{"id":14887,"date":"2024-01-06T16:25:14","date_gmt":"2024-01-06T12:55:14","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/"},"modified":"2024-01-06T16:25:14","modified_gmt":"2024-01-06T12:55:14","slug":"%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/","title":{"rendered":"\u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 &#8211; \u062a\u0626\u0648\u0631\u06cc \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/#%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d9%88%d8%b3%d8%b9%d8%aa-%d8%a7%d9%88%d9%84_%e2%80%93_%d9%86%d8%b8%d8%b1%db%8c%d9%87\" >\u062c\u0633\u062a\u062c\u0648\u06cc \u0648\u0633\u0639\u062a-\u0627\u0648\u0644 &#8211; \u0646\u0638\u0631\u06cc\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/#%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%b9%d8%b1%d8%b6-%d8%a7%d9%88%d9%84_%e2%80%93_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85\" >\u062c\u0633\u062a\u062c\u0648\u06cc \u0639\u0631\u0636-\u0627\u0648\u0644 &#8211; \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/#%d8%a7%d8%ac%d8%b1%d8%a7%db%8c_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_breadth-first_%e2%80%93_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%da%af%d8%b1%d9%87_%d9%87%d8%af%d9%81\" >\u0627\u062c\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc Breadth-First &#8211; \u062c\u0633\u062a\u062c\u0648\u06cc \u06af\u0631\u0647 \u0647\u062f\u0641<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/#%d8%b9%d8%b1%d8%b6-%d8%a7%d9%88%d9%84_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%e2%80%93_%d9%be%db%8c%d9%85%d8%a7%db%8c%d8%b4_%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1\" >\u0639\u0631\u0636-\u0627\u0648\u0644 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc &#8211; \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0646\u0645\u0648\u062f\u0627\u0631<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 7<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u062f\u0631\u0633 \u0628\u0647 \u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645 <em>\u062c\u0633\u062a\u062c\u0648 \u0648 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0639\u0631\u0636 \u0627\u0648\u0644<\/em>.  \u0627\u0648\u0644\u060c \u0645\u0627 \u062a\u0645\u0631\u06a9\u0632 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc <strong>node  \u062c\u0633\u062a\u062c\u0648 \u06a9\u0631\u062f\u0646<\/strong>\u060c \u0642\u0628\u0644 \u0627\u0632 \u067e\u0631\u062f\u0627\u062e\u062a\u0646 \u0628\u0647 <strong>\u067e\u06cc\u0645\u0627\u06cc\u0634 \u0646\u0645\u0648\u062f\u0627\u0631<\/strong> \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062f\u0648 \u0648\u0638\u06cc\u0641\u0647 \u0627\u0635\u0644\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0628\u0647 \u06a9\u0627\u0631 \u0628\u0628\u0631\u06cc\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0645\u0627 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062c\u0627\u0648\u0631\u062a-\u0644\u06cc\u0633\u062a \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0634\u062f\u0647 \u062f\u0631 \u062f\u0631\u0633 \u0631\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<\/p><\/div><\/div>\n<h3 id=\"breadthfirstsearchtheory\"><span class=\"ez-toc-section\" id=\"%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d9%88%d8%b3%d8%b9%d8%aa-%d8%a7%d9%88%d9%84_%e2%80%93_%d9%86%d8%b8%d8%b1%db%8c%d9%87\"><\/span>\u062c\u0633\u062a\u062c\u0648\u06cc \u0648\u0633\u0639\u062a-\u0627\u0648\u0644 &#8211; \u0646\u0638\u0631\u06cc\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0627\u0648\u0644 \u0639\u0631\u0636 (BFS)<\/strong> \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0633\u06cc\u0633\u062a\u0645\u0627\u062a\u06cc\u06a9 \u0637\u06cc \u0645\u06cc \u06a9\u0646\u062f\u060c <em>\u0633\u0637\u062d \u0628\u0647 \u0633\u0637\u062d<\/em>\u060c \u062a\u0634\u06a9\u06cc\u0644 \u06cc\u06a9 \u062f\u0631\u062e\u062a BFS \u062f\u0631 \u0637\u0648\u0644 \u0645\u0633\u06cc\u0631.<\/p>\n<p>\u0627\u06af\u0631 \u062c\u0633\u062a\u062c\u0648\u06cc \u062e\u0648\u062f \u0631\u0627 \u0627\u0632 node <code>v<\/code>  ( root node  \u0627\u0632 \u0646\u0645\u0648\u062f\u0627\u0631 \u06cc\u0627 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u062f\u0631\u062e\u062a\u06cc \u0645\u0627)\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0627\u0628\u062a\u062f\u0627 \u0627\u0632 \u0647\u0645\u0647 \u0645\u0648\u0627\u0631\u062f \u0628\u0627\u0632\u062f\u06cc\u062f \u0645\u06cc \u06a9\u0646\u062f <strong>\u0647\u0645\u0633\u0627\u06cc\u0647 \u0647\u0627<\/strong> \u0627\u0632 node <code>v<\/code>  (\u0627\u06cc\u0646 \u06af\u0631\u0647 \u0647\u0627\u06cc \u06a9\u0648\u062f\u06a9 \u0647\u0633\u062a\u0646\u062f\u060c \u0631\u0648\u06cc <strong>\u0645\u0631\u062d\u0644\u0647 \u0627\u0648\u0644<\/strong>) <em>\u0628\u0647 \u062a\u0631\u062a\u06cc\u0628\u06cc \u06a9\u0647 \u062f\u0631 \u0644\u06cc\u0633\u062a \u0645\u062c\u0627\u0648\u0631\u062a \u0622\u0645\u062f\u0647 \u0627\u0633\u062a<\/em>.  \u0628\u0639\u062f\u060c \u06af\u0631\u0647 \u0647\u0627\u06cc \u0641\u0631\u0632\u0646\u062f \u0622\u0646 \u0647\u0645\u0633\u0627\u06cc\u06af\u0627\u0646 \u0631\u0627 \u0645\u06cc \u06af\u06cc\u0631\u062f (<strong>\u0633\u0637\u062d \u062f\u0648<\/strong>) \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u0648\u062f \u0648 \u063a\u06cc\u0631\u0647 \u0631\u0648\u06cc.