{"id":16363,"date":"2024-01-24T02:52:12","date_gmt":"2024-01-23T23:22:12","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-8\/"},"modified":"2024-01-24T02:52:12","modified_gmt":"2024-01-23T23:22:12","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-8","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-8\/","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-8\/#a_%da%86%db%8c%d8%b3%d8%aa%d8%9f\" >A* \u0686\u06cc\u0633\u062a\u061f<\/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-8\/#%d9%85%d9%81%d8%a7%d9%87%db%8c%d9%85_%d9%be%d8%a7%db%8c%d9%87_a\" >\u0645\u0641\u0627\u0647\u06cc\u0645 \u067e\u0627\u06cc\u0647 A*<\/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-8\/#%d9%be%d8%b0%db%8c%d8%b1%d8%b4_%d9%88_%d8%b3%d8%a7%d8%b2%da%af%d8%a7%d8%b1%db%8c\" >\u067e\u0630\u06cc\u0631\u0634 \u0648 \u0633\u0627\u0632\u06af\u0627\u0631\u06cc<\/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-8\/#%d8%a7%d8%ab%d8%a8%d8%a7%d8%aa_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%82%d8%b1%d8%a7_%da%a9%d8%a7%d9%85%d9%84\" >\u0627\u062b\u0628\u0627\u062a \u0628\u0627 \u0627\u0633\u062a\u0642\u0631\u0627 \u06a9\u0627\u0645\u0644<\/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-8\/#%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c\" >\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc<\/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\"> 6<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h3 id=\"whatisa\"><span class=\"ez-toc-section\" id=\"a_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>A* \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0632 \u06cc\u06a9 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0639\u0638\u06cc\u0645 \u0639\u0628\u0648\u0631 \u06a9\u0646\u06cc\u062f.  \u0627\u06cc\u0646 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0628\u0647 \u0642\u062f\u0631\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a \u06a9\u0647 \u06cc\u0627\u0641\u062a\u0646 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\u0637\u0628\u06cc\u0639\u06cc\u060c \u0645\u0627 \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0634\u0631\u0648\u0639 \u0648 \u067e\u0627\u06cc\u0627\u0646 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0648\u0627\u0631\u062f \u0645\u0627\u0632 \u0645\u06cc \u0634\u0648\u06cc\u0645\u060c \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645.node \u0627\u0644\u0641) \u0648 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0632 \u0645\u0627\u0632 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u0645 (node \u0628).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/basic-ai-concepts-a-search-algorithm-1.png\" alt=\"\u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0628\u0627 \u06af\u0631\u0647 \u0647\u0627\u06cc \u062d\u0627\u0644\u062a\" title=\"\"><\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u06a9\u0647 \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u06a9\u0627\u0645\u0644 \u062f\u0627\u0631\u06cc\u0645\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u062d\u0627\u0644\u062a A \u0628\u0647 \u062d\u0627\u0644\u062a B \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u0645. \u062f\u0631 \u0645\u0648\u0627\u0631\u062f \u0633\u0627\u062f\u0647 (\u0645\u0627\u0646\u0646\u062f \u0627\u06cc\u0646 \u06cc\u06a9\u06cc)\u060c \u06a9\u0647 \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0644\u06cc\u062f \u0634\u062f\u0647 \u0627\u0632 \u062a\u0639\u062f\u0627\u062f \u06a9\u0645\u06cc \u06af\u0631\u0647 \u0648 \u06cc\u0627\u0644 \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c BFS\u060c DFS \u0648 \u062f\u06cc\u06a9\u0633\u062a\u0631\u0627 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0631 \u06cc\u06a9 \u0633\u0646\u0627\u0631\u06cc\u0648\u06cc \u0648\u0627\u0642\u0639\u06cc\u060c \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 \u0628\u0627 \u0645\u0634\u06a9\u0644\u0627\u062a\u06cc \u0628\u0627 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0632\u06cc\u0627\u062f \u0633\u0631 \u0648 \u06a9\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645\u060c \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0627 \u06cc\u06a9 <em>\u0639\u0638\u06cc\u0645<\/em> \u0645\u0642\u062f\u0627\u0631 \u06af\u0631\u0647 \u0647\u0627 \u0648 \u0644\u0628\u0647 \u0647\u0627  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u06cc\u06a9 \u0645\u06a9\u0639\u0628 \u0631\u0648\u0628\u06cc\u06a9 \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u062d\u0644 \u0622\u0646 \u0628\u0633\u06cc\u0627\u0631 \u062f\u0634\u0648\u0627\u0631 \u0627\u0633\u062a.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u06cc\u06a9 \u0645\u0639\u0646\u0627\u060c <em>\u0647\u062f\u0627\u06cc\u062a \u06a9\u0631\u062f<\/em>.  \u0622\u0646\u062c\u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 <em>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u0622\u06af\u0627\u0647\u0627\u0646\u0647<\/em> \u0628\u0648\u062c\u0648\u062f \u0645\u06cc \u0622\u06cc\u062f\u060c A*.<\/p>\n<p><em>\u062c\u0633\u062a\u062c\u0648\u06cc \u0622\u06af\u0627\u0647\u0627\u0646\u0647<\/em> \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0631\u0627\u06cc \u0634\u0631\u0648\u0639 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0627\u0636\u0627\u0641\u06cc \u062f\u0627\u0631\u062f.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0634\u06a9\u0644 \u062c\u0633\u062a\u062c\u0648\u06cc \u0646\u0627\u0622\u06af\u0627\u0647\u060c \u06cc\u0627\u0641\u062a\u0646 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0632 \u062e\u0627\u0646\u0647 \u062a\u0627 \u0645\u062d\u0644 \u06a9\u0627\u0631 \u06a9\u0627\u0645\u0644\u0627\u064b \u06a9\u0648\u0631 \u0627\u0633\u062a.<\/p>\n<p>\u0627\u0632 \u0637\u0631\u0641 \u062f\u06cc\u06af\u0631\u060c \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0634\u06a9\u0644 \u062c\u0633\u062a\u062c\u0648\u06cc \u0622\u06af\u0627\u0647\u0627\u0646\u0647 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0632 \u062e\u0627\u0646\u0647 \u0628\u0647 \u0645\u062d\u0644 \u06a9\u0627\u0631 \u0628\u0627 \u06a9\u0645\u06a9 \u062f\u06cc\u062f \u0634\u0645\u0627 (\u062f\u06cc\u062f\u0646 \u0645\u0633\u06cc\u0631\u06cc \u06a9\u0647 \u0634\u0645\u0627 \u0631\u0627 \u0628\u0647 \u0645\u0642\u0635\u062f \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0645\u06cc \u06a9\u0646\u062f) \u06cc\u0627 \u06cc\u06a9 \u0646\u0642\u0634\u0647 (\u062f\u0627\u0646\u0633\u062a\u0646 \u062f\u0642\u06cc\u0642 \u0641\u0627\u0635\u0644\u0647 \u0647\u0631 \u0646\u0642\u0637\u0647 \u0627\u0632 \u0622\u0646) \u0627\u0633\u062a. \u0627\u0632 \u0645\u0642\u0635\u062f \u0634\u0645\u0627).<\/p>\n<p>A* \u062a\u0646\u0647\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06cc\u06a9 \u0645\u0631\u062d\u0644\u0647 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0628\u0631 \u062e\u0644\u0627\u0641 \u0633\u0627\u06cc\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u067e\u06cc\u0645\u0627\u06cc\u0634 \u06af\u0631\u0627\u0641\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f\u0647\u0627\u06cc\u0634 \u0627\u0645\u06cc\u062f\u0648\u0627\u0631\u06a9\u0646\u0646\u062f\u0647 \u0648 \u0645\u0639\u0642\u0648\u0644 \u0628\u0647 \u0646\u0638\u0631 \u0628\u0631\u0633\u062f.  \u0628\u0647 \u0633\u0645\u062a \u0647\u062f\u0641 \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0627\u06af\u0631 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0622\u0646\u0647\u0627 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0647\u06cc\u0686 \u06af\u0627\u0645 \u063a\u06cc\u0631\u0628\u0647\u06cc\u0646\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u0645\u06cc \u06af\u06cc\u0631\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u0645\u06cc \u0634\u0648\u062f A* \u0628\u0631\u0627\u06cc \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0647\u0648\u0634\u0645\u0646\u062f \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0645\u0641\u06cc\u062f \u0628\u0627\u0634\u062f &#8211; \u0628\u0647 \u0648\u06cc\u0698\u0647 \u062f\u0631 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u0648 \u062a\u0648\u0633\u0639\u0647 \u0628\u0627\u0632\u06cc\u060c \u0632\u06cc\u0631\u0627 \u0627\u06cc\u0646 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f.<\/p>\n<h3 id=\"basicconceptsofa\"><span class=\"ez-toc-section\" id=\"%d9%85%d9%81%d8%a7%d9%87%db%8c%d9%85_%d9%be%d8%a7%db%8c%d9%87_a\"><\/span>\u0645\u0641\u0627\u0647\u06cc\u0645 \u067e\u0627\u06cc\u0647 A*<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A* \u0645\u0628\u062a\u0646\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u06cc\u0627\u0628\u06cc \u0628\u0647 <em>\u0628\u0647\u06cc\u0646\u0647 \u0628\u0648\u062f\u0646<\/em> \u0648 <em>\u06a9\u0627\u0645\u0644 \u0628\u0648\u062f\u0646<\/em>\u060c \u0648 \u06af\u0648\u0646\u0647 \u0627\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 best-first \u0627\u0633\u062a.<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648 \u062f\u0627\u0631\u0627\u06cc \u062e\u0627\u0635\u06cc\u062a \u0628\u0647\u06cc\u0646\u0647 \u0627\u0633\u062a\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u0634\u0648\u062f \u0628\u0647\u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0645\u0645\u06a9\u0646 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u062f\u060c \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627 \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062a\u0627 \u062d\u0627\u0644\u062a \u067e\u0627\u06cc\u0627\u0646.  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648 \u062f\u0627\u0631\u0627\u06cc \u062e\u0627\u0635\u06cc\u062a \u06a9\u0627\u0645\u0644 \u0628\u0648\u062f\u0646 \u0627\u0633\u062a\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u06cc\u06a9 \u0631\u0627\u0647 \u062d\u0644 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u0645\u0639\u06cc\u0646 \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u062f.<\/p>\n<p>\u0647\u0631 \u0628\u0627\u0631 \u06a9\u0647 A* \u0648\u0627\u0631\u062f \u06cc\u06a9 \u062d\u0627\u0644\u062a \u0645\u06cc \u0634\u0648\u062f\u060c \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u062f. <code>f(n)<\/code> (n \u0647\u0645\u0633\u0627\u06cc\u0647 \u0628\u0648\u062f\u0646 node)\u060c \u0628\u0631\u0627\u06cc \u0633\u0641\u0631 \u0628\u0647 \u062a\u0645\u0627\u0645 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647\u060c \u0648 \u0633\u067e\u0633 \u0648\u0627\u0631\u062f \u0645\u06cc \u0634\u0648\u062f node \u0628\u0627 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 <code>f(n)<\/code>.<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0627 \u0641\u0631\u0645\u0648\u0644 \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f:<\/p>\n<p>$$<br \/>\\mathcal f(n) = \\mathcal g(n) + \\mathcal h(n)<br \/>$$<\/p>\n<p><code>g(n)<\/code>  \u0645\u0642\u062f\u0627\u0631 \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u0627\u0633\u062a node \u0628\u0647 node <em>n<\/em>\u060c \u0648 <code>h(n)<\/code> \u06a9\u0647 \u06cc\u06a9 \u062a\u0642\u0631\u06cc\u0628 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0627\u0632 node\u0627\u0631\u0632\u0634<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0631 \u0645\u0633\u06cc\u0631\u06cc \u0631\u0627 \u0628\u0627\u0632\u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u0647\u0631 \u0645\u0633\u06cc\u0631\u06cc \u0631\u0627 \u0645\u0634\u062e\u0635 \u06a9\u0646\u06cc\u0645 node \u0628\u0627 \u0646\u0633\u0628\u06cc \u06a9\u0647 \u0628\u0647\u06cc\u0646\u0647 \u0631\u0627 \u062f\u0627\u0631\u062f <code>f(n)<\/code> \u0627\u0631\u0632\u0634.  \u0627\u06cc\u0646 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc \u062e\u0627\u0635\u06cc \u0631\u0627 \u0645\u062c\u062f\u062f\u0627\u064b \u0645\u0634\u0627\u0647\u062f\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u0628\u0647\u06cc\u0646\u0647 \u062a\u0631\u06cc\u0646 \u0628\u0633\u062a\u06af\u0627\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0646\u06cc\u0632 \u0628\u0647 \u0631\u0648\u0632 \u06a9\u0646\u06cc\u0645.  \u0628\u06cc\u0634\u062a\u0631 \u0631\u0648\u06cc \u06a9\u0647 \u0628\u0639\u062f\u0627<\/p>\n<p>\u06a9\u0627\u0631\u0627\u06cc\u06cc A* \u0628\u0633\u06cc\u0627\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u0627\u0631\u0632\u0634 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc <code>h(n)<\/code>\u060c \u0648 \u0628\u0633\u062a\u0647 \u0628\u0647 \u0631\u0648\u06cc \u0646\u0648\u0639 \u0645\u0633\u0626\u0644\u0647\u060c \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0628\u0647\u06cc\u0646\u0647 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0631\u0627\u06cc \u0622\u0646 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645.<\/p>\n<p>\u0633\u0627\u062e\u062a \u0686\u0646\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639\u06cc \u06a9\u0627\u0631 \u0622\u0633\u0627\u0646\u06cc \u0646\u06cc\u0633\u062a \u0648 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0634\u06a9\u0644\u0627\u062a \u0627\u0633\u0627\u0633\u06cc \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0627\u0633\u062a.  \u062f\u0648 \u0648\u06cc\u0698\u06af\u06cc \u0627\u0633\u0627\u0633\u06cc \u06a9\u0647 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632 <em>\u0642\u0627\u0628\u0644 \u067e\u0630\u06cc\u0631\u0634 \u0628\u0648\u062f\u0646<\/em> \u0648 <em>\u062b\u0628\u0627\u062a<\/em>.<\/p>\n<h3 id=\"admissibilityandconsistency\"><span class=\"ez-toc-section\" id=\"%d9%be%d8%b0%db%8c%d8%b1%d8%b4_%d9%88_%d8%b3%d8%a7%d8%b2%da%af%d8%a7%d8%b1%db%8c\"><\/span>\u067e\u0630\u06cc\u0631\u0634 \u0648 \u0633\u0627\u0632\u06af\u0627\u0631\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 <code>h(n)<\/code> \u0627\u0633\u062a <em>\u0642\u0627\u0628\u0644 \u0642\u0628\u0648\u0644<\/em> \u0627\u06af\u0631 \u0647\u0631\u06af\u0632 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u0628\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u06cc\u0634 \u0627\u0632 \u062d\u062f \u062a\u062e\u0645\u06cc\u0646 \u0646\u0632\u0646\u062f <em>n<\/em> \u0648 \u0647\u062f\u0641 node.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0628\u0631\u0627\u06cc \u0647\u0631 node <em>n<\/em> \u0641\u0631\u0645\u0648\u0644 \u0632\u06cc\u0631 \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p>$$<br \/>h(n)\\leq h^*(n)<br \/>$$<\/p>\n<p><code>h*(n)<\/code>  \u0628\u0648\u062f\u0646 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u0628\u06cc\u0646 <em>n<\/em> \u0648 \u0647\u062f\u0641 node.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u06af\u0631 \u062a\u0627\u0628\u0639 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u0631\u0627 \u0628\u06cc\u0634 \u0627\u0632 \u062d\u062f \u062a\u062e\u0645\u06cc\u0646 \u0628\u0632\u0646\u062f\u060c \u0627\u0645\u0627 \u0647\u0631\u06af\u0632 \u0628\u06cc\u0634 \u0627\u0632 <em>\u062f<\/em>\u060c \u0628\u0647 \u062c\u0631\u0627\u062a \u0645\u06cc \u062a\u0648\u0627\u0646 \u06af\u0641\u062a \u06a9\u0647 \u0631\u0627\u0647 \u062d\u0644\u06cc \u06a9\u0647 \u062a\u0627\u0628\u0639 \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc \u06a9\u0646\u062f \u0627\u0632 \u062f\u0642\u062a \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a <em>\u062f<\/em> (\u06cc\u0639\u0646\u06cc \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062a\u0627 \u0627\u0646\u062a\u0647\u0627 \u0628\u06cc\u0634 \u0627\u0632 \u0622\u0646 \u0628\u0631\u0622\u0648\u0631\u062f \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f <em>\u062f<\/em>).