cc\u062c\u0647 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0632\u06cc\u0631 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u062f:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-31.png\" alt=\"\" class=\"wp-image-19464\" width=\"627\" height=\"406\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-31.png 900w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-31-300x194.png 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-31-768x497.png 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/08\/image-31-585x379.png 585w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/figure><\/div>\n\n<p style=\"direction:ltr;text-align:left!important\">\n<code>graph = {<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'A': ['B', 'C', 'D'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'B': ['A', 'D'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'C': ['A', 'E'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'D': ['A', 'B'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'E': ['C', 'F'],<\/code><br \/>\n<code>&nbsp;&nbsp;&nbsp;&nbsp;'F': ['E']<\/code><br \/>\n<code>}<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<code>all_pairs_shortest_paths(graph)<\/code>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2}}<\/strong>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2}, &#8216;B&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1, &#8216;E&#8217;: 3}}<\/strong>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2}, &#8216;B&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1, &#8216;E&#8217;: 3}, &#8216;C&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 2, &#8216;C&#8217;: 0, &#8216;D&#8217;: 2, &#8216;E&#8217;: 1}}<\/strong>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2}, &#8216;B&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1, &#8216;E&#8217;: 3}, &#8216;C&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 2, &#8216;C&#8217;: 0, &#8216;D&#8217;: 2, &#8216;E&#8217;: 1}, &#8216;D&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 1, &#8216;C&#8217;: 2, &#8216;D&#8217;: 0, &#8216;E&#8217;: 3}}<\/strong>\n<\/p>\n<p style=\"direction:ltr;text-align:left!important\">\n<strong>{&#8216;A&#8217;: {&#8216;A&#8217;: 0, &#8216;B&#8217;: 1, &#8216;C&#8217;: 1, &#8216;D&#8217;: 1, &#8216;E&#8217;: 2}, &#8216;B&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 0, &#8216;C&#8217;: 2, &#8216;D&#8217;: 1, &#8216;E&#8217;: 3}, &#8216;C&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 2, &#8216;C&#8217;: 0, &#8216;D&#8217;: 2, &#8216;E&#8217;: 1}, &#8216;D&#8217;: {&#8216;A&#8217;: 1, &#8216;B&#8217;: 1, &#8216;C&#8217;: 2, &#8216;D&#8217;: 0, &#8216;E&#8217;: 3}, &#8216;E&#8217;: {&#8216;A&#8217;: 2, &#8216;B&#8217;: 3, &#8216;C&#8217;: 1, &#8216;D&#8217;: 3, &#8216;E&#8217;: 0}}<\/strong><\/p>\n\n\n\n<p>\u0645\u062c\u0645\u0648\u0639\u0647 \u06a9\u0627\u0645\u0644 \u06a9\u062f\u0647\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628\u060c \u0627\u0632 \u06af\u06cc\u062a\u200c\u0647\u0627\u0628 \u0631\u06cc\u067e\u0648\u0632\u06cc\u062a\u0648\u0631\u06cc&nbsp;<a href=\"https:\/\/github.com\/MobinaPoulaei\/Graph-Theory\/tree\/main\/Shortest%20Path%20Problem\" data-type=\"URL\" data-id=\"https:\/\/github.com\/MobinaPoulaei\/Graph-Theory\/tree\/main\/Shortest%20Path%20Problem\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Shortest Path Problem<\/mark><\/a> \u0642\u0627\u0628\u0644 \u062f\u0633\u062a\u0631\u0633\u06cc \u0627\u0633\u062a.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u062c\u0645\u0639\u200c\u0628\u0646\u062f\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-background\" style=\"background:linear-gradient(135deg,rgba(255,207,236,0.77) 0%,rgba(149,240,187,0.73) 100%)\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u0646\u0627\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u0628\u0647\u062a\u0631\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062f\u0633\u062a\u0647\u200c\u0628\u0646\u062f\u06cc<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a<\/strong><strong><\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(E + VlogV)<strong><\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">\u06cc\u06a9 \u0631\u0627\u0633 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0626\u0648\u0633<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V.E)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u06cc\u06a9 \u0631\u0627\u0633 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0626\u0648\u0633<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u0628\u0631\u0627\u06cc \u0645\u062f\u06cc\u0631\u06cc\u062a \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc \u0648 \u062a\u0634\u062e\u06cc\u0635 \u062f\u0648\u0631\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V<sup>3<\/sup>)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0647\u0645\u0647 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062c\u0627\u0646\u0633\u0648\u0646<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V.E+V<sup>2<\/sup>logV)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0647\u0645\u0647 