{"id":16098,"date":"2024-01-20T19:55:41","date_gmt":"2024-01-20T16:25:41","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-20T19:55:41","modified_gmt":"2024-01-20T16:25:41","slug":"minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"Minimax \u0628\u0627 \u0647\u0631\u0633 \u0622\u0644\u0641\u0627-\u0628\u062a\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646"},"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-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d8%b9%d8%b1%db%8c%d9%81_%d8%a7%d8%b5%d8%b7%d9%84%d8%a7%d8%ad%d8%a7%d8%aa\" >\u062a\u0639\u0631\u06cc\u0641 \u0627\u0635\u0637\u0644\u0627\u062d\u0627\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%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%be%d8%b4%d8%aa_%d9%85%db%8c%d9%86%db%8c%d9%85%da%a9%d8%b3\" >\u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0645\u06cc\u0646\u06cc\u0645\u06a9\u0633<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a8%d8%a7%d8%b2_%da%a9%d8%b1%d8%af%d9%86_%da%a9%d8%aa%d8%a7%d8%a8_%d9%87%d8%a7_%d9%88_%d8%aa%db%8c%da%a9_%d8%aa%d8%a7%da%a9\" >\u0628\u0627\u0632 \u06a9\u0631\u062f\u0646 \u06a9\u062a\u0627\u0628 \u0647\u0627 \u0648 \u062a\u06cc\u06a9 \u062a\u0627\u06a9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_minimax_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Minimax \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%87%d8%b1%d8%b3_%d8%a2%d9%84%d9%81%d8%a7_%d8%a8%d8%aa%d8%a7\" >\u0647\u0631\u0633 \u0622\u0644\u0641\u0627 \u0628\u062a\u0627<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/minimax-%d8%a8%d8%a7-%d9%87%d8%b1%d8%b3-%d8%a2%d9%84%d9%81%d8%a7-%d8%a8%d8%aa%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%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\"> 13<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0633\u06cc\u0627\u0631 \u062f\u0631 \u0627\u0648\u0627\u062e\u0631 \u062f\u0647\u0647 1920 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/John_von_Neumann\">\u062c\u0627\u0646 \u0641\u0648\u0646 \u0646\u0648\u06cc\u0645\u0627\u0646<\/a> \u0645\u0634\u06a9\u0644 \u0627\u0635\u0644\u06cc \u062f\u0631 \u062a\u0626\u0648\u0631\u06cc \u0628\u0627\u0632\u06cc\u200c\u0647\u0627 \u0631\u0627 \u06a9\u0647 \u062a\u0627 \u0628\u0647 \u0627\u0645\u0631\u0648\u0632 \u0645\u0637\u0631\u062d \u0627\u0633\u062a\u060c \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f:<\/p>\n<blockquote>\n<p>\u0628\u0627\u0632\u06cc\u06a9\u0646\u0627\u0646 \u0627\u0633<sub>1<\/sub>\u060c \u0633<sub>2<\/sub>\u060c &#8230;\u060c \u0633<sub>n<\/sub> \u062f\u0631 \u062d\u0627\u0644 \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u0628\u0627\u0632\u06cc G. \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0628\u0627\u06cc\u062f \u06a9\u062f\u0627\u0645 \u062d\u0631\u06a9\u062a \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u062f<sub>\u0645\u062a\u0631<\/sub> \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0645\u0645\u06a9\u0646 \u0628\u0627\u0632\u06cc \u06a9\u0646\u06cc\u062f\u061f<\/p>\n<\/blockquote>\n<p>\u0627\u0646\u062f\u06a9\u06cc \u067e\u0633 \u0627\u0632 \u0622\u0646\u060c \u0645\u0634\u06a9\u0644\u0627\u062a\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0633\u062a \u0628\u0647 \u0686\u0627\u0644\u0634\u06cc \u0628\u0627 \u0627\u0647\u0645\u06cc\u062a \u0628\u0631\u0627\u06cc \u062a\u0648\u0633\u0639\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u062d\u0628\u0648\u0628 \u062a\u0631\u06cc\u0646 \u0632\u0645\u06cc\u0646\u0647 \u0647\u0627\u06cc \u0627\u0645\u0631\u0648\u0632\u06cc \u062f\u0631 \u0639\u0644\u0648\u0645 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 &#8211; \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0646\u062f.  \u0628\u0631\u062e\u06cc \u0627\u0632 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062f\u0633\u062a\u0627\u0648\u0631\u062f\u0647\u0627 \u062f\u0631 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u0645\u0648\u0636\u0648\u0639 \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc\u06a9 &#8211; \u0642\u0647\u0631\u0645\u0627\u0646\u0627\u0646 \u062c\u0647\u0627\u0646 \u062f\u0631 \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc\u06a9 \u0645\u062e\u062a\u0644\u0641 \u0642\u0628\u0644\u0627\u064b \u062a\u0648\u0633\u0637 \u0631\u0627\u06cc\u0627\u0646\u0647 \u0647\u0627 \u0634\u06a9\u0633\u062a \u062e\u0648\u0631\u062f\u0647 \u0627\u0646\u062f\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u062f\u0631 \u0634\u0637\u0631\u0646\u062c\u060c \u0686\u06a9\u0631\u0632\u060c \u062a\u062e\u062a\u0647 \u0646\u0631\u062f\u060c \u0648 \u0627\u062e\u06cc\u0631\u0627\u064b (2016) \u062d\u062a\u06cc Go.<\/p>\n<p>\u0627\u06af\u0631\u0686\u0647 \u0627\u06cc\u0646 \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0648\u0641\u0642 \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0645\u0627 \u0631\u0648\u0634 \u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u0622\u0646\u0647\u0627 \u0628\u0627 \u0627\u0646\u0633\u0627\u0646 \u0647\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a.  \u0627\u06a9\u062b\u0631 \u0627\u06cc\u0646 \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627 \u0645\u0628\u062a\u0646\u06cc \u0647\u0633\u062a\u0646\u062f \u0631\u0648\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f\u060c \u0648 \u0627\u0632 \u0627\u06cc\u0646 \u0627\u0648\u0627\u062e\u0631 \u0631\u0648\u06cc \u0647\u0645\u0686\u0646\u06cc\u0646 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646\u06cc<\/p>\n<p>\u0631\u0627 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Minimax\">\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Minimax<\/a> \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0646\u0633\u0628\u062a\u0627 \u0633\u0627\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u0628\u0647\u06cc\u0646\u0647 \u062f\u0631 \u0646\u0638\u0631\u06cc\u0647 \u0628\u0627\u0632\u06cc \u0647\u0627 \u0648 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0628\u0627\u0632 \u0647\u0645\u060c \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627 \u0628\u0647 \u0634\u062f\u062a \u0645\u062a\u06a9\u06cc \u0647\u0633\u062a\u0646\u062f \u0631\u0648\u06cc \u0628\u0627 \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0648\u062f\u0646\u060c \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0648\u0627\u0646\u06cc\u0644 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0631\u0633 \u0622\u0644\u0641\u0627-\u0628\u062a\u0627 \u0628\u0647 \u0634\u062f\u062a \u0628\u0647\u0628\u0648\u062f \u0628\u062e\u0634\u06cc\u062f &#8211; \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0647\u0631 \u062f\u0648 \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a.<\/p>\n<p>\u0627\u06af\u0631\u0686\u0647 \u0645\u0627 \u0647\u0631 \u0628\u0627\u0632\u06cc \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0646\u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0628\u0647 \u0637\u0648\u0631 \u062e\u0644\u0627\u0635\u0647 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062f\u0648 \u0646\u0641\u0631\u0647 \u0645\u0631\u062a\u0628\u0637 \u0647\u0633\u062a\u0646\u062f \u062a\u0648\u0636\u06cc\u062d \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f. <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Non-cooperative_game_theory\">\u063a\u06cc\u0631 \u062a\u0639\u0627\u0648\u0646\u06cc<\/a> <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Zero-sum_game\">\u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0635\u0641\u0631<\/a> <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Symmetric_game\">\u0645\u062a\u0642\u0627\u0631\u0646<\/a> \u0628\u0627\u0632\u06cc \u0628\u0627 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Perfect_information\">\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u06a9\u0627\u0645\u0644<\/a> &#8211; \u0634\u0637\u0631\u0646\u062c\u060c \u0628\u0631\u0648\u060c \u062a\u06cc\u06a9 \u062a\u0627\u06a9\u060c \u062a\u062e\u062a\u0647 \u0646\u0631\u062f\u060c \u0631\u06cc\u0648\u0631\u0633\u06cc\u060c \u0686\u06a9\u0631\u0632\u060c \u0645\u0627\u0646\u06a9\u0627\u0644\u0627\u060c 4 \u062f\u0631 \u06cc\u06a9 \u0631\u062f\u06cc\u0641 \u0648 \u063a\u06cc\u0631\u0647 &#8230;<\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u062f\u060c \u0647\u06cc\u0686 \u06cc\u06a9 \u0627\u0632 \u0627\u06cc\u0646 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc\u06cc \u0646\u06cc\u0633\u062a\u0646\u062f \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0646\u062f\u0627\u0646\u062f \u06a9\u0627\u0631\u062a\u200c\u0647\u0627\u06cc \u062d\u0631\u06cc\u0641 \u062f\u0627\u0631\u062f\u060c \u06cc\u0627 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0628\u0627\u06cc\u062f \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062e\u0627\u0635\u06cc \u0631\u0627 \u062d\u062f\u0633 \u0628\u0632\u0646\u062f.<\/p>\n<h2 id=\"definingterms\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%b9%d8%b1%db%8c%d9%81_%d8%a7%d8%b5%d8%b7%d9%84%d8%a7%d8%ad%d8%a7%d8%aa\"><\/span>\u062a\u0639\u0631\u06cc\u0641 \u0627\u0635\u0637\u0644\u0627\u062d\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0642\u0648\u0627\u0646\u06cc\u0646 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0628\u0627\u0632\u06cc \u0647\u0627 \u062a\u0648\u0633\u0637 <em>\u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc \u0642\u0627\u0646\u0648\u0646\u06cc<\/em> (\u06cc\u0627 <em>\u06a9\u0634\u0648\u0631\u0647\u0627\u06cc \u0642\u0627\u0646\u0648\u0646\u06cc<\/em>) \u0648 <em>\u062d\u0631\u06a9\u0627\u062a \u0642\u0627\u0646\u0648\u0646\u06cc<\/em> \u0628\u0631\u0627\u06cc \u0647\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0642\u0627\u0646\u0648\u0646\u06cc  \u0628\u0631\u0627\u06cc \u0647\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u062d\u0642\u0648\u0642\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u062a\u0645\u0627\u0645 \u062d\u0631\u06a9\u062a \u0647\u0627\u06cc \u0642\u0627\u0646\u0648\u0646\u06cc \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0631\u062f.  \u0628\u0631\u062e\u06cc \u0627\u0632 \u0645\u0648\u0627\u0636\u0639 \u062d\u0642\u0648\u0642\u06cc \u0647\u0633\u062a\u0646\u062f <em>\u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc \u0634\u0631\u0648\u0639<\/em> \u0648 \u0628\u0631\u062e\u06cc 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\u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u062d\u0631\u06a9\u062a \u06cc\u06a9\u06cc \u0627\u0632 \u0628\u0627\u0632\u06cc\u06a9\u0646\u0627\u0646 \u0627\u0633\u062a \u0648 \u0648\u0636\u0639\u06cc\u062a \u0628\u0627\u0632\u06cc \u0627\u0632 \u06cc\u06a9 \u0645\u0648\u0642\u0639\u06cc\u062a \u0642\u0627\u0646\u0648\u0646\u06cc \u0628\u0647 \u0645\u0648\u0642\u0639\u06cc\u062a \u062f\u06cc\u06af\u0631 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u062a\u0635\u0648\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u062a\u06cc\u06a9 \u062a\u0627\u06a9 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/minimax-and-alpha-beta-pruning-in-python-1.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0622\u0628\u06cc \u0631\u0646\u06af \u0646\u0648\u0628\u062a \u0628\u0627\u0632\u06cc\u06a9\u0646 X \u0648 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0642\u0631\u0645\u0632 \u0631\u0646\u06af \u0646\u0648\u0628\u062a \u0628\u0627\u0632\u06cc\u06a9\u0646 O \u0647\u0633\u062a\u0646\u062f.  \u0645\u0648\u0642\u0639\u06cc\u062a \u067e\u0627\u06cc\u0627\u0646\u06cc (\u0628\u0631\u06af \u062f\u0631\u062e\u062a) \u0647\u0631 \u0634\u0628\u06a9\u0647 \u0627\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0628\u0627\u0632\u06cc\u06a9\u0646\u0627\u0646 \u0628\u0631\u0646\u062f\u0647 \u0634\u0648\u062f \u06cc\u0627 \u062a\u062e\u062a\u0647 \u067e\u0631 \u0628\u0627\u0634\u062f \u0648 \u0647\u06cc\u0686 \u0628\u0631\u0646\u062f\u0647 \u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u0631\u0627 <em>\u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u06a9\u0627\u0645\u0644<\/em> \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 root \u0645\u0648\u0642\u0639\u06cc\u062a \u0634\u0631\u0648\u0639 \u0627\u0633\u062a \u0648 \u062a\u0645\u0627\u0645 \u0628\u0631\u06af \u0647\u0627 \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc \u067e\u0627\u06cc\u0627\u0646\u06cc \u0647\u0633\u062a\u0646\u062f.  \u0647\u0631 \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u06a9\u0627\u0645\u0644 \u0628\u0647 \u0647\u0645\u0627\u0646 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0647 \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0627\u0632\u06cc \u0646\u062a\u0627\u06cc\u062c \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062d\u0631\u06a9\u062a \u0642\u0627\u0646\u0648\u0646\u06cc \u0627\u0646\u062c\u0627\u0645 \u0634\u062f\u0647 \u062f\u0627\u0631\u062f.  \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f \u06a9\u0647 \u062d\u062a\u06cc \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9 \u0645\u0627\u0646\u0646\u062f tic-tac-toe \u062f\u0631\u062e\u062a \u06a9\u0627\u0645\u0644 \u0628\u0627\u0632\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a.  \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644\u060c \u0627\u06cc\u062c\u0627\u062f \u0635\u0631\u06cc\u062d \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u06a9\u0627\u0645\u0644 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631 \u062d\u06cc\u0646 \u0646\u0648\u0634\u062a\u0646 \u0628\u0631\u0646\u0627\u0645\u0647 \u0627\u06cc \u06a9\u0647 \u0642\u0631\u0627\u0631 \u0627\u0633\u062a \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0631\u0627 \u062f\u0631 \u0647\u0631 \u0644\u062d\u0638\u0647 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u06a9\u0646\u062f\u060c \u062a\u0645\u0631\u06cc\u0646 \u062e\u0648\u0628\u06cc \u0646\u06cc\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u06af\u0631\u0647 \u0647\u0627 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0637\u0648\u0631 \u0636\u0645\u0646\u06cc \u062f\u0631 \u0627\u06cc\u062c\u0627\u062f \u0634\u0648\u0646\u062f process \u0627\u0632 \u0628\u0627\u0632\u062f\u06cc\u062f<\/p>\n<p>\u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u062d\u0627\u0644\u062a-\u0641\u0636\u0627\u06cc \u06cc\u06a9 \u0628\u0627\u0632\u06cc<\/em> \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0639\u062f\u0627\u062f\u06cc \u0627\u0632 \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc \u0628\u0627\u0632\u06cc \u0642\u0627\u0646\u0648\u0646\u06cc \u0642\u0627\u0628\u0644 \u062f\u0633\u062a\u0631\u0633\u06cc \u0627\u0632 \u0645\u0648\u0642\u0639\u06cc\u062a \u0634\u0631\u0648\u0639 \u0628\u0627\u0632\u06cc\u060c \u0648 <em>\u0639\u0627\u0645\u0644 \u0627\u0646\u0634\u0639\u0627\u0628<\/em> \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u062f\u0631 \u0647\u0631 \u06a9\u062f\u0627\u0645 node (\u0627\u06af\u0631 \u0627\u06cc\u0646 \u0639\u062f\u062f \u062b\u0627\u0628\u062a \u0646\u06cc\u0633\u062a\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0645\u0639\u0645\u0648\u0644 \u0627\u0633\u062a).<\/p>\n<p>\u0628\u0631\u0627\u06cc tic-tac-toe\u060c \u062d\u062f \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u0641\u0636\u0627\u06cc \u062d\u0627\u0644\u062a 3 \u0627\u0633\u062a<sup>9<\/sup>=19683.  \u0627\u06cc\u0646 \u0639\u062f\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc\u06cc \u0645\u0627\u0646\u0646\u062f \u0634\u0637\u0631\u0646\u062c \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f!  \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u060c \u062c\u0633\u062a\u062c\u0648 \u062f\u0631 \u06a9\u0644 \u062f\u0631\u062e\u062a \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0645\u0627 \u062f\u0631 \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u0628\u0647 \u0646\u0648\u0628\u062a \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645\u060c \u0628\u0633\u06cc\u0627\u0631 \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u06a9\u0646\u062f \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n<p>\u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 Minimax \u062f\u0631 \u062a\u0626\u0648\u0631\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627 \u0627\u0632 \u0627\u0647\u0645\u06cc\u062a \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<h2 id=\"theorybehindminimax\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%a6%d9%88%d8%b1%db%8c_%d9%be%d8%b4%d8%aa_%d9%85%db%8c%d9%86%db%8c%d9%85%da%a9%d8%b3\"><\/span>\u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0645\u06cc\u0646\u06cc\u0645\u06a9\u0633<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Minimax \u0645\u062a\u06a9\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0633\u06cc\u0633\u062a\u0645\u0627\u062a\u06cc\u06a9\u060c \u06cc\u0627 \u0628\u0647 \u0637\u0648\u0631 \u062f\u0642\u06cc\u0642 \u062a\u0631 \u06af\u0641\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f &#8211; \u0631\u0648\u06cc <strong>\u0646\u06cc\u0631\u0648\u06cc \u0628\u06cc \u0631\u062d\u0645<\/strong> \u0648 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0633\u0627\u062f\u0647.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0641\u0631\u0636 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0631 \u0628\u0627\u0631 \u062f\u0631 \u0637\u0648\u0644 \u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u0628\u0631\u0627\u06cc \u062d\u0631\u06a9\u062a \u0628\u0639\u062f\u06cc\u060c \u06cc\u06a9 \u062f\u0631\u062e\u062a \u06a9\u0627\u0645\u0644 \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u062a\u0627 \u0628\u0631\u06af \u0647\u0627.  \u0645\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u062a\u0645\u0627\u0645 \u0646\u062a\u0627\u06cc\u062c \u0645\u0645\u06a9\u0646 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0647\u0631 \u0628\u0627\u0631 \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0645\u0645\u06a9\u0646 \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u063a\u06cc\u0631 \u067e\u06cc\u0634 \u067e\u0627 \u0627\u0641\u062a\u0627\u062f\u0647\u060c \u0627\u06cc\u0646 \u0639\u0645\u0644 \u063a\u06cc\u0631 \u0642\u0627\u0628\u0644 \u0627\u062c\u0631\u0627 \u0627\u0633\u062a.  \u062d\u062a\u06cc \u062c\u0633\u062a\u062c\u0648 \u062f\u0631 \u0639\u0645\u0642 \u0645\u0639\u06cc\u0646 \u06af\u0627\u0647\u06cc \u0627\u0648\u0642\u0627\u062a \u0632\u0645\u0627\u0646 \u063a\u06cc\u0631 \u0642\u0627\u0628\u0644 \u0642\u0628\u0648\u0644\u06cc \u0631\u0627 \u0645\u06cc \u0637\u0644\u0628\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c Minimax \u062c\u0633\u062a\u062c\u0648 \u0631\u0627 \u062f\u0631 \u0639\u0645\u0642 \u062f\u0631\u062e\u062a \u0646\u0633\u0628\u062a\u0627\u064b \u06a9\u0645 \u0628\u0627 \u06a9\u0645\u06a9 \u0645\u0646\u0627\u0633\u0628 \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u06a9\u0646\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Heuristic\">\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc<\/a>\u060c \u0648 \u0628\u0647 \u062e\u0648\u0628\u06cc \u0637\u0631\u0627\u062d\u06cc \u0634\u062f\u0647 \u0648 \u062f\u0631 \u0639\u06cc\u0646 \u062d\u0627\u0644 \u0633\u0627\u062f\u0647 \u0627\u0633\u062a <em>\u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc<\/em>.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0645\u0627 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u06cc\u0627\u0641\u062a\u0646 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0645\u0645\u06a9\u0646 \u0627\u0632 \u062f\u0633\u062a \u0645\u06cc \u062f\u0647\u06cc\u0645\u060c \u0627\u0645\u0627 \u062f\u0631 \u0627\u06a9\u062b\u0631 \u0645\u0648\u0627\u0631\u062f \u062a\u0635\u0645\u06cc\u0645\u06cc \u06a9\u0647 \u0645\u06cc\u0646\u06cc \u0645\u06a9\u0633 \u0645\u06cc \u06af\u06cc\u0631\u062f \u0628\u0633\u06cc\u0627\u0631 \u0628\u0647\u062a\u0631 \u0627\u0632 \u062a\u0635\u0645\u06cc\u0645 \u0647\u0631 \u0627\u0646\u0633\u0627\u0646\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u062f\u0642\u06cc\u0642\u200c\u062a\u0631 \u0628\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u0630\u06a9\u0631 \u06a9\u0631\u062f\u06cc\u0645 \u0628\u06cc\u0627\u0646\u062f\u0627\u0632\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u06cc\u06a9 \u062d\u0631\u06a9\u062a \u062e\u0648\u0628 (\u0646\u0647 \u0644\u0632\u0648\u0645\u0627 \u0628\u0647\u062a\u0631\u06cc\u0646) \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u062e\u0627\u0635\u060c \u0628\u0627\u06cc\u062f \u0628\u0647 \u0646\u062d\u0648\u06cc \u06af\u0631\u0647 \u0647\u0627 (\u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627) \u0631\u0627 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9\u06cc \u0631\u0627 \u0627\u0632 \u0646\u0638\u0631 \u06a9\u06cc\u0641\u06cc\u062a \u0628\u0627 \u062f\u06cc\u06af\u0631\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n<blockquote>\n<p>\u062a\u0627\u0628\u0639 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06cc\u06a9 \u0639\u062f\u062f \u062b\u0627\u0628\u062a \u0627\u0633\u062a \u06a9\u0647 \u0645\u0637\u0627\u0628\u0642 \u0628\u0627 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062e\u0648\u062f \u0628\u0627\u0632\u06cc\u060c \u0628\u0647 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f node (\u0645\u0648\u0642\u0639\u06cc\u062a).