<\/p>\n<p>\u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 <code>h(n)<\/code> \u0627\u0633\u062a <em>\u0627\u0633\u062a\u0648\u0627\u0631<\/em> \u0627\u06af\u0631 \u0628\u0631\u0622\u0648\u0631\u062f \u0647\u0645\u06cc\u0634\u0647 \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0641\u0627\u0635\u0644\u0647 \u062a\u062e\u0645\u06cc\u0646\u06cc \u0628\u06cc\u0646 \u0647\u062f\u0641 \u0628\u0627\u0634\u062f <em>n<\/em> \u0648 \u0647\u0631 \u0647\u0645\u0633\u0627\u06cc\u0647 \u0645\u0639\u06cc\u0646\u060c \u0628\u0647 \u0627\u0636\u0627\u0641\u0647 \u0647\u0632\u06cc\u0646\u0647 \u062a\u062e\u0645\u06cc\u0646\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646 \u0647\u0645\u0633\u0627\u06cc\u0647:<\/p>\n<p>$$<br \/>c(n,m)+h(m)\\geq h(n)<br \/>$$<\/p>\n<p><code>c(n,m)<\/code>  \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u06af\u0631\u0647 \u0647\u0627 <code>n<\/code> \u0648 <code>m<\/code>.  \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u0627\u06af\u0631 <code>h(n)<\/code> \u0633\u0627\u0632\u06af\u0627\u0631 \u0627\u0633\u062a\u060c \u0633\u067e\u0633 \u0645\u0627 \u0645\u0633\u06cc\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0631\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 node \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u0628\u0627\u0632\u0631\u0633\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0627\u0633\u062a <em>\u0628\u0647\u06cc\u0646\u0647<\/em>.<\/p>\n<p><strong>\u0642\u0636\u06cc\u0647<\/strong>: \u0627\u06af\u0631 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627\u0634\u062f\u060c \u0622\u0646 \u0631\u0627 \u0646\u06cc\u0632 \u0642\u0627\u0628\u0644 \u0642\u0628\u0648\u0644 \u0627\u0633\u062a.<\/p>\n<h3 id=\"proofbycompleteinduction\"><span class=\"ez-toc-section\" id=\"%d8%a7%d8%ab%d8%a8%d8%a7%d8%aa_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%82%d8%b1%d8%a7_%da%a9%d8%a7%d9%85%d9%84\"><\/span>\u0627\u062b\u0628\u0627\u062a \u0628\u0627 \u0627\u0633\u062a\u0642\u0631\u0627 \u06a9\u0627\u0645\u0644<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0627\u0644\u0642\u0627\u06cc\u06cc <code>N<\/code> \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0647 \u0647\u0627\u06cc \u0628\u06cc\u0646 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f node <code>n<\/code>  \u0648 \u067e\u0627\u06cc\u0627\u0646 node <code>s<\/code> \u0631\u0648\u06cc  \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u06cc\u0646 \u0627\u06cc\u0646 \u062f\u0648<\/p>\n<p><strong>\u067e\u0627\u06cc\u0647<\/strong>: N=0<\/p>\n<p>\u0627\u06af\u0631 \u0647\u06cc\u0686 \u06af\u0631\u0647 \u0627\u06cc \u0628\u06cc\u0646 \u0622\u0646 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f <code>n<\/code> \u0648 <code>s<\/code>\u0648 \u0686\u0648\u0646 \u0645\u0627 \u0627\u06cc\u0646 \u0631\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 <code>h(n)<\/code> \u0633\u0627\u0632\u06af\u0627\u0631 \u0627\u0633\u062a\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0632\u06cc\u0631 \u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>c(n,s)+h(s)\\geq h(n)<br \/>$$<\/p>\n<p>\u062f\u0627\u0646\u0633\u062a\u0646 <code>h*(n)=c(n,s)<\/code> \u0648 <code>h(s)=0<\/code> \u0628\u0627 \u062e\u06cc\u0627\u0644 \u0631\u0627\u062d\u062a \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u062a\u06cc\u062c\u0647 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647:<\/p>\n<p>$$<br \/>h^*(n)\\geq h(n)<br \/>$$<\/p>\n<p><strong>\u0641\u0631\u0636\u06cc\u0647 \u0627\u0633\u062a\u0642\u0631\u0627<\/strong>: N < k<\/p>\n<p>\u0645\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0642\u0627\u0646\u0648\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0635\u0627\u062f\u0642 \u0627\u0633\u062a <code>N &lt; k<\/code>.