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627\u060c \u0645\u0646\u0627\u0633\u0628 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (<\/strong><strong>BFS<\/strong><strong>)<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V+E)<strong><\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">\u06cc\u06a9 \u0631\u0627\u0633 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0626\u0648\u0633<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0645\u0627\u06cc\u0634 \u06af\u0631\u0627\u0641 \u0648 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 <\/strong><strong>DAG<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V+E)<strong><\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">\u06cc\u06a9 \u0631\u0627\u0633 \u062a\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0626\u0648\u0633<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0627\u0635 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062f\u0648\u0631 (DAG) \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (<\/strong><strong>BFS<\/strong><strong>)<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">O(V<sup>2<\/sup>+V.E)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0647\u0645\u0647 \u062c\u0641\u062a \u0631\u0627\u0633\u200c\u0647\u0627<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u06a9\u0644\u0627\u0645 \u0622\u062e\u0631 \u062f\u0631\u0628\u0627\u0631\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641<\/h2>\n\n\n\n<p>\u0645\u0633\u0626\u0644\u0647 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0628\u0646\u06cc\u0627\u062f\u06cc\u0646 \u0648 \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc \u062f\u0631 \u0639\u0644\u0648\u0645 \u0631\u0627\u06cc\u0627\u0646\u0647 \u0648 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0645\u0627\u0646\u0646\u062f \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u062d\u0645\u0644\u200c\u0648\u0646\u0642\u0644\u060c \u0637\u0631\u0627\u062d\u06cc \u0645\u062f\u0627\u0631\u0647\u0627\u06cc \u0627\u0644\u06a9\u062a\u0631\u06cc\u06a9\u06cc \u0648 \u062d\u062a\u06cc \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc \u0648\u06cc\u062f\u0626\u0648\u06cc\u06cc \u0627\u0647\u0645\u06cc\u062a \u0648\u06cc\u0698\u0647\u200c\u0627\u06cc \u062f\u0627\u0631\u062f. \u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647\u060c \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0628\u0647 \u062f\u0633\u062a\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0627\u0632 \u062c\u0645\u0644\u0647 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u062c\u0647\u062a\u200c\u062f\u0627\u0631\u060c \u0628\u062f\u0648\u0646 \u062c\u0647\u062a\u060c \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0648 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/p>\n\n\n\n<p>\u0647\u0631 \u062f\u0633\u062a\u0647 \u0627\u0632 \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062e\u0627\u0635 \u062e\u0648\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0627\u0631\u0646\u062f. \u0627\u0632 \u0645\u06cc\u0627\u0646 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627\u060c \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f\u060c \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644\u060c \u062c\u0627\u0646\u0633\u0648\u0646 \u0648 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (BFS) \u0627\u0634\u0627\u0631\u0647 \u06a9\u0631\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u063a\u06cc\u0631\u0645\u0646\u0641\u06cc \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0642\u0627\u062f\u0631 \u0628\u0647 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0646\u06cc\u0632 \u0647\u0633\u062a. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a\u060c \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0646\u0648\u0639 \u06af\u0631\u0627\u0641 \u0648 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc \u0645\u0633\u0626\u0644\u0647\u060c \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0646\u0627\u0633\u0628 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u062d\u0644 \u0628\u0647\u06cc\u0646\u0647 \u0648 \u0633\u0631\u06cc\u0639 \u0645\u0633\u0627\u0626\u0644 \u0645\u062e\u062a\u0644\u0641 \u06a9\u0645\u06a9 \u06a9\u0646\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647\u060c \u062f\u0631\u06a9 \u062f\u0631\u0633\u062a \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0648 \u0645\u0633\u0626\u0644\u0647 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u060c \u0646\u0642\u0634 \u06a9\u0644\u06cc\u062f\u06cc \u062f\u0631 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0627\u0631\u062f.