<\/p>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u06af\u0631\u0627\u0641 \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0633\u062a <strong>\u067e\u06cc\u0645\u0627\u06cc\u0634<\/strong> \u0648 <strong>\u062c\u0633\u062a\u062c\u0648 \u06a9\u0631\u062f\u0646<\/strong>.  \u0647\u0646\u06af\u0627\u0645 \u062c\u0633\u062a\u062c\u0648 \u0628\u0631\u0627\u06cc a node \u06a9\u0647 \u0634\u0631\u0627\u06cc\u0637 \u062e\u0627\u0635\u06cc \u0631\u0627 \u0628\u0631\u0622\u0648\u0631\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f (\u0647\u062f\u0641 node)\u060c \u0645\u0633\u06cc\u0631 \u0628\u0627 <strong>\u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647<\/strong> \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 node \u0628\u0647 \u0647\u062f\u0641 node.  \u0641\u0627\u0635\u0644\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0639\u062f\u0627\u062f \u0634\u0627\u062e\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0645\u0648\u062f\u0647 \u0634\u062f\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/bfs-gif.gif\" alt=\"\u0627\u0646\u06cc\u0645\u06cc\u0634\u0646 BFS\" title=\"\"><\/p>\n<p><em>\u062c\u0633\u062a\u062c\u0648\u06cc \u0639\u0631\u0636-\u0627\u0648\u0644<\/em> \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0627\u0632 \u062c\u0645\u0644\u0647 \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u062f\u0648 \u06af\u0631\u0647\u060c \u062a\u0639\u06cc\u06cc\u0646 \u0633\u0637\u0648\u062d \u0647\u0631 \u06cc\u06a9 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. node\u0648 \u062d\u062a\u06cc \u062d\u0644 \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u067e\u0627\u0632\u0644 \u0648 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0647\u0627.<\/p>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0627\u06cc \u062d\u0644 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0647\u0627 \u0648 \u0645\u0639\u0645\u0627\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0646\u06cc\u0633\u062a &#8211; \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc\u06cc \u0645\u0627\u0646\u0646\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Dijkstra \u0648 A* \u0627\u0632 \u0622\u0646 \u0628\u0631\u062a\u0631\u06cc \u062f\u0627\u0631\u062f &#8211; \u0647\u0645\u0686\u0646\u0627\u0646 \u0646\u0642\u0634 \u0645\u0647\u0645\u06cc \u062f\u0631 \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647 \u0628\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0628\u0633\u062a\u0647 \u0628\u0647 \u0622\u0646 \u0631\u0648\u06cc \u0645\u0634\u06a9\u0644 \u062f\u0631 \u062f\u0633\u062a &#8211; DFS \u0648 BFS \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0627\u0632 \u067e\u0633\u0631\u0639\u0645\u0648\u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u062e\u0648\u062f \u0628\u0647\u062a\u0631 \u0639\u0645\u0644 \u06a9\u0646\u0646\u062f.<\/p>\n<h3 id=\"breadthfirstsearchalgorithm\"><span class=\"ez-toc-section\" id=\"%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%b9%d8%b1%d8%b6-%d8%a7%d9%88%d9%84_%e2%80%93_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85\"><\/span>\u062c\u0633\u062a\u062c\u0648\u06cc \u0639\u0631\u0636-\u0627\u0648\u0644 &#8211; \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0647\u0646\u06af\u0627\u0645 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc BFS\u060c \u0645\u0627 \u0645\u0639\u0645\u0648\u0644\u0627 \u0627\u0632 a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <strong>FIFO<\/strong> \u0633\u0627\u062e\u062a\u0627\u0631\u06cc \u0645\u0627\u0646\u0646\u062f a <code>Queue<\/code> \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u06af\u0631\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f \u062e\u0648\u0627\u0647\u0646\u062f \u0634\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 a <code>Queue<\/code> \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u0645\u0627 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 import \u0645\u0631\u0628\u0648\u0637\u0647 <code>Queue<\/code> \u06a9\u0644\u0627\u0633 \u0627\u0632 <code>queue<\/code> \u0645\u062f\u0648\u0644.<\/p>\n<\/p><\/div><\/div>\n<p>\u0645\u0627 \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u06a9\u0647 \u062f\u0631\u06af\u06cc\u0631 \u0646\u0634\u0648\u06cc\u0645 <em>\u062d\u0644\u0642\u0647 \u0647\u0627\u06cc \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a<\/em> \u0628\u0627 \u0628\u0627\u0632\u0628\u06cc\u0646\u06cc \u0645\u062c\u062f\u062f \u0648 \u0645\u06a9\u0631\u0631 \u0647\u0645\u0627\u0646 \u06af\u0631\u0647\u200c\u0647\u0627\u060c \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0628\u0627 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc \u0627\u062a\u0641\u0627\u0642 \u0628\u06cc\u0641\u062a\u062f <strong>\u0686\u0631\u062e\u0647 \u0647\u0627<\/strong>.  \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639\u060c \u06af\u0631\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0648\u062f\u0647 \u0627\u0646\u062f \u0631\u0627 \u067e\u06cc\u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <strong>\u0645\u0644\u0627\u0642\u0627\u062a \u06a9\u0631\u062f<\/strong>.  \u0627\u06cc\u0646 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0644\u0627\u0632\u0645 \u0646\u06cc\u0633\u062a \u0628\u0647 \u0637\u0648\u0631 \u0635\u0631\u06cc\u062d \u0630\u062e\u06cc\u0631\u0647 \u0634\u0648\u0646\u062f\u060c \u0645\u0627 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u067e\u06cc\u06af\u06cc\u0631\u06cc \u06a9\u0646\u06cc\u0645 <strong>\u0648\u0627\u0644\u062f\u06cc\u0646<\/strong> \u06af\u0631\u0647 \u0647\u0627\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0647 \u0637\u0648\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0633 \u0627\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632 \u06cc\u06a9\u06cc \u0628\u0647 \u0622\u0646 \u0628\u0627\u0632 \u0646\u0645\u06cc \u06af\u0631\u062f\u06cc\u0645.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u062c\u0645\u0639 \u0628\u0646\u062f\u06cc \u0645\u0646\u0637\u0642\u060c \u0645\u0631\u0627\u062d\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<ol>\n<li>\u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 root\/\u0634\u0631\u0648\u0639 node \u0628\u0647 <code>Queue<\/code>.<\/li>\n<li>\u0628\u0631\u0627\u06cc \u0647\u0631 node\u060c \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u0646\u0647\u0627 \u06cc\u06a9 \u0648\u0627\u0644\u062f \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f node.<\/li>\n<li>\u062a\u0627 <code>Queue<\/code> \u062e\u0627\u0644\u06cc \u0627\u0633\u062a:\n<ul>\n<li>\u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u06a9\u0646\u06cc\u062f node \u0627\u0632 \u0627\u0628\u062a\u062f\u0627\u06cc <code>Queue<\/code>.<\/li>\n<li>\u067e\u0631\u062f\u0627\u0632\u0634 \u062e\u0631\u0648\u062c\u06cc \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f.<\/li>\n<li>\u0628\u0631\u0627\u06cc \u0647\u0631 \u0647\u0645\u0633\u0627\u06cc\u0647 \u062c\u0631\u06cc\u0627\u0646 node \u06a9\u0647 <strong>\u0646\u0645\u06cc \u06a9\u0646\u062f<\/strong> \u06cc\u06a9 \u0648\u0627\u0644\u062f \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f (\u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647 \u0627\u0633\u062a)\u060c \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0622\u0646 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f <code>Queue<\/code>\u0648 \u062c\u0631\u06cc\u0627\u0646 \u0631\u0627 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u06cc\u062f node \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0627\u0644\u062f\u06cc\u0646 \u0622\u0646\u0647\u0627<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<p><strong>\u067e\u0631\u062f\u0627\u0632\u0634 \u062e\u0631\u0648\u062c\u06cc<\/strong> \u0628\u0633\u062a\u0647 \u0628\u0647 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f \u0631\u0648\u06cc \u0647\u062f\u0641 \u067e\u0634\u062a \u062c\u0633\u062a\u062c\u0648\u06cc \u0646\u0645\u0648\u062f\u0627\u0631  \u0647\u0646\u06af\u0627\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0647\u062f\u0641 node\u060c \u067e\u0631\u062f\u0627\u0632\u0634 \u062e\u0631\u0648\u062c\u06cc \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u062f\u0631 \u062d\u0627\u0644 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0627\u0633\u062a node \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0647\u062f\u0641 \u0627\u0633\u062a node.  \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u062e\u0644\u0627\u0642 \u0634\u0648\u06cc\u062f!<\/p>\n<\/p><\/div><\/div>\n<h3 id=\"breadthfirstsearchimplementationtargetnodesearch\"><span class=\"ez-toc-section\" id=\"%d8%a7%d8%ac%d8%b1%d8%a7%db%8c_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_breadth-first_%e2%80%93_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%da%af%d8%b1%d9%87_%d9%87%d8%af%d9%81\"><\/span>\u0627\u062c\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc Breadth-First &#8211; \u062c\u0633\u062a\u062c\u0648\u06cc \u06af\u0631\u0647 \u0647\u062f\u0641<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645 <em>\u062c\u0633\u062a\u062c\u0648 \u06a9\u0631\u062f\u0646<\/em> &#8211; \u0648 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0647\u062f\u0641 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u062f node.  \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0647\u062f\u0641 node\u060c \u0645\u0627 \u0628\u0647 \u06cc\u06a9 \u0634\u0631\u0648\u0639 \u0646\u06cc\u0627\u0632 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a node \u0647\u0645\u0686\u0646\u06cc\u0646.  \u062e\u0631\u0648\u062c\u06cc \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 a \u0627\u0633\u062a <strong>\u0645\u0633\u06cc\u0631<\/strong> \u06a9\u0647 \u0627\u0632 \u0647\u0645\u0627\u0646 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627 \u0631\u0627 \u0647\u062f\u0627\u06cc\u062a \u0645\u06cc \u06a9\u0646\u062f node \u0628\u0647 \u0647\u062f\u0641 node.<\/p>\n<p>\u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0622\u0646\u0647\u0627 \u0648 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0645\u0631\u0627\u062d\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645.  \u0645\u0627 a \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>Graph<\/code> \u06a9\u0644\u0627\u0633 \u0628\u0631\u0627\u06cc &#8220;\u067e\u0648\u0634\u0634&#8221; \u0627\u062c\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc BFS.