<\/p>\n<p><strong>\u0645\u0631\u062d\u0644\u0647 \u0627\u0644\u0642\u0627\u0621:<\/strong><\/p>\n<p>\u062f\u0631 \u0634\u0631\u0627\u06cc\u0637\u06cc \u06a9\u0647 <code>N = k<\/code> \u06af\u0631\u0647 \u0647\u0627 \u0631\u0648\u06cc \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 <code>n<\/code> \u0628\u0647 <code>s<\/code>\u060c \u0645\u0627 \u062c\u0627\u0646\u0634\u06cc\u0646 \u0627\u0648\u0644 \u0631\u0627 \u0628\u0627\u0632\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 (node <code>m<\/code>) \u0627\u0632 \u067e\u0627\u06cc\u0627\u0646 node <code>n<\/code>.  \u0632\u06cc\u0631\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0632 \u0622\u0646 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f <code>m<\/code> \u0628\u0647 <code>n<\/code>\u060c \u0648 \u0645\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0634\u0627\u0645\u0644 <code>k-1<\/code> \u06af\u0631\u0647 \u0647\u0627\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0632\u06cc\u0631 \u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>\u210e^*(\ud835\udc5b) = \ud835\udc50(\ud835\udc5b\u060c \ud835\udc5a) + \u210e^*(\ud835\udc5a) \u2265 \ud835\udc50(<br \/>$$<\/p>\n<p><strong>QED<\/strong><\/p>\n<h3 id=\"implementation\"><span class=\"ez-toc-section\" id=\"%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c\"><\/span>\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u062c\u0631\u0627\u06cc \u0645\u0633\u062a\u0642\u06cc\u0645 A* \u0627\u0633\u062a \u0631\u0648\u06cc \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u0646\u0645\u0648\u062f\u0627\u0631  \u062a\u0627\u0628\u0639 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u0633\u0627\u062f\u06af\u06cc \u0648 \u0627\u062e\u062a\u0635\u0627\u0631 \u0628\u0647 \u0635\u0648\u0631\u062a 1 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u06af\u0631\u0647 \u0647\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0645\u062c\u0627\u0648\u0631 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u06a9\u0644\u06cc\u062f\u0647\u0627 \u06af\u0631\u0647 \u0647\u0627\u06cc \u06af\u0631\u0627\u0641 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u0646\u062f\u060c \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062d\u0627\u0648\u06cc \u0644\u06cc\u0633\u062a\u06cc \u0627\u0632 \u06cc\u0627\u0644 \u0647\u0627 \u0628\u0627 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647 \u0645\u0631\u0628\u0648\u0637\u0647 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 A* \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0634\u062f\u0647 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u062f \u06cc\u0627\u0641\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">from<\/span> collections <span class=\"hljs-keyword\">import<\/span> deque\n\n<span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">Graph<\/span>:<\/span>\n    \n    \n    \n    \n    \n    \n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__init__<\/span>(<span class=\"hljs-params\">self, adjacency_list<\/span>):<\/span>\n        self.adjacency_list = adjacency_list\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">get_neighbors<\/span>(<span class=\"hljs-params\">self, v<\/span>):<\/span>\n        <span class=\"hljs-keyword\">return<\/span> self.adjacency_list(v)\n\n    \n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">h<\/span>(<span class=\"hljs-params\">self, n<\/span>):<\/span>\n        H = {\n            <span