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"307\" src=\"https:\/\/storage.cafetadris.com\/blog\/2024\/07\/FAQs-2-1024x307-1.jpg\" alt=\"FAQs\" class=\"wp-image-19316\" srcset=\"https:\/\/storage.cafetadris.com\/blog\/2024\/07\/FAQs-2-1024x307-1.jpg 1024w, https:\/\/storage.cafetadris.com\/blog\/2024\/07\/FAQs-2-1024x307-1-300x90.jpg 300w, https:\/\/storage.cafetadris.com\/blog\/2024\/07\/FAQs-2-1024x307-1-768x230.jpg 768w, https:\/\/storage.cafetadris.com\/blog\/2024\/07\/FAQs-2-1024x307-1-585x175.jpg 585w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">\u067e\u0631\u0633\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u062f\u0627\u0648\u0644<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0686\u06cc\u0633\u062a \u0648 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 (Dijkstra&#8217;s Algorithm) \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 (Greedy Algorithm) \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u0628\u062f\u0627 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 (Weighted Graph) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0633\u06cc\u0631 \u0628\u0627 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0647\u0632\u06cc\u0646\u0647 \u062f\u0631 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647\u060c \u0628\u0647 \u062a\u062f\u0631\u06cc\u062c \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0686\u06af\u0648\u0646\u0647 \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0645\u0642\u0627\u0628\u0644\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f (Bellman-Ford Algorithm) \u0642\u0627\u062f\u0631 \u0628\u0647 \u0645\u062f\u06cc\u0631\u06cc\u062a \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0645\u0646\u0641\u06cc \u0627\u0633\u062a \u0648 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u062f\u0648\u0631\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc (Negative Cycles) \u0631\u0627 \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627 \u0686\u0646\u062f\u06cc\u0646 \u0628\u0627\u0631 \u0639\u0628\u0648\u0631 \u0627\u0632 \u0631\u0648\u06cc \u062a\u0645\u0627\u0645\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u060c \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0627\u06af\u0631 \u062a\u063a\u06cc\u06cc\u0631\u06cc \u062f\u0631 \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627 \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u0648\u062f\u060c \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0648\u062c\u0648\u062f \u062f\u0648\u0631 \u0645\u0646\u0641\u06cc \u062f\u0631 \u06af\u0631\u0627\u0641 \u0627\u0633\u062a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 \u0686\u0647 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc\u06cc \u062f\u0627\u0631\u062f \u0648 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0644\u0648\u06cc\u062f-\u0648\u0627\u0631\u0634\u0627\u0644 (Floyd-Warshall Algorithm) \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 (Dynamic Programming) \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0627\u0635\u0644\u0647 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0647 \u062a\u062f\u0631\u06cc\u062c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0645\u0627\u0645\u06cc \u0631\u0627\u0633\u200c\u0647\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0631\u0627\u0633 \u0648\u0627\u0633\u0637\u0647\u060c \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0686\u06af\u0648\u0646\u0647 \u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u061f<\/h3>\n\n\n\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 (Johnson&#8217;s Algorithm) \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0648 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0627\u0633\u062a \u0648 \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 (Sparse Graphs) \u0628\u0627 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 \u06cc\u06a9 \u0631\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0647 \u06af\u0631\u0627\u0641 \u0648 \u062a\u0646\u0638\u06cc\u0645 \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u060c \u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0631\u0627 \u063a\u06cc\u0631\u0645\u0646\u0641\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0633\u067e\u0633 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0686\u0647 \u062a\u0641\u0627\u0648\u062a\u200c\u0647\u0627\u06cc\u06cc \u0628\u06cc\u0646 \u06af\u0631\u0627\u0641 \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0648 \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0648 \u0686\u06af\u0648\u0646\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u0622\u0646\u200c\u0647\u0627 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u061f<\/h3>\n\n\n\n<p>\u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u062f\u0627\u0631\u0627\u06cc \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627 \u0648\u0632\u0646 \u0645\u0634\u062e\u0635 \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0647\u0632\u06cc\u0646\u0647 \u06cc\u0627 \u0641\u0627\u0635\u0644\u0647 \u0628\u0627\u0634\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u062a\u0646\u0647\u0627 \u0648\u062c\u0648\u062f \u06cc\u0627 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062f\u0627\u06cc\u062c\u0633\u062a\u0631\u0627 \u0648 \u0628\u0644\u0645\u0646-\u0641\u0648\u0631\u062f \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0648\u0632\u0646\u200c\u062f\u0627\u0631 \u0645\u0646\u0627\u0633\u0628 \u0647\u0633\u062a\u0646\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u0637\u062d \u0627\u0648\u0644 (BFS) \u0628\u0631\u0627\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646 \u0628\u0647 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0627\u0632 \u0627\u0645\u0631\u0648\u0632 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f!