<\/p>\n<p><code>Graph<\/code>  \u0634\u0627\u0645\u0644 \u06cc\u06a9 \u0646\u0645\u0627\u06cc\u0634 \u06af\u0631\u0627\u0641 &#8211; \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062c\u0627\u0648\u0631\u062a\u060c \u0648 \u0647\u0645\u0647 \u0631\u0648\u0634 \u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0647\u0646\u06af\u0627\u0645 \u06a9\u0627\u0631 \u0628\u0627 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0628\u0647 \u0622\u0646 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f.  \u0647\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc BFS \u0648 \u0647\u0645 \u067e\u06cc\u0645\u0627\u06cc\u0634 BFS \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062a\u062f\u0647\u0627\u06cc \u0622\u0646 \u06a9\u0644\u0627\u0633 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">from<\/span> queue <span class=\"hljs-keyword\">import<\/span> Queue\n\n<span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">Graph<\/span>:<\/span>\n    \n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__init__<\/span>(<span class=\"hljs-params\">self, num_of_nodes, directed=<span class=\"hljs-literal\">True<\/span><\/span>):<\/span>\n        self.m_num_of_nodes = num_of_nodes\n        self.m_nodes = <span class=\"hljs-built_in\">range<\/span>(self.m_num_of_nodes)\n\t\t\n        \n        self.m_directed = directed\n\t\t\n        \n        \n        self.m_adj_list = {node: <span class=\"hljs-built_in\">set<\/span>() <span class=\"hljs-keyword\">for<\/span> node <span class=\"hljs-keyword\">in<\/span> self.m_nodes}      \n\t\n    \n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">add_edge<\/span>(<span class=\"hljs-params\">self, node1, node2, weight=<span class=\"hljs-number\">1<\/span><\/span>):<\/span>\n        self.m_adj_list(node1).add((node2, weight))\n\n        <span class=\"hljs-keyword\">if<\/span> <span class=\"hljs-keyword\">not<\/span> self.m_directed:\n            self.m_adj_list(node2).add((node1, weight))\n    \n    \n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">print_adj_list<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n      <span class=\"hljs-keyword\">for<\/span> key <span class=\"hljs-keyword\">in<\/span> self.m_adj_list.keys():\n        <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"node\"<\/span>, key, <span class=\"hljs-string\">\": \"<\/span>, self.m_adj_list(key))\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u0641 <em>\u0644\u0641\u0627\u0641<\/em> \u06a9\u0644\u0627\u0633\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc BFS \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u0622\u0646 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">bfs<\/span>(<span class=\"hljs-params\">self, start_node, target_node<\/span>):<\/span>\n    \n    visited = <span class=\"hljs-built_in\">set<\/span>()\n    queue = Queue()\n\n    \n    queue.put(start_node)\n    visited.add(start_node)\n    \n    \n    parent = <span class=\"hljs-built_in\">dict<\/span>()\n    parent(start_node) = <span class=\"hljs-literal\">None<\/span>\n\n    \n    path_found = <span class=\"hljs-literal\">False<\/span>\n    <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-keyword\">not<\/span> queue.empty():\n        current_node = queue.get()\n        <span class=\"hljs-keyword\">if<\/span> current_node == target_node:\n            path_found = <span class=\"hljs-literal\">True<\/span>\n            <span class=\"hljs-keyword\">break<\/span>\n\n        <span class=\"hljs-keyword\">for<\/span> (next_node, weight) <span class=\"hljs-keyword\">in<\/span> self.m_adj_list(current_node):\n            <span class=\"hljs-keyword\">if<\/span> next_node <span class=\"hljs-keyword\">not<\/span> <span class=\"hljs-keyword\">in<\/span> visited:\n                queue.put(next_node)\n                parent(next_node) = current_node\n                visited.add(next_node)\n                \n    \n    path = ()\n    <span class=\"hljs-keyword\">if<\/span> path_found:\n        path.append(target_node)\n        <span class=\"hljs-keyword\">while<\/span> parent(target_node) <span class=\"hljs-keyword\">is<\/span> <span class=\"hljs-keyword\">not<\/span> <span class=\"hljs-literal\">None<\/span>:\n            path.append(parent(target_node)) \n            target_node = parent(target_node)\n        path.reverse()\n    <span class=\"hljs-keyword\">return<\/span> path \n<\/code><\/pre>\n<p>\u0648\u0642\u062a\u06cc \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0628\u0627\u0632\u0633\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 (\u0627\u06af\u0631 \u067e\u06cc\u062f\u0627 \u0634\u062f)\u060c \u0627\u0632 \u0647\u062f\u0641 \u0628\u0647 \u0639\u0642\u0628 \u0628\u0631 \u0645\u06cc \u06af\u0631\u062f\u06cc\u0645 node\u060c \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u062f\u0631 \u0648 \u0645\u0627\u062f\u0631 \u062e\u0648\u062f\u060c \u0631\u062f\u06cc\u0627\u0628\u06cc \u0645\u062c\u062f\u062f \u062a\u0645\u0627\u0645 \u0631\u0627\u0647 \u0628\u0647 \u0634\u0631\u0648\u0639 node.  \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u0645\u0627 <strong>\u0645\u0639\u06a9\u0648\u0633<\/strong> \u0645\u0633\u06cc\u0631\u06cc \u0628\u0631\u0627\u06cc \u0634\u0647\u0648\u062f \u062e\u0648\u062f\u0645\u0627\u0646 \u0628\u0631\u0627\u06cc \u0631\u0641\u062a\u0646 \u0627\u0632 <code>start_node<\/code> \u0628\u0647 \u0633\u0645\u062a <code>target_node<\/code>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0627\u062e\u062a\u06cc\u0627\u0631\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u0627\u0632 \u0637\u0631\u0641 \u062f\u06cc\u06af\u0631\u060c \u0627\u06af\u0631 \u0645\u0633\u06cc\u0631\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u062e\u0627\u0644\u06cc \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f.<\/p>\n<p>\u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0642\u0628\u0644\u06cc\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0627\u062c\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc BFS \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062b\u0627\u0644:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/graphs-in-python-breadth-first-search-bfs-algorithm-1.png\" alt=\"\u0646\u0645\u0648\u062f\u0627\u0631 \u062c\u0633\u062a\u062c\u0648\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u06cc\u0646 \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0627 \u0628\u0627\u0632\u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645 <code>Graph<\/code> \u06a9\u0644\u0627\u0633  \u0627\u06cc\u0646 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u0628\u062f\u0648\u0646 \u062c\u0647\u062a \u0628\u0627 6 \u06af\u0631\u0647 \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0627 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0646\u0645\u0648\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">graph = Graph(<span class=\"hljs-number\">6<\/span>, directed=<span class=\"hljs-literal\">False<\/span>)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u0628\u0627\u06cc\u062f \u062a\u0645\u0627\u0645 \u0644\u0628\u0647 \u0647\u0627\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0646\u0645\u0648\u0646\u0647 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645 <code>Graph<\/code> \u06a9\u0644\u0627\u0633\u06cc \u06a9\u0647 \u0645\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">graph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">2<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">4<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">5<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span>)\n<\/code><\/pre>\n<p>\u062d\u0627\u0644\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u06af\u0648\u0646\u0647 <code>Graph<\/code> \u06a9\u0644\u0627\u0633 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0627\u062e\u0644\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0646\u0645\u0648\u0646\u0647 \u0645\u0627 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<pre><code class=\"hljs\">graph.print_adj_list()\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0627\u0631\u0627\u062f\u0647 print \u0644\u06cc\u0633\u062a \u0645\u062c\u0627\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u0646\u0645\u0648\u062f\u0627\u0631\u06cc \u06a9\u0647 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">node 0 :  {(3, 1), (1, 1), (4, 1), (2, 1)}\nnode 1 :  {(0, 1), (2, 1)}\nnode 2 :  {(0, 1), (1, 1), (5, 1), (3, 1)}\nnode 3 :  {(0, 1), (5, 1), (4, 1), (2, 1)}\nnode 4 :  {(0, 1), (5, 1), (3, 1)}\nnode 5 :  {(3, 1), (4, 1), (2, 1)}\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0644\u062d\u0638\u0647\u060c \u0645\u0627 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u0645 \u0648 \u062f\u0631\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062c\u0627\u0648\u0631\u062a \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.  \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u062a\u0645\u0627\u0645 \u0627\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062e\u0648\u062f \u062c\u0633\u062a\u062c\u0648 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.  \u0628\u06af\u0648\u06cc\u06cc\u062f \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645 <em>node<\/em> <code>5<\/code>  \u0634\u0631\u0648\u0639 \u0627\u0632 <em>node<\/em> <code>0<\/code>:<\/p>\n<pre><code class=\"hljs\">path = ()\npath = graph.bfs(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">5<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(path)\n<\/code><\/pre>\n<p>\u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u062f \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\">(0, 3, 5)\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0646\u06af\u0627\u0647\u06cc \u06af\u0630\u0631\u0627 \u0628\u0647 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062b\u0627\u0644\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 <code>0<\/code> \u0648 <code>5<\/code> \u0627\u0633\u062a <em>\u062f\u0631 \u0648\u0627\u0642\u0639<\/em> <code>(0, 3, 5)<\/code>.  \u0627\u06af\u0631\u0686\u0647\u060c \u0634\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u067e\u06cc\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u062f <code>(0, 2, 5)<\/code> \u0648 <code>(0, 4, 5)<\/code>.  \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631\u0647\u0627\u06cc \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0627\u0633\u0627\u0633\u0627\u064b \u0647\u0645\u0627\u0646 \u0641\u0627\u0635\u0644\u0647 \u0647\u0633\u062a\u0646\u062f <code>(0, 3, 5)<\/code> &#8211; \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0631\u0648\u0634 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06af\u0631\u0647 \u0647\u0627 \u062a\u0648\u0633\u0637 BFS \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f.  \u0627\u0632 \u0622\u0646 &#8220;\u0627\u0633\u06a9\u0646&#8221; \u0645\u06cc \u06a9\u0646\u062f <em>\u0686\u067e \u0628\u0647 \u0631\u0627\u0633\u062a<\/em> \u0648 <code>3<\/code> \u0627\u0648\u0644\u06cc\u0646 \u0627\u0633\u062a node \u0631\u0648\u06cc  \u0633\u0645\u062a \u0686\u067e \u0644\u06cc\u0633\u062a \u0645\u062c\u0627\u0648\u0631\u062a \u06a9\u0647 \u0628\u0647 <code>5<\/code>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u062c\u0627\u06cc \u0628\u0642\u06cc\u0647 \u0637\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc BFS \u0627\u0633\u062a \u06a9\u0647 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u06a9\u0646\u06cc\u062f.  \u0627\u0632 \u0686\u067e \u0628\u0647 \u0631\u0627\u0633\u062a \u062c\u0633\u062a\u062c\u0648 \u0645\u06cc \u06a9\u0646\u062f &#8211; \u0648 <em>\u0646\u0645\u06cc \u062e\u0648\u0627\u0647\u062f<\/em> \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u0647\u0645\u0627\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0639\u062a\u0628\u0631 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f \u0627\u06af\u0631 &#8220;\u0628\u0639\u062f \u0627\u0632&#8221; \u0645\u0633\u06cc\u0631 \u0627\u0648\u0644 \u067e\u06cc\u062f\u0627 \u0634\u0648\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0645\u0648\u0627\u0631\u062f\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u0633\u06cc\u0631\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u06af\u0631\u0647 \u067e\u06cc\u062f\u0627 \u0646\u0645\u06cc \u0634\u0648\u062f.  \u0627\u06cc\u0646 \u0633\u0646\u0627\u0631\u06cc\u0648 \u0628\u0631\u0627\u06cc <strong>\u0642\u0637\u0639 \u0634\u062f\u0647<\/strong> \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u062d\u062f\u0627\u0642\u0644 \u062f\u0648 \u06af\u0631\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062a\u0648\u0633\u0637 \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u0647\u0645 \u0645\u062a\u0635\u0644 \u0646\u06cc\u0633\u062a\u0646\u062f.<\/p>\n<\/p><\/div><\/div>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0642\u0637\u0639 \u0634\u062f\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/graphs-in-python-breadth-first-search-bfs-algorithm-2.png\" alt=\"\u0646\u0645\u0648\u062f\u0627\u0631 \u0642\u0637\u0639 \u0634\u062f\u0647\" title=\"\"><\/p>\n<p>\u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u06af\u0631\u0647 \u0647\u0627 \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645 <code>0<\/code> \u0648 <code>3<\/code> \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0645\u0648\u062f\u0627\u0631\u060c \u0622\u0646 \u062c\u0633\u062a\u062c\u0648 \u0646\u0627\u0645\u0648\u0641\u0642 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u0648 \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u062e\u0627\u0644\u06cc \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h3 id=\"breadthfirstimplementationgraphtraversal\"><span class=\"ez-toc-section\" id=\"%d8%b9%d8%b1%d8%b6-%d8%a7%d9%88%d9%84_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%e2%80%93_%d9%be%db%8c%d9%85%d8%a7%db%8c%d8%b4_%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1\"><\/span>\u0639\u0631\u0636-\u0627\u0648\u0644 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc &#8211; \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0646\u0645\u0648\u062f\u0627\u0631<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u0639\u0631\u0636-\u0627\u0648\u0644\u06cc\u0646 \u067e\u06cc\u0645\u0627\u06cc\u0634<\/strong> \u06cc\u06a9 \u0645\u0648\u0631\u062f \u062e\u0627\u0635 \u0627\u0632 Breadth-First Search \u0627\u0633\u062a \u06a9\u0647 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0637\u06cc \u0645\u06cc \u06a9\u0646\u062f <strong>\u06a9\u0644<\/strong> \u0646\u0645\u0648\u062f\u0627\u0631\u060c \u0628\u0647 \u062c\u0627\u06cc \u062c\u0633\u062a\u062c\u0648 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0647\u062f\u0641 node.  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0631\u062f\u0647 \u0628\u0648\u062f\u06cc\u0645 \u0628\u0627\u0642\u06cc \u0645\u06cc \u0645\u0627\u0646\u062f\u060c \u062a\u0641\u0627\u0648\u062a \u062f\u0631 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0647\u062f\u0641 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0646\u0645\u06cc \u06a9\u0646\u06cc\u0645. node \u0648 \u0645\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u06cc\u0627\u0641\u062a\u0646 \u0645\u0633\u06cc\u0631\u06cc \u0646\u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0622\u0646 \u0645\u0646\u062a\u0647\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0633\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f &#8211; \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0641\u0642\u0637 print \u0627\u0632 \u0647\u0631 \u06a9\u062f\u0627\u0645 node \u0628\u0631\u0627\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0634\u0647\u0648\u062f\u06cc \u0627\u0632 \u0631\u0648\u0634 \u0639\u0628\u0648\u0631 \u0622\u0646 \u0627\u0632 \u06af\u0631\u0647 \u0647\u0627 \u0639\u0628\u0648\u0631 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">bfs_traversal<\/span>(<span class=\"hljs-params\">self, start_node<\/span>):<\/span>\n    visited = <span class=\"hljs-built_in\">set<\/span>()\n    queue = Queue()\n    queue.put(start_node)\n    visited.add(start_node)\n\n    <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-keyword\">not<\/span> queue.empty():\n        current_node = queue.get()\n        <span class=\"hljs-built_in\">print<\/span>(current_node, end = <span class=\"hljs-string\">\" \"<\/span>)\n        <span class=\"hljs-keyword\">for<\/span> (next_node, weight) <span class=\"hljs-keyword\">in<\/span> self.m_adj_list(current_node):\n            <span class=\"hljs-keyword\">if<\/span> next_node <span class=\"hljs-keyword\">not<\/span> <span class=\"hljs-keyword\">in<\/span> visited:\n                queue.put(next_node)\n                visited.add(next_node)  \n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u062e\u0634\u06cc \u0627\u0632 <code>Graph<\/code> \u06a9\u0644\u0627\u0633 \u0627\u062c\u0631\u0627 \u0634\u062f\u0647 \u0642\u0628\u0644\u0627<\/p>\n<\/p><\/div><\/div>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062b\u0627\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u0634\u06a9\u0644\u06cc \u06a9\u0647 \u0642\u0628\u0644\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/graphs-in-python-breadth-first-search-bfs-algorithm-3.png\" alt=\"\u0646\u0645\u0648\u062f\u0627\u0631 \u0639\u0628\u0648\u0631\u06cc\" title=\"\"><\/p>\n<pre><code class=\"hljs\">\n\ngraph = Graph(<span class=\"hljs-number\">5<\/span>, directed=<span class=\"hljs-literal\">False<\/span>)\n\n\ngraph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">2<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>)\ngraph.add_edge(<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u06a9\u062f \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">graph.bfs_traversal(<span class=\"hljs-number\">0<\/span>)\n<\/code><\/pre>\n<p>\u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u062f \u0627\u0646\u062c\u0627\u0645 \u062e\u0648\u0627\u0647\u062f \u0634\u062f print \u06af\u0631\u0647 \u0647\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628\u06cc \u06a9\u0647 BFS \u0622\u0646\u0647\u0627 \u0631\u0627 \u0627\u0633\u06a9\u0646 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">0 1 2 4 3\n<\/code><\/pre>\n<h4 id=\"stepbystep\">\u06af\u0627\u0645 \u0628\u0647 \u06af\u0627\u0645<\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u06a9\u0645\u06cc \u0639\u0645\u06cc\u0642 \u062a\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0628\u067e\u0631\u062f\u0627\u0632\u06cc\u0645 \u0648 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06af\u0627\u0645 \u0628\u0647 \u06af\u0627\u0645 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f.  \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0631\u0627 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 node <code>0<\/code>\u060c \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0647 \u0627\u0633\u062a <code>visited<\/code> \u062a\u0646\u0638\u06cc\u0645 \u0648 \u0628\u0647 <code>queue<\/code> \u0647\u0645\u0686\u0646\u06cc\u0646.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u0627 \u0647\u0646\u0648\u0632 \u06af\u0631\u0647 \u0647\u0627\u06cc\u06cc \u062f\u0631 \u0622\u0646 \u062f\u0627\u0631\u06cc\u0645 <code>queue<\/code>\u060c \u0627\u0648\u0644\u06cc \u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c print \u0648 \u0647\u0645\u0647 \u0647\u0645\u0633\u0627\u06cc\u06af\u0627\u0646\u0634 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645 \u0639\u0628\u0648\u0631 \u0627\u0632 \u0647\u0645\u0633\u0627\u06cc\u06af\u0627\u0646\u060c \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0622\u0646\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631\u060c \u0648 \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0622\u0646\u0647\u0627 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>queue<\/code> \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u0627\u0632\u062f\u06cc\u062f \u0634\u062f\u0647 \u0639\u0644\u0627\u0645\u062a \u06af\u0630\u0627\u0631\u06cc \u06a9\u0646\u06cc\u062f:<\/p>\n<table class=\"table table-striped\">\n<tr>\n<th>\u0645\u0631\u0627\u062d\u0644<\/th>\n<th>\u0635\u0641<\/th>\n<th>\u0645\u0644\u0627\u0642\u0627\u062a \u06a9\u0631\u062f<\/th>\n<\/tr>\n<tr>\n<td>\u0634\u0631\u0648\u0639 \u0631\u0627 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f node 0<\/td>\n<td>(0)<\/td>\n<td>{0}<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0632 0 \u0628\u0627\u0632\u062f\u06cc\u062f \u06a9\u0646\u06cc\u062f\u060c 1 \u0648 2 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f<\/td>\n<td>(1\u060c 2)<\/td>\n<td>{0}<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0632 1 \u0628\u0627\u0632\u062f\u06cc\u062f \u06a9\u0646\u06cc\u062f\u060c 4 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f<\/td>\n<td>(2\u060c 4)<\/td>\n<td>{0\u060c 2}<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0632 2 \u0628\u0627\u0632\u062f\u06cc\u062f \u06a9\u0646\u06cc\u062f\u060c 3 \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f<\/td>\n<td>(4\u060c 