<\/p>\n<\/blockquote>\n<p>\u0630\u06a9\u0631 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0646\u0628\u0627\u06cc\u062f \u0645\u062a\u06a9\u06cc \u0628\u0627\u0634\u062f \u0631\u0648\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u06af\u0631\u0647 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0648 \u0646\u0647 \u0645\u0648\u0627\u0631\u062f \u0632\u06cc\u0631.  \u0628\u0627\u06cc\u062f \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0648\u0636\u0639\u06cc\u062a \u0628\u0627\u0632\u06cc \u0648 \u0634\u0631\u0627\u06cc\u0637\u06cc \u0631\u0627 \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u062f\u0631 \u0622\u0646 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u0646\u062f \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u06a9\u0646\u062f.<\/p>\n<p>\u0644\u0627\u0632\u0645 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0627\u0628\u0639 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u062a\u0627 \u062d\u062f \u0627\u0645\u06a9\u0627\u0646 \u062d\u0627\u0648\u06cc \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0645\u0631\u062a\u0628\u0637 \u0628\u0627\u0634\u062f\u060c \u0627\u0645\u0627 \u0631\u0648\u06cc \u0627\u0632 \u0633\u0648\u06cc \u062f\u06cc\u06af\u0631 &#8211; \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u0633\u062a <strong>\u0632\u06cc\u0627\u062f<\/strong> \u0628\u0627\u0631 &#8211; \u0628\u0627\u06cc\u062f \u0633\u0627\u062f\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0645\u062c\u0645\u0648\u0639\u0647 \u062a\u0645\u0627\u0645 \u0645\u0648\u0642\u0639\u06cc\u062a\u200c\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0631\u0627 \u062f\u0631 \u0628\u062e\u0634 \u0645\u062a\u0642\u0627\u0631\u0646 \u062a\u0631\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f:<\/p>\n<p>$$<br \/>\\mathcal{F} : \\mathcal{P} \\rightarrow (-M, M)<br \/>$$<\/p>\n<p>\u0627\u0631\u0632\u0634 <code>M<\/code> \u0641\u0642\u0637 \u0628\u0647 \u0628\u0631\u06af\u0647\u0627\u06cc\u06cc \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0628\u0631\u0646\u062f\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0627\u0633\u062a \u0648 \u0627\u0631\u0632\u0634 \u062f\u0627\u0631\u062f <code>-M<\/code> \u0628\u0647 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0631\u0646\u062f\u0647 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u062f\u0648\u0645 \u0627\u0633\u062a \u062a\u0631\u06a9 \u06a9\u0646\u062f.<\/p>\n<p>\u062f\u0631 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0635\u0641\u0631\u060c \u0645\u0642\u062f\u0627\u0631 \u062a\u0627\u0628\u0639 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0645\u0639\u0646\u0627\u06cc \u0645\u062e\u0627\u0644\u0641 \u062f\u0627\u0631\u062f &#8211; \u0622\u0646\u0686\u0647 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0627\u0648\u0644 \u0628\u0647\u062a\u0631 \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 \u062f\u0648\u0645 \u0628\u062f\u062a\u0631 \u0627\u0633\u062a \u0648 \u0628\u0627\u0644\u0639\u06a9\u0633.  \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u060c \u0645\u0642\u062f\u0627\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc \u0645\u062a\u0642\u0627\u0631\u0646 (\u0627\u06af\u0631 \u0628\u0627\u0632\u06cc\u06a9\u0646\u0627\u0646 \u0646\u0642\u0634 \u0647\u0627 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u0646\u062f) \u0628\u0627\u06cc\u062f \u0641\u0642\u0637 \u0628\u0627 \u0639\u0644\u0627\u0645\u062a \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0627\u0634\u062f.<\/p>\n<p>\u06cc\u06a9 \u0631\u0648\u0634 \u0645\u0639\u0645\u0648\u0644 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc\u200c\u0647\u0627\u06cc \u0628\u0631\u06af\u200c\u0647\u0627 \u0631\u0627 \u0628\u0627 \u06a9\u0645 \u06a9\u0631\u062f\u0646 \u0639\u0645\u0642 \u062f\u0642\u06cc\u0642\u0627\u064b \u0622\u0646 \u0628\u0631\u06af \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f\u060c \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0627\u0632 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645 \u062d\u0631\u06a9\u0627\u062a\u06cc \u06a9\u0647 \u0645\u0646\u062c\u0631 \u0628\u0647 \u067e\u06cc\u0631\u0648\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u062a\u0648\u0627\u0646\u062f \u062d\u0631\u06a9\u062a\u06cc \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062f\u0631 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u0645\u0631\u0627\u062d\u0644 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u062f (\u06cc\u0627 \u062d\u0631\u06a9\u062a\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0647 \u062a\u0639\u0648\u06cc\u0642 \u0645\u06cc\u200c\u0627\u0641\u062a\u062f \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u062f. \u0636\u0631\u0631 \u0627\u06af\u0631 \u0627\u062c\u062a\u0646\u0627\u0628 \u0646\u0627\u067e\u0630\u06cc\u0631 \u0628\u0627\u0634\u062f).<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u062a\u0635\u0648\u06cc\u0631 \u0633\u0627\u062f\u0647 \u0627\u0632 \u0645\u0631\u0627\u062d\u0644 Minimax \u0622\u0648\u0631\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u062d\u062f\u0627\u0642\u0644 \u0645\u0642\u062f\u0627\u0631 \u0647\u0633\u062a\u06cc\u0645.<\/p>\n<p>\u0644\u0627\u06cc\u0647 \u0633\u0628\u0632 \u0631\u0646\u06af \u0631\u0627 \u0641\u0631\u0627 \u0645\u06cc \u062e\u0648\u0627\u0646\u062f <code>Max()<\/code> \u0631\u0648\u0634 \u0631\u0648\u06cc \u06af\u0631\u0647 \u0647\u0627 \u062f\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0641\u0631\u0632\u0646\u062f \u0648 \u0644\u0627\u06cc\u0647 \u0642\u0631\u0645\u0632 \u0631\u0646\u06af \u0631\u0627 \u0641\u0631\u0627 \u0645\u06cc \u062e\u0648\u0627\u0646\u062f <code>Min()<\/code> \u0631\u0648\u0634 \u0631\u0648\u06cc \u06af\u0631\u0647 \u0647\u0627\u06cc \u06a9\u0648\u062f\u06a9<\/p>\n<ol>\n<li>\u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0628\u0631\u06af\u0647\u0627:<\/li>\n<\/ol>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/minimax-and-alpha-beta-pruning-in-python-2.png\" alt=\"\" title=\"\"><\/p>\n<ol start=\"2\">\n<li>\u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0633\u0628\u0632 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0639\u0645\u0642 3:<\/li>\n<\/ol>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/minimax-and-alpha-beta-pruning-in-python-3.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0627\u06cc\u062f\u0647 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0645\u0645\u06a9\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0645\u0639\u06cc\u0646 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f node\u060c \u0639\u0645\u0642 \u0648 \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0641\u0631\u0636 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u06a9\u0647 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0633\u0628\u0632 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062b\u0628\u062a \u0627\u0633\u062a\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0635\u0648\u0631\u062a\u06cc \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u0627\u0631\u0632\u0634 \u0647\u0627\u06cc \u0645\u0646\u0641\u06cc \u0627\u0633\u062a.  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0631 \u062f\u0631\u062c\u0647 \u0627\u0648\u0644 \u0641\u0642\u0637 \u06af\u0631\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0639\u0645\u0642 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0628\u0642\u06cc\u0647 \u0645\u0631\u0627\u062d\u0644 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Recursion_(computer_science)\">\u0628\u0627\u0632\u06af\u0634\u062a\u06cc<\/a>.  \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0642\u06cc\u0647 \u06af\u0631\u0647 \u0647\u0627 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u0645\u0631\u0628\u0648\u0637\u0647 \u0622\u0646\u0647\u0627\u0633\u062a \u0627\u06af\u0631 \u0646\u0648\u0628\u062a \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0633\u0628\u0632 \u0628\u0627\u0634\u062f\u060c \u06cc\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u062d\u062f\u0627\u0642\u0644 \u0645\u0642\u062f\u0627\u0631 \u0627\u06af\u0631 \u0646\u0648\u0628\u062a \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0635\u0648\u0631\u062a\u06cc \u0628\u0627\u0634\u062f.  \u0627\u0631\u0632\u0634 \u062f\u0631 \u0647\u0631 \u06a9\u062f\u0627\u0645 node \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0631\u06a9\u062a \u0628\u0639\u062f\u06cc \u0631\u0627 \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc\u060c \u0641\u0642\u0637 \u06af\u0631\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u06cc\u06a9 \u0639\u0645\u0642 \u062b\u0627\u0628\u062a (\u062f\u0627\u062f\u0647 \u0634\u062f\u0647)\u060c \u0646\u0647 \u0642\u0628\u0644 \u0648 \u0646\u0647 \u0628\u0639\u062f.  \u0627\u06cc\u0646 \u067e\u062f\u06cc\u062f\u0647 \u0627\u063a\u0644\u0628 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Horizon_effect\">\u0627\u062b\u0631 \u0627\u0641\u0642<\/a>.