class=\"hljs-string\">'A'<\/span>: <span class=\"hljs-number\">1<\/span>,\n            <span class=\"hljs-string\">'B'<\/span>: <span class=\"hljs-number\">1<\/span>,\n            <span class=\"hljs-string\">'C'<\/span>: <span class=\"hljs-number\">1<\/span>,\n            <span class=\"hljs-string\">'D'<\/span>: <span class=\"hljs-number\">1<\/span>\n        }\n\n        <span class=\"hljs-keyword\">return<\/span> H(n)\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">a_star_algorithm<\/span>(<span class=\"hljs-params\">self, start_node, stop_node<\/span>):<\/span>\n        \n        \n        \n        \n        open_list = <span class=\"hljs-built_in\">set<\/span>((start_node))\n        closed_list = <span class=\"hljs-built_in\">set<\/span>(())\n\n        \n        \n        g = {}\n\n        g(start_node) = <span class=\"hljs-number\">0<\/span>\n\n        \n        parents = {}\n        parents(start_node) = start_node\n\n        <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-built_in\">len<\/span>(open_list) &gt; <span class=\"hljs-number\">0<\/span>:\n            n = <span class=\"hljs-literal\">None<\/span>\n\n            \n            <span class=\"hljs-keyword\">for<\/span> v <span class=\"hljs-keyword\">in<\/span> open_list:\n                <span class=\"hljs-keyword\">if<\/span> n == <span class=\"hljs-literal\">None<\/span> <span class=\"hljs-keyword\">or<\/span> g(v) + self.h(v) &lt; g(n) + self.h(n):\n                    n = v;\n\n            <span class=\"hljs-keyword\">if<\/span> n == <span class=\"hljs-literal\">None<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Path does not exist!'<\/span>)\n                <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">None<\/span>\n\n            \n            \n            <span class=\"hljs-keyword\">if<\/span> n == stop_node:\n                reconst_path = ()\n\n                <span class=\"hljs-keyword\">while<\/span> parents(n) != n:\n                    reconst_path.append(n)\n                    n = parents(n)\n\n                reconst_path.append(start_node)\n\n                reconst_path.reverse()\n\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Path found: {}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(reconst_path))\n                <span class=\"hljs-keyword\">return<\/span> reconst_path\n\n            \n            <span class=\"hljs-keyword\">for<\/span> (m, weight) <span class=\"hljs-keyword\">in<\/span> self.get_neighbors(n):\n                \n                \n                <span class=\"hljs-keyword\">if<\/span> m <span class=\"hljs-keyword\">not<\/span> <span class=\"hljs-keyword\">in<\/span> open_list <span class=\"hljs-keyword\">and<\/span> m <span class=\"hljs-keyword\">not<\/span> <span class=\"hljs-keyword\">in<\/span> closed_list:\n                    open_list.add(m)\n                    parents(m) = n\n                    g(m) = g(n) + weight\n\n                \n                \n                \n                <span class=\"hljs-keyword\">else<\/span>:\n                    <span class=\"hljs-keyword\">if<\/span> g(m) &gt; g(n) + weight:\n                        g(m) = g(n) + weight\n                        parents(m) = n\n\n                        <span class=\"hljs-keyword\">if<\/span> m <span class=\"hljs-keyword\">in<\/span> closed_list:\n                            closed_list.remove(m)\n                            open_list.add(m)\n\n            \n            \n            open_list.remove(n)\n            closed_list.add(n)\n\n        <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Path does not exist!'