<\/h2>\n\n\n\n<p>\u062f\u0646\u06cc\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u062c\u0630\u0627\u0628 \u0627\u0633\u062a \u0648 \u062f\u0627\u0646\u0633\u062a\u0646 \u0639\u0644\u0645 \u062f\u0627\u062f\u0647\u060c \u062a\u0648\u0627\u0646\u0627\u06cc\u06cc \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647\u200c\u060c \u06cc\u0627 \u0628\u0627\u0632\u0627\u0631\u06cc\u0627\u0628\u06cc \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u062f\u0627\u062f\u0647\u060c \u0634\u0645\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0641\u0631\u0635\u062a\u200c\u0647\u0627\u06cc \u0634\u063a\u0644\u06cc \u0628\u0633\u06cc\u0627\u0631\u06cc \u0645\u0646\u0627\u0633\u0628 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0641\u0627\u0631\u063a \u0627\u0632 \u0631\u0634\u062a\u0647\u200c \u0648 \u067e\u06cc\u0634\u200c\u0632\u0645\u06cc\u0646\u0647\u200c\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u062d\u0627\u0644\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f \u0648 \u0627\u0632 \u0633\u0637\u062d \u0645\u0642\u062f\u0645\u0627\u062a\u06cc \u062a\u0627 \u067e\u06cc\u0634\u0631\u0641\u062a\u0647 \u0628\u06cc\u0627\u0645\u0648\u0632\u06cc\u062f. \u0627\u06af\u0631 \u062f\u0648\u0633\u062a \u062f\u0627\u0631\u06cc\u062f \u0628\u0647 \u0627\u06cc\u0646 \u062d\u0648\u0632\u0647 \u0648\u0627\u0631\u062f \u0634\u0648\u06cc\u062f\u060c \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0628\u0627 \u06a9\u0644\u06cc\u06a9 \u0631\u0648\u06cc \u0627\u06cc\u0646 \u0644\u06cc\u0646\u06a9 \u0642\u062f\u0645 \u0627\u0648\u0644 \u0631\u0627 \u0647\u0645\u06cc\u0646 \u062d\u0627\u0644\u0627 \u0628\u0631\u062f\u0627\u0631\u06cc\u062f.<\/p>\n\n\n\n<p>\u0645\u0634\u0627\u0648\u0631\u0627\u0646 \u06a9\u0627\u0641\u0647\u200c\u062a\u062f\u0631\u06cc\u0633 \u0628\u0647 \u0634\u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0645\u0633\u06cc\u0631 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0628\u0631\u0627\u06cc \u0648\u0631\u0648\u062f \u0628\u0647 \u0627\u06cc\u0646 \u062d\u0648\u0632\u0647 \u0631\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f:<\/p>\n\n\n<p><a class=\"call-to-btn\" href=\"https:\/\/cafetadris.com\/datascience\" target=\"_blank\" rel=\"noopener noreferrer\" data-wplink-edit=\"true\">\u062f\u0648\u0631\u0647 \u062c\u0627\u0645\u0639 \u062f\u06cc\u062a\u0627 \u0633\u0627\u06cc\u0646\u0633 \u0648 \u0645\u0627\u0634\u06cc\u0646 \u0644\u0631\u0646\u06cc\u0646\u06af<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u0645\u0633\u0626\u0644\u0647 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u06cc\u06a9 \u06af\u0631\u0627\u0641 (Shortest path problem)\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0627\u0633\u0627\u0633\u06cc \u0648 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u0639\u0644\u0648\u0645 \u0631\u0627\u06cc\u0627\u0646\u0647 \u0648 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u062f\u0631 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627 \u0627\u0632 \u062c\u0645\u0644\u0647 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u062d\u0645\u0644\u200c\u0648\u0646\u0642\u0644\u060c \u0637\u0631\u0627\u062d\u06cc \u0645\u062f\u0627\u0631\u0647\u0627\u06cc \u0627\u0644\u06a9\u062a\u0631\u06cc\u06a9\u06cc \u0648 \u062d\u062a\u06cc \u062f\u0631 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc \u0648\u06cc\u062f\u0626\u0648\u06cc\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646&#8230;<\/p>\n","protected":false},"author":11,"featured_media":19427,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[558],"tags":[1257,1256,1253,1254,1252,1255,1251],"yst_prominent_words":[],"class_list":["post-19414","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-558","tag-bfs","tag-dag","tag-1253","tag-1254","tag-1252","tag-1255","tag-1251"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/posts\/19414","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/comments?post=19414"}],"version-history":[{"count":81,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/posts\/19414\/revisions"}],"predecessor-version":[{"id":19765,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/posts\/19414\/revisions\/19765"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/media\/19427"}],"wp:attachment":[{"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/media?parent=19414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/categories?post=19414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/tags?post=19414"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/cafetadris.com\/blog\/wp-json\/wp\/v2\/yst_prominent_words?post=19414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}