<\/p>\n<h2 id=\"openingbooksandtictactoe\"><span class=\"ez-toc-section\" id=\"%d8%a8%d8%a7%d8%b2_%da%a9%d8%b1%d8%af%d9%86_%da%a9%d8%aa%d8%a7%d8%a8_%d9%87%d8%a7_%d9%88_%d8%aa%db%8c%da%a9_%d8%aa%d8%a7%da%a9\"><\/span>\u0628\u0627\u0632 \u06a9\u0631\u062f\u0646 \u06a9\u062a\u0627\u0628 \u0647\u0627 \u0648 \u062a\u06cc\u06a9 \u062a\u0627\u06a9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc\u06a9\u060c \u0628\u0647 \u062c\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0631\u0646\u0627\u0645\u0647 \u062c\u0633\u062a\u062c\u0648 \u0631\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0646\u062f process \u062f\u0631 \u0647\u0645\u0627\u0646 \u0627\u0628\u062a\u062f\u0627\u06cc \u0628\u0627\u0632\u06cc\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <em>\u0628\u0627\u0632 \u06a9\u0631\u062f\u0646 \u06a9\u062a\u0627\u0628 \u0647\u0627<\/em> &#8211; \u0644\u06cc\u0633\u062a\u06cc \u0627\u0632 \u062d\u0631\u06a9\u0627\u062a \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0648 \u0633\u0627\u0632\u0646\u062f\u0647 \u06a9\u0647 \u0645\u06a9\u0631\u0631 \u0648 \u0633\u0627\u0632\u0646\u062f\u0647 \u0634\u0646\u0627\u062e\u062a\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u06af\u0631 \u0628\u0647 \u062a\u0627\u0628\u0644\u0648 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 \u0647\u0646\u0648\u0632 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u0648\u0636\u0639\u06cc\u062a \u062e\u0648\u062f \u0628\u0627\u0632\u06cc \u0646\u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u060c \u0628\u0627\u0632\u06cc \u062e\u06cc\u0644\u06cc \u0632\u0648\u062f \u0627\u0633\u062a \u0648 \u062a\u0639\u062f\u0627\u062f \u0645\u0648\u0642\u0639\u06cc\u062a\u200c\u0647\u0627\u06cc \u0628\u0627\u0644\u0642\u0648\u0647 \u0622\u0646\u0642\u062f\u0631 \u0632\u06cc\u0627\u062f \u0627\u0633\u062a \u06a9\u0647 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0637\u0648\u0631 \u062e\u0648\u062f\u06a9\u0627\u0631 \u062a\u0635\u0645\u06cc\u0645 \u06af\u0631\u0641\u062a \u06a9\u0647 \u06a9\u062f\u0627\u0645 \u062d\u0631\u06a9\u062a \u0645\u0637\u0645\u0626\u0646\u0627\u064b \u0628\u0647 \u0648\u0636\u0639\u06cc\u062a \u0628\u0627\u0632\u06cc \u0628\u0647\u062a\u0631 (\u06cc\u0627 \u0628\u0631\u0646\u062f\u0647 \u0634\u062f\u0646) \u0645\u0646\u062c\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062d\u0631\u06a9\u062a\u200c\u0647\u0627\u06cc \u0628\u0627\u0644\u0642\u0648\u0647 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0647\u0631 \u0646\u0648\u0628\u062a \u062f\u0648\u0628\u0627\u0631\u0647 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0647\u0645\u06cc\u0634\u0647 \u0645\u0633\u06cc\u0631\u06cc \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0644\u062d\u0638\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc\u200c\u0631\u0633\u062f \u0633\u0631\u06cc\u0639\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0631\u0648\u0632\u06cc \u0628\u0627\u0634\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0627\u0642\u062f\u0627\u0645\u0627\u062a\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062a\u06a9\u0645\u06cc\u0644 \u0622\u0646\u0647\u0627 \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u062d\u0631\u06a9\u062a \u0637\u0648\u0644 \u0645\u06cc\u200c\u06a9\u0634\u062f\u060c \u0627\u062c\u0631\u0627 \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u0648 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0642\u0627\u062f\u0631 \u0628\u0647 \u0627\u0646\u062c\u0627\u0645 \u0628\u0631\u062e\u06cc \u00ab\u062a\u0631\u0641\u0646\u062f\u0647\u0627\u06cc\u00bb \u0634\u0646\u0627\u062e\u062a\u0647\u200c\u0634\u062f\u0647 \u0646\u06cc\u0633\u062a.  \u0627\u06af\u0631 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0639\u0644\u06cc\u0647 \u06cc\u06a9 \u0627\u0646\u0633\u0627\u0646 \u0628\u0627\u0632\u06cc \u06a9\u0646\u062f\u060c \u0628\u0647 \u0627\u062d\u062a\u0645\u0627\u0644 \u0632\u06cc\u0627\u062f \u0627\u0646\u0633\u0627\u0646 \u0647\u0627 \u0641\u0648\u0631\u0627\u064b \u0642\u0627\u062f\u0631 \u0628\u0647 \u062c\u0644\u0648\u06af\u06cc\u0631\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0627\u0645\u0631 \u062e\u0648\u0627\u0647\u0646\u062f \u0628\u0648\u062f.<\/p>\n<p>\u0627\u06af\u0631\u060c \u0631\u0648\u06cc \u0627\u0632 \u0633\u0648\u06cc \u062f\u06cc\u06af\u0631\u060c \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0634\u0637\u0631\u0646\u062c \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645\u060c \u0628\u0647 \u0633\u0631\u0639\u062a \u0645\u062a\u0648\u062c\u0647 \u063a\u06cc\u0631\u0639\u0645\u0644\u06cc \u0628\u0648\u062f\u0646 \u062d\u0644 \u0634\u0637\u0631\u0646\u062c \u0628\u0627 \u0627\u062c\u0628\u0627\u0631 \u0628\u06cc \u0631\u062d\u0645\u0627\u0646\u0647 \u062f\u0631 \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0634\u062f.  \u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u0627\u06cc\u0646\u060c <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Claude_Shannon\">\u06a9\u0644\u0648\u062f \u0634\u0627\u0646\u0648\u0646<\/a> \u062d\u062f \u067e\u0627\u06cc\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06cc \u0634\u0637\u0631\u0646\u062c \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u062f\u0648\u062f <strong>10<sup>120<\/sup> \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0645\u0645\u06a9\u0646<\/strong>.<\/p>\n<p>\u0627\u06cc\u0646 \u0639\u062f\u062f \u0686\u0642\u062f\u0631 \u0627\u0633\u062a\u061f  \u0628\u0631\u0627\u06cc \u0645\u0631\u062c\u0639\u060c \u0627\u06af\u0631 \u062c\u0631\u0645 \u06cc\u06a9 \u0627\u0644\u06a9\u062a\u0631\u0648\u0646 \u0631\u0627 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0646\u06cc\u0645 (10<sup>-30<\/sup>\u06a9\u06cc\u0644\u0648\u06af\u0631\u0645) \u0628\u0647 \u062c\u0631\u0645 <em>\u06a9\u0644 \u062c\u0647\u0627\u0646 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647<\/em> (10<sup>50<\/sup>-10<sup>60<\/sup>\u06a9\u06cc\u0644\u0648\u06af\u0631\u0645)\u060c \u0646\u0633\u0628\u062a \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 10 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f<sup>80<\/sup>-10<sup>90<\/sup>.<\/p>\n<p>\u0627\u06cc\u0646 ~0.00000000000000000000000000000000000000000000000000000000000000000000000000000001\u066a \u0627\u0632 \u0639\u062f\u062f \u0634\u0627\u0646\u0648\u0646 \u0627\u0633\u062a.<\/p>\n<p>\u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0648\u0638\u06cc\u0641\u0647 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u062f <em>\u062a\u06a9 \u062a\u06a9<\/em> \u0627\u0632 \u0622\u0646 \u062a\u0631\u06a9\u06cc\u0628\u0627\u062a \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u06af\u0631\u0641\u062a\u0646 \u06cc\u06a9 \u062a\u0635\u0645\u06cc\u0645 \u0648\u0627\u062d\u062f.  \u0639\u0645\u0644\u0627 \u063a\u06cc\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a.<\/p>\n<p>\u062d\u062a\u06cc \u067e\u0633 \u0627\u0632 10 \u062d\u0631\u06a9\u062a\u060c \u062a\u0639\u062f\u0627\u062f \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u0633\u06cc\u0627\u0631 \u0632\u06cc\u0627\u062f \u0627\u0633\u062a:<\/p>\n<table class=\"table table-striped\" style=\"white-space:nowrap;font-size:15px\">\n<tbody>\n<tr>\n<th>\u062a\u0639\u062f\u0627\u062f \u062d\u0631\u06a9\u0627\u062a<\/th>\n<th>\u062a\u0639\u062f\u0627\u062f \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u0645\u0645\u06a9\u0646<\/th>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>40<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>8902<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>197281<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4,865,609<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>119,060,324<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>3,195,901,860<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>84,998,978,956<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>2,439,530,234,167<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>69,352,859,712,417<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u062a\u06cc\u06a9 \u062a\u0627\u06a9 \u0628\u0628\u0631\u06cc\u0645.  \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u062f\u060c \u0645\u0639\u0631\u0648\u0641 \u062a\u0631\u06cc\u0646 \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 X \u0634\u0631\u0648\u0639 \u062f\u0631 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u06af\u0648\u0634\u0647 \u0647\u0627 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0628\u0627\u0632\u06cc\u06a9\u0646 O \u0628\u06cc\u0634\u062a\u0631\u06cc\u0646 \u0641\u0631\u0635\u062a \u0628\u0631\u0627\u06cc \u0627\u0634\u062a\u0628\u0627\u0647 \u0631\u0627 \u0645\u06cc \u062f\u0647\u062f.  \u0627\u06af\u0631 \u0628\u0627\u0632\u06cc\u06a9\u0646 O \u0628\u0647 \u063a\u06cc\u0631 \u0627\u0632 \u0645\u0631\u06a9\u0632 \u0628\u0627\u0632\u06cc \u06a9\u0646\u062f \u0648 X \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u0627\u0648\u0644\u06cc\u0647 \u062e\u0648\u062f \u0631\u0627 \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u062f\u060c \u0627\u06cc\u0646 \u06cc\u06a9 \u0628\u0631\u062f \u062a\u0636\u0645\u06cc\u0646\u06cc \u0628\u0631\u0627\u06cc X \u0627\u0633\u062a. \u06a9\u062a\u0627\u0628 \u0647\u0627\u06cc \u0627\u0641\u062a\u062a\u0627\u062d\u06cc\u0647 \u062f\u0642\u06cc\u0642\u0627\u064b \u0627\u06cc\u0646 \u0647\u0633\u062a\u0646\u062f &#8211; \u0686\u0646\u062f \u0631\u0627\u0647 \u062e\u0648\u0628 \u0628\u0631\u0627\u06cc \u0641\u0631\u06cc\u0628 \u062f\u0627\u062f\u0646 \u062d\u0631\u06cc\u0641 \u062f\u0631 \u0647\u0645\u0627\u0646 \u0627\u0628\u062a\u062f\u0627 \u0628\u0631\u0627\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0645\u0632\u06cc\u062a\u060c \u06cc\u0627 \u062f\u0631 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a\u060c \u06cc\u06a9 \u0628\u0631\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u062f \u0648 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0647\u0633\u062a\u0647\u200c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u062f\u0631 \u0645\u062b\u0627\u0644 \u0641\u0635\u0644 \u0628\u0639\u062f\u060c \u0645\u0627 \u0627\u0632 \u06a9\u062a\u0627\u0628\u200c\u0647\u0627\u06cc \u0628\u0627\u0632 \u06a9\u0631\u062f\u0646 \u06cc\u0627 \u0647\u06cc\u0686 \u062a\u0631\u0641\u0646\u062f\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0646\u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0627\u0632 \u0647\u0645\u0627\u0646 \u0627\u0628\u062a\u062f\u0627 \u0627\u062c\u0627\u0632\u0647 \u062c\u0633\u062a\u062c\u0648\u06cc \u0645\u06cc\u0646\u06cc\u0645\u06a9\u0633 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062a\u0639\u062c\u0628 \u0646\u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0631\u06af\u0632 \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u06af\u0648\u0634\u0647 \u0631\u0627 \u062a\u0648\u0635\u06cc\u0647 \u0646\u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h2 id=\"minimaximplementationinpython\"><span class=\"ez-toc-section\" id=\"%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_minimax_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Minimax \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u06a9\u062f \u0632\u06cc\u0631\u060c \u0645\u0627 \u0627\u0632 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u06a9\u0647 \u0646\u0633\u0628\u062a\u0627\u064b \u0633\u0627\u062f\u0647 \u0648 \u0631\u0627\u06cc\u062c \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0628\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646\u200c\u0647\u0627 \u0627\u0645\u06a9\u0627\u0646 \u062c\u0633\u062a\u062c\u0648\u06cc \u06a9\u0644 \u062f\u0631\u062e\u062a\u060c \u062a\u0627 \u0628\u0631\u06af\u200c\u0647\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u062f\u0627\u0631\u0627\u06cc 3 \u0645\u0642\u062f\u0627\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a:<\/p>\n<ul>\n<li>-1 \u0627\u06af\u0631 \u0628\u0627\u0632\u06cc\u06a9\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0646\u062f\u0647 \u0627\u0633\u062a<\/li>\n<li>0 \u0627\u06af\u0631 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627\u0634\u062f<\/li>\n<li>1 \u0627\u06af\u0631 \u0628\u0627\u0632\u06cc\u06a9\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0628\u0631\u0646\u062f\u0647 \u0627\u0633\u062a<\/li>\n<\/ul>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 \u0627\u06cc\u0646 \u0631\u0627 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u06cc\u06a9 \u0628\u0627\u0632\u06cc tic-tac-toe \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0644\u0648\u06a9 \u0647\u0627\u06cc \u0633\u0627\u0632\u0646\u062f\u0647 \u0631\u0627 \u0645\u0631\u0648\u0631 \u06a9\u0646\u06cc\u0645.  \u0627\u0628\u062a\u062f\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u0633\u0627\u0632\u0646\u062f\u0647 \u0628\u0633\u0627\u0632\u06cc\u0645 \u0648 \u062a\u0627\u0628\u0644\u0648 \u0631\u0627 \u062a\u0631\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">\n\n\n\n<span class=\"hljs-keyword\">import<\/span> time\n\n<span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">Game<\/span>:<\/span>\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__init__<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        self.initialize_game()\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">initialize_game<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        self.current_state = ((<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>),\n                              (<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>),\n                              (<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>,<span class=\"hljs-string\">'.'<\/span>))\n\n        \n        self.player_turn = <span class=\"hljs-string\">'X'<\/span>\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">draw_board<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'{}|'<\/span>.<span class=\"hljs-built_in\">format<\/span>(self.current_state(i)(j)), end=<span class=\"hljs-string\">\" \"<\/span>)\n            <span class=\"hljs-built_in\">print<\/span>()\n        <span class=\"hljs-built_in\">print<\/span>()\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p>\u0647\u0645\u0647 \u0631\u0648\u0634 \u0647\u0627\u06cc \u0631\u0633\u06cc\u062f\u06af\u06cc \u0628\u0647 \u062c\u0632 \u0631\u0648\u0634 \u0627\u0635\u0644\u06cc \u0645\u062a\u0639\u0644\u0642 \u0628\u0647 <code>Game<\/code> \u06a9\u0644\u0627\u0633<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0645\u0627 \u0635\u062d\u0628\u062a \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 <em>\u062d\u0631\u06a9\u0627\u062a \u0642\u0627\u0646\u0648\u0646\u06cc<\/em> \u062f\u0631 \u0628\u062e\u0634 \u0647\u0627\u06cc \u0627\u0628\u062a\u062f\u0627\u06cc\u06cc \u0645\u0642\u0627\u0644\u0647  \u0628\u0631\u0627\u06cc \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0642\u0648\u0627\u0646\u06cc\u0646 \u0631\u0627 \u0631\u0639\u0627\u06cc\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0628\u0647 \u0631\u0627\u0647\u06cc \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0642\u0627\u0646\u0648\u0646\u06cc \u0628\u0648\u062f\u0646 \u06cc\u06a9 \u062d\u0631\u06a9\u062a \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">is_valid<\/span>(<span class=\"hljs-params\">self, px, py<\/span>):<\/span>\n    <span class=\"hljs-keyword\">if<\/span> px &lt; <span class=\"hljs-number\">0<\/span> <span class=\"hljs-keyword\">or<\/span> px &gt; <span class=\"hljs-number\">2<\/span> <span class=\"hljs-keyword\">or<\/span> py &lt; <span class=\"hljs-number\">0<\/span> <span class=\"hljs-keyword\">or<\/span> py &gt; <span class=\"hljs-number\">2<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">False<\/span>\n    <span class=\"hljs-keyword\">elif<\/span> self.current_state(px)(py) != <span class=\"hljs-string\">'.'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">False<\/span>\n    <span class=\"hljs-keyword\">else<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">True<\/span>\n<\/code><\/pre>\n<p>\u0633\u067e\u0633\u060c \u0645\u0627 \u0628\u0647 \u06cc\u06a9 \u0631\u0627\u0647 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u0628\u0627\u0632\u06cc \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646 \u0631\u0633\u06cc\u062f\u0647 \u0627\u0633\u062a \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.  \u062f\u0631 \u062a\u06cc\u06a9 \u062a\u0627\u06a9\u060c \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u0627\u062a\u0635\u0627\u0644 \u0633\u0647 \u0639\u0644\u0627\u0645\u062a \u0645\u062a\u0648\u0627\u0644\u06cc \u062f\u0631 \u06cc\u06a9 \u062e\u0637 \u0627\u0641\u0642\u06cc\u060c \u0645\u0648\u0631\u0628 \u06cc\u0627 \u0639\u0645\u0648\u062f\u06cc \u0628\u0631\u0646\u062f\u0647 \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">is_end<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n    \n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n        <span class=\"hljs-keyword\">if<\/span> (self.current_state(<span class=\"hljs-number\">0<\/span>)(i) != <span class=\"hljs-string\">'.'<\/span> <span class=\"hljs-keyword\">and<\/span>\n            self.current_state(<span class=\"hljs-number\">0<\/span>)(i) == self.current_state(<span class=\"hljs-number\">1<\/span>)(i) <span class=\"hljs-keyword\">and<\/span>\n            self.current_state(<span class=\"hljs-number\">1<\/span>)(i) == self.current_state(<span class=\"hljs-number\">2<\/span>)(i)):\n            <span class=\"hljs-keyword\">return<\/span> self.current_state(<span class=\"hljs-number\">0<\/span>)(i)\n\n    \n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n        <span class=\"hljs-keyword\">if<\/span> (self.current_state(i) == (<span class=\"hljs-string\">'X'<\/span>, <span class=\"hljs-string\">'X'<\/span>, <span class=\"hljs-string\">'X'<\/span>)):\n            <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-string\">'X'<\/span>\n        <span class=\"hljs-keyword\">elif<\/span> (self.current_state(i) == (<span class=\"hljs-string\">'O'<\/span>, <span class=\"hljs-string\">'O'<\/span>, <span class=\"hljs-string\">'O'<\/span>)):\n            <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-string\">'O'<\/span>\n\n    \n    <span class=\"hljs-keyword\">if<\/span> (self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>) != <span class=\"hljs-string\">'.'<\/span> <span class=\"hljs-keyword\">and<\/span>\n        self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>) == self.current_state(<span class=\"hljs-number\">1<\/span>)(<span class=\"hljs-number\">1<\/span>) <span class=\"hljs-keyword\">and<\/span>\n        self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>) == self.current_state(<span class=\"hljs-number\">2<\/span>)(<span class=\"hljs-number\">2<\/span>)):\n        <span class=\"hljs-keyword\">return<\/span> self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>)\n\n    \n    <span class=\"hljs-keyword\">if<\/span> (self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">2<\/span>) != <span class=\"hljs-string\">'.'<\/span> <span class=\"hljs-keyword\">and<\/span>\n        self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">2<\/span>) == self.current_state(<span class=\"hljs-number\">1<\/span>)(<span class=\"hljs-number\">1<\/span>) <span class=\"hljs-keyword\">and<\/span>\n        self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">2<\/span>) == self.current_state(<span class=\"hljs-number\">2<\/span>)(<span class=\"hljs-number\">0<\/span>)):\n        <span class=\"hljs-keyword\">return<\/span> self.current_state(<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">2<\/span>)\n\n    \n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n        <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            \n            <span class=\"hljs-keyword\">if<\/span> (self.current_state(i)(j) == <span class=\"hljs-string\">'.'<\/span>):\n                <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-literal\">None<\/span>\n\n    \n    <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-string\">'.'<\/span>\n<\/code><\/pre>\n<p>\u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0647 \u0645\u0627 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0622\u0646 \u0628\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u062f\u0648 \u0686\u06cc\u0632 \u0627\u0633\u062a &#8211; \u0628\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0631\u0633\u0627\u0646\u062f\u0646 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062e\u0648\u062f \u0648 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0631\u0633\u0627\u0646\u062f\u0646 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0645\u0627.