<\/span>)\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">None<\/span>\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0628\u0627 \u0646\u0645\u0648\u062f\u0627\u0631 \u0648\u0632\u0646\u06cc \u0632\u06cc\u0631 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p>\u0645\u0627 \u06a9\u062f \u0631\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u062c\u0631\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">adjacency_list = {\n    <span class=\"hljs-string\">'A'<\/span>: ((<span class=\"hljs-string\">'B'<\/span>, <span class=\"hljs-number\">1<\/span>), (<span class=\"hljs-string\">'C'<\/span>, <span class=\"hljs-number\">3<\/span>), (<span class=\"hljs-string\">'D'<\/span>, <span class=\"hljs-number\">7<\/span>)),\n    <span class=\"hljs-string\">'B'<\/span>: ((<span class=\"hljs-string\">'D'<\/span>, <span class=\"hljs-number\">5<\/span>)),\n    <span class=\"hljs-string\">'C'<\/span>: ((<span class=\"hljs-string\">'D'<\/span>, <span class=\"hljs-number\">12<\/span>))\n}\ngraph1 = Graph(adjacency_list)\ngraph1.a_star_algorithm(<span class=\"hljs-string\">'A'<\/span>, <span class=\"hljs-string\">'D'<\/span>)\n<\/code><\/pre>\n<p>\u0648 \u062e\u0631\u0648\u062c\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">Path found: (<span class=\"hljs-string\">'A'<\/span>, <span class=\"hljs-string\">'B'<\/span>, <span class=\"hljs-string\">'D'<\/span>)\n(<span class=\"hljs-string\">'A'<\/span>, <span class=\"hljs-string\">'B'<\/span>, <span class=\"hljs-string\">'D'<\/span>)\n<\/code><\/pre>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0633\u06cc\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0627\u0632 <code>A<\/code> \u0628\u0647 <code>D<\/code>\u060c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 A* \u06cc\u0627\u0641\u062a \u0645\u06cc \u0634\u0648\u062f <code>A<\/code>-><code>B<\/code>-><code>D<\/code>.<\/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 1403-01-24 02:52:03<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;16363&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\"> 6<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>A* \u0686\u06cc\u0633\u062a\u061f \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0632 \u06cc\u06a9 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0639\u0638\u06cc\u0645 \u0639\u0628\u0648\u0631 \u06a9\u0646\u06cc\u062f. \u0627\u06cc\u0646 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0628\u0647 \u0642\u062f\u0631\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a \u06a9\u0647 \u06cc\u0627\u0641\u062a\u0646 \u062f\u0633\u062a\u06cc \u0647\u062f\u0641 \u0633\u0627\u0639\u062a \u0647\u0627 \u0637\u0648\u0644 \u0645\u06cc \u06a9\u0634\u062f. \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0631\u0627 &#8220;\u0628\u0627 \u067e\u0627&#8221; \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646 \u0631\u0633\u0627\u0646\u062f\u06cc\u062f\u060c \u0642\u0631\u0627\u0631 \u0627\u0633\u062a \u06cc\u06a9\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646 \u0628\u0631\u0633\u0627\u0646\u06cc\u062f. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\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":[1743,620,1686],"tags":[1747,1746,1753,1744,3420,3483,2750,1805,1755,3482],"class_list":["post-16363","post","type-post","status-publish","format-standard","hentry","category-python","category-programming","category-ai","tag-python-vps","tag-vps-","tag-1753","tag-1744","tag-3420","tag-3483","tag-2750","tag-1805","tag-1755","tag-3482"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16363","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=16363"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16363\/revisions"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=16363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=16363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=16363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}