3)<\/td>\n<td>{0\u060c 1\u060c 2}<\/td>\n<\/tr>\n<tr>\n<td>\u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632 4\u060c \u0628\u062f\u0648\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647<\/td>\n<td>(3)<\/td>\n<td>{0\u060c 1\u060c 1\u060c 4}<\/td>\n<\/tr>\n<tr>\n<td>\u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632 3\u060c \u0628\u062f\u0648\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0627\u0632\u062f\u06cc\u062f \u0646\u0634\u062f\u0647<\/td>\n<td>( )<\/td>\n<td>{0\u060c 1\u060c 2\u060c 4\u060c 3}<\/td>\n<\/tr>\n<\/table>\n<h4 id=\"timecomplexity\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/h4>\n<p>\u062f\u0631 \u062d\u06cc\u0646 <strong>\u0639\u0631\u0636-\u0627\u0648\u0644\u06cc\u0646 \u067e\u06cc\u0645\u0627\u06cc\u0634<\/strong>\u060c \u0647\u0631 node \u062f\u0642\u06cc\u0642\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u0645\u06cc \u0634\u0648\u062f <em>\u06cc\u06a9 \u0628\u0627\u0631<\/em>\u060c \u0648 \u0647\u0631 \u0634\u0627\u062e\u0647 \u0646\u06cc\u0632 \u0645\u0634\u0627\u0647\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f <em>\u06cc\u06a9 \u0628\u0627\u0631<\/em> \u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u0644\u0641 <strong>\u062c\u0647\u062a \u062f\u0627\u0631<\/strong> \u0646\u0645\u0648\u062f\u0627\u0631\u060c \u06cc\u0639\u0646\u06cc <em>\u062f\u0648 \u0628\u0631\u0627\u0628\u0631<\/em> \u0627\u06af\u0631 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627\u0634\u062f <strong>\u0628\u062f\u0648\u0646 \u062c\u0647\u062a<\/strong>.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS \u0627\u0633\u062a <strong><em>O(|V| + |E|)<\/em><\/strong>\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 <em>V<\/em> \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u06af\u0631\u0647 \u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0627\u0633\u062a \u0648 <em>E<\/em> \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u062a\u0645\u0627\u0645 \u0634\u0627\u062e\u0647 \u0647\u0627\u06cc \u0622\u0646 (\u0644\u0628\u0647 \u0647\u0627) \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<h3 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u062f\u0631\u0633\u060c \u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u067e\u0647\u0646\u0627-\u0627\u0648\u0644 \u0631\u0627 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0648 \u0645\u0631\u0627\u062d\u0644 \u0622\u0646 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u0645.<\/p>\n<p>\u0645\u0627 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc Python \u0631\u0627 \u0628\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc Breadth-First \u0648 Breadth-First Traversal \u0628\u0647 \u062a\u0635\u0648\u06cc\u0631 \u06a9\u0634\u06cc\u062f\u0647\u200c\u0627\u06cc\u0645 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u0645. \u0631\u0648\u06cc \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0631\u0627 \u0645\u062b\u0627\u0644 \u0628\u0632\u0646\u06cc\u062f \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u062f \u0686\u06af\u0648\u0646\u0647 \u06af\u0627\u0645 \u0628\u0647 \u06af\u0627\u0645 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f.  \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0627\u06cc\u0645.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script><br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-06 16:25:03<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;14887&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 - \u062a\u0626\u0648\u0631\u06cc \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 7<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u062f\u0631 \u0627\u06cc\u0646 \u062f\u0631\u0633 \u0628\u0647 \u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645 \u062c\u0633\u062a\u062c\u0648 \u0648 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0639\u0631\u0636 \u0627\u0648\u0644. \u0627\u0648\u0644\u060c \u0645\u0627 \u062a\u0645\u0631\u06a9\u0632 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc node \u062c\u0633\u062a\u062c\u0648 \u06a9\u0631\u062f\u0646\u060c \u0642\u0628\u0644 \u0627\u0632 \u067e\u0631\u062f\u0627\u062e\u062a\u0646 \u0628\u0647 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 BFS\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062f\u0648 \u0648\u0638\u06cc\u0641\u0647 \u0627\u0635\u0644\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0628\u0647 \u06a9\u0627\u0631 \u0628\u0628\u0631\u06cc\u062f. \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[1747,1754,1753,1744,3420,3483,2750,1805,3482,1745],"class_list":["post-14887","post","type-post","status-publish","format-standard","hentry","category-python","category-programming","tag-python-vps","tag-1754","tag-1753","tag-1744","tag-3420","tag-3483","tag-2750","tag-1805","tag-3482","tag-1745"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/14887","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=14887"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/14887\/revisions"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=14887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=14887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=14887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}