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0645\u0627 \u06cc\u06a9 <code>max()<\/code> \u0631\u0648\u0634\u06cc \u06a9\u0647 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\u0631\u0627\u06cc \u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<pre><code class=\"hljs\">\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">max<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n\n    \n    \n    \n    \n\n    \n    maxv = -<span class=\"hljs-number\">2<\/span>\n\n    px = <span class=\"hljs-literal\">None<\/span>\n    py = <span class=\"hljs-literal\">None<\/span>\n\n    result = self.is_end()\n\n    \n    \n    \n    \n    \n    <span class=\"hljs-keyword\">if<\/span> result == <span class=\"hljs-string\">'X'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (-<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n    <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'O'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n    <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'.'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n\n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n        <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            <span class=\"hljs-keyword\">if<\/span> self.current_state(i)(j) == <span class=\"hljs-string\">'.'<\/span>:\n                \n                \n                self.current_state(i)(j) = <span class=\"hljs-string\">'O'<\/span>\n                (m, min_i, min_j) = self.<span class=\"hljs-built_in\">min<\/span>()\n                \n                <span class=\"hljs-keyword\">if<\/span> m &gt; maxv:\n                    maxv = m\n                    px = i\n                    py = j\n                \n                self.current_state(i)(j) = <span class=\"hljs-string\">'.'<\/span>\n    <span class=\"hljs-keyword\">return<\/span> (maxv, px, py)\n<\/code><\/pre>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0634\u0627\u0645\u0644 \u06cc\u06a9 <code>min()<\/code> \u0631\u0648\u0634\u06cc \u06a9\u0647 \u0628\u0647 \u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0633\u0627\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">min<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n\n    \n    \n    \n    \n\n    \n    minv = <span class=\"hljs-number\">2<\/span>\n\n    qx = <span class=\"hljs-literal\">None<\/span>\n    qy = <span class=\"hljs-literal\">None<\/span>\n\n    result = self.is_end()\n\n    <span class=\"hljs-keyword\">if<\/span> result == <span class=\"hljs-string\">'X'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (-<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n    <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'O'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n    <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'.'<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n\n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n        <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            <span class=\"hljs-keyword\">if<\/span> self.current_state(i)(j) == <span class=\"hljs-string\">'.'<\/span>:\n                self.current_state(i)(j) = <span class=\"hljs-string\">'X'<\/span>\n                (m, max_i, max_j) = self.<span class=\"hljs-built_in\">max<\/span>()\n                <span class=\"hljs-keyword\">if<\/span> m &lt; minv:\n                    minv = m\n                    qx = i\n                    qy = j\n                self.current_state(i)(j) = <span class=\"hljs-string\">'.'<\/span>\n\n    <span class=\"hljs-keyword\">return<\/span> (minv, qx, qy)\n<\/code><\/pre>\n<p>\u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u062d\u0644\u0642\u0647 \u0628\u0627\u0632\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0645\u0627 \u0627\u0645\u06a9\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\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\">play<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n    <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n        self.draw_board()\n        self.result = self.is_end()\n\n        \n        <span class=\"hljs-keyword\">if<\/span> self.result != <span class=\"hljs-literal\">None<\/span>:\n            <span class=\"hljs-keyword\">if<\/span> self.result == <span class=\"hljs-string\">'X'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The winner is X!'<\/span>)\n            <span class=\"hljs-keyword\">elif<\/span> self.result == <span class=\"hljs-string\">'O'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The winner is O!'<\/span>)\n            <span class=\"hljs-keyword\">elif<\/span> self.result == <span class=\"hljs-string\">'.'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"It's a tie!\"<\/span>)\n\n            self.initialize_game()\n            <span class=\"hljs-keyword\">return<\/span>\n\n        \n        <span class=\"hljs-keyword\">if<\/span> self.player_turn == <span class=\"hljs-string\">'X'<\/span>:\n\n            <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n\n                start = time.time()\n                (m, qx, qy) = self.<span class=\"hljs-built_in\">min<\/span>()\n                end = time.time()\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Evaluation time: {}s'<\/span>.<span class=\"hljs-built_in\">format<\/span>(<span class=\"hljs-built_in\">round<\/span>(end - start, <span class=\"hljs-number\">7<\/span>)))\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Recommended move: X = {}, Y = {}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(qx, qy))\n\n                px = <span class=\"hljs-built_in\">int<\/span>(<span class=\"hljs-built_in\">input<\/span>(<span class=\"hljs-string\">'Insert the X coordinate: '<\/span>))\n                py = <span class=\"hljs-built_in\">int<\/span>(<span class=\"hljs-built_in\">input<\/span>(<span class=\"hljs-string\">'Insert the Y coordinate: '<\/span>))\n\n                (qx, qy) = (px, py)\n\n                <span class=\"hljs-keyword\">if<\/span> self.is_valid(px, py):\n                    self.current_state(px)(py) = <span class=\"hljs-string\">'X'<\/span>\n                    self.player_turn = <span class=\"hljs-string\">'O'<\/span>\n                    <span class=\"hljs-keyword\">break<\/span>\n                <span class=\"hljs-keyword\">else<\/span>:\n                    <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The move is not valid! Try again.'<\/span>)\n\n        \n        <span class=\"hljs-keyword\">else<\/span>:\n            (m, px, py) = self.<span class=\"hljs-built_in\">max<\/span>()\n            self.current_state(px)(py) = <span class=\"hljs-string\">'O'<\/span>\n            self.player_turn = <span class=\"hljs-string\">'X'<\/span>\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627\u0632\u06cc \u0631\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645!<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">main<\/span>():<\/span>\n    g = Game()\n    g.play()\n\n<span class=\"hljs-keyword\">if<\/span> __name__ == <span class=\"hljs-string\">\"__main__\"<\/span>:\n    main()\n<\/code><\/pre>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0646\u06af\u0627\u0647\u06cc \u0645\u06cc \u0627\u0646\u062f\u0627\u0632\u06cc\u0645 \u0628\u0647 \u0627\u06cc\u0646 \u06a9\u0647 \u0648\u0642\u062a\u06cc \u062f\u0646\u0628\u0627\u0644\u0647 \u0686\u0631\u062e\u0634 \u0647\u0627\u06cc \u062a\u0648\u0635\u06cc\u0647 \u0634\u062f\u0647 \u0631\u0627 \u062f\u0646\u0628\u0627\u0644 \u06a9\u0646\u06cc\u0645 \u0686\u0647 \u0627\u062a\u0641\u0627\u0642\u06cc \u0645\u06cc \u0627\u0641\u062a\u062f &#8211; \u06cc\u0639\u0646\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0628\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">.| .| .|\n.| .| .|\n.| .| .|\n\nEvaluation time: 5.0726919s\nRecommended move: X = 0, Y = 0\nInsert the X coordinate: 0\nInsert the Y coordinate: 0\nX| .| .|\n.| .| .|\n.| .| .|\n\nX| .| .|\n.| O| .|\n.| .| .|\n\nEvaluation time: 0.06496s\nRecommended move: X = 0, Y = 1\nInsert the X coordinate: 0\nInsert the Y coordinate: 1\nX| X| .|\n.| O| .|\n.| .| .|\n\nX| X| O|\n.| O| .|\n.| .| .|\n\nEvaluation time: 0.0020001s\nRecommended move: X = 2, Y = 0\nInsert the X coordinate: 2\nInsert the Y coordinate: 0\nX| X| O|\n.| O| .|\nX| .| .|\n\nX| X| O|\nO| O| .|\nX| .| .|\n\nEvaluation time: 0.0s\nRecommended move: X = 1, Y = 2\nInsert the X coordinate: 1\nInsert the Y coordinate: 2\nX| X| O|\nO| O| X|\nX| .| .|\n\nX| X| O|\nO| O| X|\nX| O| .|\n\nEvaluation time: 0.0s\nRecommended move: X = 2, Y = 2\nInsert the X coordinate: 2\nInsert the Y coordinate: 2\nX| X| O|\nO| O| X|\nX| O| X|\n\nIt's a tie!\n<\/code><\/pre>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u062f\u060c \u067e\u06cc\u0631\u0648\u0632\u06cc \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u063a\u06cc\u0631\u0645\u0645\u06a9\u0646 \u0627\u0633\u062a.  \u0627\u06af\u0631 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0645 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0648 \u0647\u0645 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\u0647 \u062e\u0648\u0628\u06cc \u0628\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0628\u0627\u0632\u06cc \u0647\u0645\u06cc\u0634\u0647 \u0645\u0633\u0627\u0648\u06cc \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0647\u0645\u06cc\u0634\u0647 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u062f\u060c \u0627\u06af\u0631 \u0644\u063a\u0632\u0634 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u0632\u0646\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0648\u062f.<\/p>\n<p>\u0628\u0647 \u0632\u0645\u0627\u0646 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u062f\u0642\u062a \u06a9\u0646\u06cc\u062f\u060c \u0632\u06cc\u0631\u0627 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0628\u0639\u062f\u06cc \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0646\u0633\u062e\u0647 \u0628\u0647\u0628\u0648\u062f \u06cc\u0627\u0641\u062a\u0647 \u0628\u0639\u062f\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0642\u0627\u06cc\u0633\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<h2 id=\"alphabetapruning\"><span class=\"ez-toc-section\" id=\"%d9%87%d8%b1%d8%b3_%d8%a2%d9%84%d9%81%d8%a7_%d8%a8%d8%aa%d8%a7\"><\/span>\u0647\u0631\u0633 \u0622\u0644\u0641\u0627 \u0628\u062a\u0627<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u0622\u0644\u0641\u0627\u2013\u0628\u062a\u0627 (\ud835\udefc\u2212\ud835\udefd)<\/strong> \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0633\u062a\u0642\u0644 \u062a\u0648\u0633\u0637 \u0686\u0646\u062f \u0645\u062d\u0642\u0642 \u062f\u0631 \u0627\u0648\u0627\u0633\u0637 \u062f\u0647\u0647 1900 \u06a9\u0634\u0641 \u0634\u062f.  \u0622\u0644\u0641\u0627-\u0628\u062a\u0627 \u062f\u0631 \u0648\u0627\u0642\u0639 \u06cc\u06a9 \u0645\u06cc\u0646\u06cc\u0645\u06a9\u0633 \u0628\u0647\u0628\u0648\u062f \u06cc\u0627\u0641\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0627\u0633\u062a.  \u0648\u0642\u062a\u06cc \u0645\u0637\u0645\u0626\u0646 \u0634\u0648\u062f \u06a9\u0647 \u062d\u0631\u06a9\u062a\u06cc \u0628\u062f\u062a\u0631 \u0627\u0632 \u062d\u0631\u06a9\u062a\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a\u060c \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0622\u0646 \u0631\u0627 \u0645\u062a\u0648\u0642\u0641 \u0645\u06cc \u06a9\u0646\u062f.  \u0686\u0646\u06cc\u0646 \u062d\u0631\u06a9\u0627\u062a\u06cc \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0628\u06cc\u0634\u062a\u0631 \u0646\u062f\u0627\u0631\u062f.<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0633\u0627\u062f\u0647 \u0645\u06cc\u0646\u06cc\u200c\u0645\u06a9\u0633 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0647\u0645\u0627\u0646 \u062e\u0631\u0648\u062c\u06cc \u0631\u0627 \u0645\u06cc\u200c\u062f\u0647\u062f\u060c \u0627\u0645\u0627 \u0634\u0627\u062e\u0647\u200c\u0647\u0627\u06cc \u062e\u0627\u0635\u06cc \u0631\u0627 \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0631 \u062a\u0635\u0645\u06cc\u0645 \u0646\u0647\u0627\u06cc\u06cc \u062a\u0623\u062b\u06cc\u0631 \u0628\u06af\u0630\u0627\u0631\u062f\u060c \u0642\u0637\u0639 \u0645\u06cc\u200c\u06a9\u0646\u062f &#8211; \u0639\u0645\u0644\u06a9\u0631\u062f \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u0628\u0647\u0628\u0648\u062f \u0645\u06cc\u200c\u0628\u062e\u0634\u062f.<\/p>\n<p>\u0645\u0641\u0647\u0648\u0645 \u0627\u0635\u0644\u06cc \u062d\u0641\u0638 \u062f\u0648 \u0645\u0642\u062f\u0627\u0631 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u06a9\u0644 \u062c\u0633\u062a\u062c\u0648 \u0627\u0633\u062a:<\/p>\n<ul>\n<li><strong>\u0622\u0644\u0641\u0627<\/strong>: \u0628\u0647\u062a\u0631\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647 \u0642\u0628\u0644\u0627\u064b \u0628\u0631\u0631\u0633\u06cc \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 Max<\/li>\n<li><strong>\u0628\u062a\u0627<\/strong>: \u0628\u0647\u062a\u0631\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647 \u0642\u0628\u0644\u0627\u064b \u0628\u0631\u0631\u0633\u06cc \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u06a9\u0646 Min<\/li>\n<\/ul>\n<p>\u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u060c \u0622\u0644\u0641\u0627 \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a \u0645\u0646\u0641\u06cc \u0648 \u0628\u062a\u0627 \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a \u0645\u062b\u0628\u062a \u0627\u0633\u062a\u060c \u06cc\u0639\u0646\u06cc \u062f\u0631 \u06a9\u062f \u0645\u0627 \u0627\u0632 \u0628\u062f\u062a\u0631\u06cc\u0646 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0627\u06af\u0631 \u0631\u0648\u0634 \u0622\u0644\u0641\u0627-\u0628\u062a\u0627 \u0631\u0627 \u0627\u0639\u0645\u0627\u0644 \u06a9\u0646\u06cc\u0645\u060c \u062f\u0631\u062e\u062a \u0642\u0628\u0644\u06cc \u0686\u06af\u0648\u0646\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\/minimax-and-alpha-beta-pruning-in-python-4.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u062c\u0633\u062a\u062c\u0648 \u0628\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0645\u0646\u0637\u0642\u0647 \u062e\u0627\u06a9\u0633\u062a\u0631\u06cc (8) \u0645\u06cc \u0631\u0633\u062f\u060c \u0628\u0647\u062a\u0631\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647 \u0641\u0639\u0644\u06cc (\u0628\u0627 \u062d\u062f\u0627\u0642\u0644 \u0645\u0642\u062f\u0627\u0631) \u0631\u0627 \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u062f\u0631 \u0645\u0633\u06cc\u0631 \u06a9\u0627\u0648\u0634 \u0634\u062f\u0647 \u0627\u0633\u062a \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0645\u06cc\u0646\u0647 \u06a9\u0646\u0646\u062f\u0647 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0644\u062d\u0638\u0647 7 \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 8 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 7 \u0627\u0633\u062a\u060c \u0645\u0627 \u0627\u062c\u0627\u0632\u0647 \u062f\u0627\u0631\u0646\u062f \u062a\u0645\u0627\u0645 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u0628\u0639\u062f\u06cc \u0631\u0627 \u0642\u0637\u0639 \u06a9\u0646\u0646\u062f node \u0645\u0627 \u062f\u0631 \u062d\u0627\u0644 \u0647\u0633\u062a\u06cc\u0645 (\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0647\u06cc\u0686 \u06a9\u062f\u0627\u0645 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f)\u060c \u0632\u06cc\u0631\u0627 \u0627\u06af\u0631 \u0622\u0646 \u062d\u0631\u06a9\u062a \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645\u060c \u062d\u0631\u06cc\u0641 \u062d\u0631\u06a9\u062a\u06cc \u0628\u0627 \u0627\u0631\u0632\u0634 8 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0627 \u0628\u062f\u062a\u0631 \u0627\u0632 \u0647\u0631 \u062d\u0631\u06a9\u062a \u0645\u0645\u06a9\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062d\u0631\u06cc\u0641 \u0645\u06cc \u062a\u0648\u0627\u0646\u0633\u062a \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u062f \u0627\u06af\u0631 \u0645\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0627\u062f\u06cc\u0645. \u06cc\u06a9 \u062d\u0631\u06a9\u062a \u062f\u06cc\u06af\u0631<\/p>\n<p>\u0645\u062b\u0627\u0644 \u0628\u0647\u062a\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0632\u0645\u0627\u0646\u06cc \u0628\u0627\u0634\u062f \u06a9\u0647 \u0646\u0648\u0628\u062a \u0628\u0647 \u0631\u0646\u06af \u062e\u0627\u06a9\u0633\u062a\u0631\u06cc \u0628\u0639\u062f\u06cc \u0645\u06cc \u0631\u0633\u062f.  \u0628\u0647 \u06af\u0631\u0647 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0645\u0642\u062f\u0627\u0631 -9 \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f.  \u062f\u0631 \u0622\u0646 \u0646\u0642\u0637\u0647\u060c \u0628\u0647\u062a\u0631\u06cc\u0646 (\u0628\u0627 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u0642\u062f\u0627\u0631) \u06af\u0632\u06cc\u0646\u0647 \u06a9\u0627\u0648\u0634 \u0634\u062f\u0647 \u062f\u0631 \u0637\u0648\u0644 \u0645\u0633\u06cc\u0631 \u0628\u0631\u0627\u06cc \u0645\u0627\u06a9\u0632\u06cc\u0645\u0627\u06cc\u0632\u0631 -4 \u0627\u0633\u062a.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 -9 \u06a9\u0645\u062a\u0631 \u0627\u0632 -4 \u0627\u0633\u062a\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062a\u0645\u0627\u0645 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0642\u0637\u0639 \u06a9\u0646\u06cc\u0645 node \u0645\u0627 \u062f\u0631<\/p>\n<p>\u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0647 \u0645\u0627 \u0627\u06cc\u0646 \u0627\u0645\u06a9\u0627\u0646 \u0631\u0627 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0634\u0627\u062e\u0647\u200c\u0647\u0627 \u0631\u0627 \u0646\u0627\u062f\u06cc\u062f\u0647 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0627\u0631\u0632\u0634\u200c\u0647\u0627\u06cc\u06cc \u0645\u0646\u062a\u0647\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u0647\u06cc\u0686 \u06a9\u0645\u06a9\u06cc \u0628\u0647 \u062a\u0635\u0645\u06cc\u0645 \u0645\u0627 \u0646\u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0648 \u0628\u0647 \u0647\u06cc\u0686 \u0648\u062c\u0647 \u0628\u0631 \u0622\u0646 \u062a\u0623\u062b\u06cc\u0631 \u0646\u0645\u06cc\u200c\u06af\u0630\u0627\u0631\u0646\u062f.<\/p>\n<p>\u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0622\u0646\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0627\u0635\u0644\u0627\u062d \u06a9\u0646\u06cc\u0645 <code>min()<\/code> \u0648 <code>max()<\/code> \u0631\u0648\u0634 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">max_alpha_beta<\/span>(<span class=\"hljs-params\">self, alpha, beta<\/span>):<\/span>\n        maxv = -<span class=\"hljs-number\">2<\/span>\n        px = <span class=\"hljs-literal\">None<\/span>\n        py = <span class=\"hljs-literal\">None<\/span>\n\n        result = self.is_end()\n\n        <span class=\"hljs-keyword\">if<\/span> result == <span class=\"hljs-string\">'X'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (-<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n        <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'O'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n        <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'.'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n\n        <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n                <span class=\"hljs-keyword\">if<\/span> self.current_state(i)(j) == <span class=\"hljs-string\">'.'<\/span>:\n                    self.current_state(i)(j) = <span class=\"hljs-string\">'O'<\/span>\n                    (m, min_i, in_j) = self.min_alpha_beta(alpha, beta)\n                    <span class=\"hljs-keyword\">if<\/span> m &gt; maxv:\n                        maxv = m\n                        px = i\n                        py = j\n                    self.current_state(i)(j) = <span class=\"hljs-string\">'.'<\/span>\n\n                    \n                    <span class=\"hljs-keyword\">if<\/span> maxv &gt;= beta:\n                        <span class=\"hljs-keyword\">return<\/span> (maxv, px, py)\n\n                    <span class=\"hljs-keyword\">if<\/span> maxv &gt; alpha:\n                        alpha = maxv\n\n        <span class=\"hljs-keyword\">return<\/span> (maxv, px, py)\n<\/code><\/pre>\n<pre><code class=\"hljs\"> <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">min_alpha_beta<\/span>(<span class=\"hljs-params\">self, alpha, beta<\/span>):<\/span>\n\n        minv = <span class=\"hljs-number\">2<\/span>\n\n        qx = <span class=\"hljs-literal\">None<\/span>\n        qy = <span class=\"hljs-literal\">None<\/span>\n\n        result = self.is_end()\n\n        <span class=\"hljs-keyword\">if<\/span> result == <span class=\"hljs-string\">'X'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (-<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n        <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'O'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n        <span class=\"hljs-keyword\">elif<\/span> result == <span class=\"hljs-string\">'.'<\/span>:\n            <span class=\"hljs-keyword\">return<\/span> (<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n\n        <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n            <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">3<\/span>):\n                <span class=\"hljs-keyword\">if<\/span> self.current_state(i)(j) == <span class=\"hljs-string\">'.'<\/span>:\n                    self.current_state(i)(j) = <span class=\"hljs-string\">'X'<\/span>\n                    (m, max_i, max_j) = self.max_alpha_beta(alpha, beta)\n                    <span class=\"hljs-keyword\">if<\/span> m &lt; minv:\n                        minv = m\n                        qx = i\n                        qy = j\n                    self.current_state(i)(j) = <span class=\"hljs-string\">'.'<\/span>\n\n                    <span class=\"hljs-keyword\">if<\/span> minv &lt;= alpha:\n                        <span class=\"hljs-keyword\">return<\/span> (minv, qx, qy)\n\n                    <span class=\"hljs-keyword\">if<\/span> minv &lt; beta:\n                        beta = minv\n\n        <span class=\"hljs-keyword\">return<\/span> (minv, qx, qy)\n<\/code><\/pre>\n<p>\u0648 \u062d\u0627\u0644\u0627\u060c \u062d\u0644\u0642\u0647 \u0628\u0627\u0632\u06cc:<\/p>\n<pre><code class=\"hljs\">  <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">play_alpha_beta<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n     <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n        self.draw_board()\n        self.result = self.is_end()\n\n        <span class=\"hljs-keyword\">if<\/span> self.result != <span class=\"hljs-literal\">None<\/span>:\n            <span class=\"hljs-keyword\">if<\/span> self.result == <span class=\"hljs-string\">'X'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The winner is X!'<\/span>)\n            <span class=\"hljs-keyword\">elif<\/span> self.result == <span class=\"hljs-string\">'O'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The winner is O!'<\/span>)\n            <span class=\"hljs-keyword\">elif<\/span> self.result == <span class=\"hljs-string\">'.'<\/span>:\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"It's a tie!\"<\/span>)\n\n\n            self.initialize_game()\n            <span class=\"hljs-keyword\">return<\/span>\n\n        <span class=\"hljs-keyword\">if<\/span> self.player_turn == <span class=\"hljs-string\">'X'<\/span>:\n\n            <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n                start = time.time()\n                (m, qx, qy) = self.min_alpha_beta(-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>)\n                end = time.time()\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Evaluation time: {}s'<\/span>.<span class=\"hljs-built_in\">format<\/span>(<span class=\"hljs-built_in\">round<\/span>(end - start, <span class=\"hljs-number\">7<\/span>)))\n                <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Recommended move: X = {}, Y = {}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(qx, qy))\n\n                px = <span class=\"hljs-built_in\">int<\/span>(<span class=\"hljs-built_in\">input<\/span>(<span class=\"hljs-string\">'Insert the X coordinate: '<\/span>))\n                py = <span class=\"hljs-built_in\">int<\/span>(<span class=\"hljs-built_in\">input<\/span>(<span class=\"hljs-string\">'Insert the Y coordinate: '<\/span>))\n\n                qx = px\n                qy = py\n\n                <span class=\"hljs-keyword\">if<\/span> self.is_valid(px, py):\n                    self.current_state(px)(py) = <span class=\"hljs-string\">'X'<\/span>\n                    self.player_turn = <span class=\"hljs-string\">'O'<\/span>\n                    <span class=\"hljs-keyword\">break<\/span>\n                <span class=\"hljs-keyword\">else<\/span>:\n                    <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'The move is not valid! Try again.'<\/span>)\n\n        <span class=\"hljs-keyword\">else<\/span>:\n            (m, px, py) = self.max_alpha_beta(-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>)\n            self.current_state(px)(py) = <span class=\"hljs-string\">'O'<\/span>\n            self.player_turn = <span class=\"hljs-string\">'X'<\/span>\n<\/code><\/pre>\n<p>\u0627\u0646\u062c\u0627\u0645 \u0628\u0627\u0632\u06cc \u0645\u0627\u0646\u0646\u062f \u0642\u0628\u0644 \u0627\u0633\u062a\u060c \u0627\u06af\u0631\u0686\u0647 \u0627\u06af\u0631 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0628\u0647\u06cc\u0646\u0647 \u062a\u0648\u0633\u0637 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645\u060c \u06cc\u06a9 \u062a\u0641\u0627\u0648\u062a \u0628\u0632\u0631\u06af \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">.| .| .|\n.| .| .|\n.| .| .|\n\nEvaluation time: 0.1688969s\nRecommended move: X = 0, Y = 0\n\n\nEvaluation time: 0.0069957s\nRecommended move: X = 0, Y = 1\n\n\nEvaluation time: 0.0009975s\nRecommended move: X = 2, Y = 0\n\n\nEvaluation time: 0.0s\nRecommended move: X = 1, Y = 2\n\n\nEvaluation time: 0.0s\nRecommended move: X = 2, Y = 2\n\nIt's a tie!\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0686\u0646\u062f \u0628\u0627\u0631 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0648 \u0634\u0631\u0648\u0639 \u0628\u0631\u0646\u0627\u0645\u0647 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627\u060c \u0646\u062a\u0627\u06cc\u062c \u0645\u0642\u0627\u06cc\u0633\u0647 \u062f\u0631 \u062c\u062f\u0648\u0644 \u0632\u06cc\u0631 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<table class=\"table table-striped\" style=\"white-space:nowrap;font-size:15px\">\n<tbody>\n<tr>\n<th>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645<\/th>\n<th>\u062d\u062f\u0627\u0642\u0644 \u0632\u0645\u0627\u0646<\/th>\n<th>\u062d\u062f\u0627\u06a9\u062b\u0631 \u0632\u0645\u0627\u0646<\/th>\n<\/tr>\n<tr>\n<td>Minimax<\/td>\n<td>4.57 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>5.34 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<\/tr>\n<tr>\n<td>\u0647\u0631\u0633 \u0622\u0644\u0641\u0627 \u0628\u062a\u0627<\/td>\n<td>0.16 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>0.2 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 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><\/h2>\n<p>\u0647\u0631\u0633 \u0622\u0644\u0641\u0627 \u0628\u062a\u0627 \u062a\u0641\u0627\u0648\u062a \u0639\u0645\u062f\u0647 \u0627\u06cc \u062f\u0631 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u062f\u0631\u062e\u062a\u0627\u0646 \u0628\u0627\u0632\u06cc \u0628\u0632\u0631\u06af \u0648 \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f.  \u062d\u062a\u06cc \u0627\u06af\u0631 tic-tac-toe \u062e\u0648\u062f \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u0633\u0627\u062f\u0647 \u0627\u0633\u062a\u060c \u0647\u0646\u0648\u0632 \u0647\u0645 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u062a\u0648\u062c\u0647 \u0634\u0648\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0628\u062f\u0648\u0646 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0622\u0644\u0641\u0627-\u0628\u062a\u0627\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0632\u0645\u0627\u0646 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0635\u06cc\u0647 \u062d\u0631\u06a9\u062a \u062f\u0631 \u0646\u0648\u0628\u062a \u0627\u0648\u0644 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/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>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-20 19:55:04<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;16098&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;Minimax \u0628\u0627 \u0647\u0631\u0633 \u0622\u0644\u0641\u0627-\u0628\u062a\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646&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\"> 13<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062f\u0631 \u0627\u0648\u0627\u062e\u0631 \u062f\u0647\u0647 1920 \u062c\u0627\u0646 \u0641\u0648\u0646 \u0646\u0648\u06cc\u0645\u0627\u0646 \u0645\u0634\u06a9\u0644 \u0627\u0635\u0644\u06cc \u062f\u0631 \u062a\u0626\u0648\u0631\u06cc \u0628\u0627\u0632\u06cc\u200c\u0647\u0627 \u0631\u0627 \u06a9\u0647 \u062a\u0627 \u0628\u0647 \u0627\u0645\u0631\u0648\u0632 \u0645\u0637\u0631\u062d \u0627\u0633\u062a\u060c \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f: \u0628\u0627\u0632\u06cc\u06a9\u0646\u0627\u0646 \u0627\u06331\u060c \u06332\u060c &#8230;\u060c \u0633n \u062f\u0631 \u062d\u0627\u0644 \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u0628\u0627\u0632\u06cc G. \u0628\u0627\u0632\u06cc\u06a9\u0646 \u0628\u0627\u06cc\u062f \u06a9\u062f\u0627\u0645 \u062d\u0631\u06a9\u062a \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u062f\u0645\u062a\u0631 \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0645\u0645\u06a9\u0646 \u0628\u0627\u0632\u06cc \u06a9\u0646\u06cc\u062f\u061f \u0627\u0646\u062f\u06a9\u06cc \u067e\u0633 \u0627\u0632 \u0622\u0646\u060c \u0645\u0634\u06a9\u0644\u0627\u062a\u06cc \u0627\u0632 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