{"id":16346,"date":"2024-01-23T21:14:27","date_gmt":"2024-01-23T17:44:27","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-23T21:14:27","modified_gmt":"2024-01-23T17:44:27","slug":"%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%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\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\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-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%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-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%ad%d8%a8%d8%a7%d8%a8\" >\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c\" >\u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%b1%d8%ac\" >\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d9%be%d8%b4%d8%aa%d9%87\" >\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u067e\u0634\u062a\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%d8%af%d8%ba%d8%a7%d9%85_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c\" >\u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%b3%d8%b1%db%8c%d8%b9\" >\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%a7%d8%ae%d9%84%db%8c_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u062a\u0648\u0627\u0628\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0627\u062e\u0644\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d9%82%d8%a7%db%8c%d8%b3%d9%87_%d8%b3%d8%b1%d8%b9%d8%aa\" >\u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0631\u0639\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85-%d9%87%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\"> 10<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h3 id=\"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><\/h3>\n<p>\u06af\u0627\u0647\u06cc \u0627\u0648\u0642\u0627\u062a\u060c \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u0628\u0631\u0646\u0627\u0645\u0647 \u0630\u062e\u06cc\u0631\u0647 \u06cc\u0627 \u0628\u0627\u0632\u06cc\u0627\u0628\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u062a\u0631\u062a\u06cc\u0628 \u06a9\u0645\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f \u06cc\u0627 \u0627\u0635\u0644\u0627\u064b \u0633\u0641\u0627\u0631\u0634\u06cc \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f.  \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u062c\u0628\u0648\u0631 \u0634\u0648\u06cc\u0645 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645 process \u06cc\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.  \u062f\u0631 \u0637\u0648\u0644 \u0633\u0627\u0644\u200c\u0647\u0627\u060c \u062f\u0627\u0646\u0634\u0645\u0646\u062f\u0627\u0646 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0628\u0631\u0627\u06cc \u0633\u0627\u0632\u0645\u0627\u0646\u200c\u062f\u0647\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u0647\u200c\u0627\u0646\u062f.<\/p>\n<blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0645\u062d\u0628\u0648\u0628 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a\u060c \u0631\u0648\u0634 \u06a9\u0627\u0631 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631\u06a9 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u06a9\u062f\u0646\u0648\u06cc\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0628\u0627 \u0686\u0647 \u0633\u0631\u0639\u062a\u06cc \u0645\u0648\u0627\u0631\u062f \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u0646\u062f.<\/p>\n<\/blockquote>\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><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc\u060c \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u06cc\u062f \u0641\u0647\u0631\u0633\u062a \u0627\u0639\u062f\u0627\u062f \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0635\u0639\u0648\u062f\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0646\u062f.  \u0627\u0644\u0628\u062a\u0647\u060c \u0634\u0645\u0627 \u0622\u0632\u0627\u062f\u06cc\u062f \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0646\u06cc\u0627\u0632\u0647\u0627\u06cc \u062e\u0648\u062f \u062a\u0637\u0628\u06cc\u0642 \u062f\u0647\u06cc\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"bubblesort\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%ad%d8%a8%d8%a7%d8%a8\"><\/span>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0633\u0627\u062f\u0647 \u0631\u0648\u06cc \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062c\u0641\u062a\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0639\u0648\u0636 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0639\u0646\u0627\u0635\u0631 \u0628\u0632\u0631\u06af\u200c\u062a\u0631 \u062a\u0627 \u0627\u0646\u062a\u0647\u0627\u06cc \u0644\u06cc\u0633\u062a \u00ab\u062d\u0628\u0627\u0628\u00bb \u0634\u0648\u0646\u062f \u0648 \u0639\u0646\u0627\u0635\u0631 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631 \u062f\u0631 \u00ab\u067e\u0627\u06cc\u06cc\u0646\u00bb \u0628\u0627\u0642\u06cc \u0628\u0645\u0627\u0646\u0646\u062f.<\/p>\n<h4 id=\"howdoesbubblesortwork\">\u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628\u06cc \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f\u061f<\/h4>\n<p>\u0645\u0627 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0645\u0642\u0627\u06cc\u0633\u0647 \u062f\u0648 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644<\/em> \u0627\u0632 \u0644\u06cc\u0633\u062a  \u0627\u06af\u0631 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0639\u0646\u0635\u0631 \u062f\u0648\u0645 \u0628\u0627\u0634\u062f\u060c \u0645\u0627 swap \u0622\u0646\u0647\u0627  \u0627\u06af\u0631 \u0622\u0646\u0647\u0627 \u0627\u0632 \u0642\u0628\u0644 \u0645\u0631\u062a\u0628 \u0647\u0633\u062a\u0646\u062f \u0622\u0646\u0647\u0627 \u0631\u0627 \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0647\u0633\u062a\u0646\u062f \u0631\u0647\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0633\u067e\u0633 \u0628\u0647 \u062c\u0641\u062a \u0639\u0646\u0635\u0631 \u0628\u0639\u062f\u06cc \u0645\u06cc \u0631\u0648\u06cc\u0645\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 swap \u062a\u0627 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0644\u0627\u0632\u0645 \u0627\u0633\u062a.  \u0627\u06cc\u0646 process \u062a\u0627 \u0622\u062e\u0631\u06cc\u0646 \u062c\u0641\u062a \u0627\u0632 \u0622\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0644\u06cc\u0633\u062a \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc \u06cc\u0627\u0628\u062f.<\/p>\n<p>\u067e\u0633 \u0627\u0632 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0627\u0646\u062a\u0647\u0627\u06cc \u0644\u06cc\u0633\u062a\u060c \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f process \u0628\u0631\u0627\u06cc \u0647\u0631 \u0645\u0648\u0631\u062f  \u0627\u06af\u0631\u0686\u0647\u060c \u0627\u06cc\u0646 \u0627\u0633\u062a <em>\u0628\u0633\u06cc\u0627\u0631 \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f<\/em>.  \u0686\u0647 \u0645\u06cc \u0634\u0648\u062f \u0627\u06af\u0631 \u0641\u0642\u0637 \u06cc\u06a9 \u0645\u062c\u0631\u062f swap \u0628\u0627\u06cc\u062f \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0633\u0627\u062e\u062a\u0647 \u0634\u0648\u062f\u061f  \u0686\u0631\u0627 \u0647\u0646\u0648\u0632 \u0628\u0627\u06cc\u062f \\(n^{2}\\) \u0628\u0627\u0631 \u0622\u0646 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645\u060c \u062d\u062a\u06cc \u0627\u06af\u0631 \u0642\u0628\u0644\u0627 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a\u061f<\/p>\n<p>\u0628\u062f\u06cc\u0647\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0628\u0627\u06cc\u062f \u067e\u0633 \u0627\u0632 \u0627\u062a\u0645\u0627\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc\u060c \u0622\u0646 \u0631\u0627 \u0645\u062a\u0648\u0642\u0641 \u06a9\u0646\u06cc\u0645\u060c \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a\u060c \u0622\u0631\u0627\u06cc\u0647\u200c\u0627\u06cc \u06a9\u0647 \u0642\u0628\u0644\u0627 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647\u200c\u0627\u0646\u062f \u0631\u0627 \u0628\u0627\u0631\u0647\u0627 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<p>\u0686\u06af\u0648\u0646\u0647 \u0628\u0641\u0647\u0645\u06cc\u0645 \u06a9\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0631\u0627 \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646 \u0631\u0633\u0627\u0646\u062f\u0647 \u0627\u06cc\u0645\u061f  \u0627\u06af\u0631 \u0627\u0642\u0644\u0627\u0645 \u0645\u0631\u062a\u0628 \u0628\u0648\u062f\u0646\u062f\u060c \u0645\u062c\u0628\u0648\u0631 \u0646\u0628\u0648\u062f\u06cc\u0645 swap \u0647\u0631  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u0645\u0627 swap \u0645\u0642\u0627\u062f\u06cc\u0631\u06cc \u06a9\u0647 \u06cc\u06a9 \u067e\u0631\u0686\u0645 \u0631\u0627 \u0631\u0648\u06cc \u0622\u0646\u0647\u0627 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645 <code>True<\/code> \u0628\u0631\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc process.  \u0627\u06af\u0631 \u0645\u0628\u0627\u062f\u0644\u0647 \u0627\u06cc \u0631\u062e \u0646\u062f\u0627\u062f\u060c \u067e\u0631\u0686\u0645 \u0628\u0627\u0642\u06cc \u0645\u06cc \u0645\u0627\u0646\u062f <code>False<\/code> \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u062a\u0648\u0642\u0641 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h4 id=\"howtoimplementbubblesortinpython\">\u0686\u06af\u0648\u0646\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628 \u0631\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645\u061f<\/h4>\n<p>\u0628\u0627 \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628 \u0631\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">bubble_sort<\/span>(<span class=\"hljs-params\">nums<\/span>):<\/span>\n    \n    swapped = <span class=\"hljs-literal\">True<\/span>\n    <span class=\"hljs-keyword\">while<\/span> swapped:\n        swapped = <span class=\"hljs-literal\">False<\/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-built_in\">len<\/span>(nums) - <span class=\"hljs-number\">1<\/span>):\n            <span class=\"hljs-keyword\">if<\/span> nums(i) &gt; nums(i + <span class=\"hljs-number\">1<\/span>):\n                \n                nums(i), nums(i + <span class=\"hljs-number\">1<\/span>) = nums(i + <span class=\"hljs-number\">1<\/span>), nums(i)\n                \n                swapped = <span class=\"hljs-literal\">True<\/span>\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">4<\/span>)\nbubble_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062f\u0631 a \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f <code>while<\/code> \u062d\u0644\u0642\u0647\u060c \u062a\u0646\u0647\u0627 \u0632\u0645\u0627\u0646\u06cc \u0634\u06a9\u0633\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0647\u06cc\u0686 \u0645\u0648\u0631\u062f\u06cc \u0645\u0628\u0627\u062f\u0644\u0647 \u0646\u0634\u0648\u062f.  \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0631\u062f\u06cc\u0645 <code>swapped<\/code> \u0628\u0647 <code>True<\/code> \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0637\u0645\u0626\u0646 \u0634\u0648\u06cc\u062f \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062d\u062f\u0627\u0642\u0644 \u06cc\u06a9 \u0628\u0627\u0631 \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h4 id=\"timecomplexityofthebubblesort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628<\/h4>\n<p>\u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u0633\u0646\u0627\u0631\u06cc\u0648 (\u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0644\u06cc\u0633\u062a \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0639\u06a9\u0648\u0633 \u0627\u0633\u062a)\u060c \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u06cc\u062f swap \u062a\u06a9 \u062a\u06a9 \u0622\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0622\u0631\u0627\u06cc\u0647  \u0645\u0627 <code>swapped<\/code> \u067e\u0631\u0686\u0645 \u062a\u0646\u0638\u06cc\u0645 \u062e\u0648\u0627\u0647\u062f \u0634\u062f <code>True<\/code> \u0631\u0648\u06cc  \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u06af\u0631 \u062f\u0627\u0631\u06cc\u0645 <em>n<\/em> \u0639\u0646\u0627\u0635\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0644\u06cc\u0633\u062a \u062e\u0648\u062f \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a <em>n<\/em> \u062a\u06a9\u0631\u0627\u0631 \u062f\u0631 \u0647\u0631 \u0645\u0648\u0631\u062f &#8211; \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628\u06cc \\(O(n^2)\\) \u0627\u0633\u062a.<\/p>\n<h3 id=\"selectionsort\"><span class=\"ez-toc-section\" id=\"%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c\"><\/span>\u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 <em>\u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u062e\u0634 \u0645\u06cc \u06a9\u0646\u062f<\/em> \u0628\u0647 \u062f\u0648 \u0628\u062e\u0634: <em>\u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a<\/em> \u0648 <em>\u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0646\u0634\u062f\u0647<\/em>.  \u0645\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u062f\u0627\u0648\u0645 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0644\u06cc\u0633\u062a \u0631\u0627 \u062d\u0630\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"howdoesselectionsortwork\">\u0686\u06af\u0648\u0646\u0647 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061f<\/h4>\n<p>\u062f\u0631 \u0639\u0645\u0644\u060c \u0645\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0639\u0646\u0627\u0635\u0631 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0646\u062f\u0627\u0631\u06cc\u0645\u060c \u06a9\u0627\u0631\u06cc \u06a9\u0647 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0633\u0645\u062a \u0686\u067e \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645.  \u0633\u067e\u0633 \u06a9\u0644 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u062c\u0633\u062a\u062c\u0648 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 swap \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 \u0622\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f\u0647 \u0631\u0627 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 swap \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0639\u0646\u0635\u0631 \u062f\u0648\u0645.  \u0627\u06cc\u0646 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0627\u0632 \u0644\u06cc\u0633\u062a\u060c \u0639\u0646\u0635\u0631 \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f\u0647 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0628\u0627\u0634\u062f.<\/p>\n<h4 id=\"howtoimplementselectionsortinpython\">\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Selection Sort \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h4>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">selection_sort<\/span>(<span class=\"hljs-params\">nums<\/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-built_in\">len<\/span>(nums)):\n        \n        lowest_value_index = i\n        \n        <span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(i + <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-built_in\">len<\/span>(nums)):\n            <span class=\"hljs-keyword\">if<\/span> nums(j) &lt; nums(lowest_value_index):\n                lowest_value_index = j\n        \n        \n        nums(i), nums(lowest_value_index) = nums(lowest_value_index), nums(i)\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">12<\/span>, <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">20<\/span>, <span class=\"hljs-number\">11<\/span>)\nselection_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<p>\u0645\u0627 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 <code>i<\/code> \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u0645\u0648\u0627\u0631\u062f \u06a9\u0645\u062a\u0631\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"timecomplexityoftheselectionsort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0646\u062a\u062e\u0627\u0628<\/h4>\n<p>\u0645\u0627 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0631\u0627 \u0628\u0627 \u0628\u0631\u0631\u0633\u06cc \u0622\u0646 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645 <code>for<\/code> \u062d\u0644\u0642\u0647 \u0647\u0627 \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Selection Sort.  \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0628\u0627 <em>n<\/em> \u0639\u0646\u0627\u0635\u0631\u060c \u062d\u0644\u0642\u0647 \u0628\u06cc\u0631\u0648\u0646\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f <em>n<\/em> \u0628\u0627\u0631.<\/p>\n<p>\u062d\u0644\u0642\u0647 \u062f\u0627\u062e\u0644\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f <em>n-1<\/em> \u0686\u0647 \u0632\u0645\u0627\u0646\u06cc <em>\u0645\u0646<\/em> \u0628\u0631\u0627\u0628\u0631 1 \u0627\u0633\u062a \u0648 \u0633\u067e\u0633 <em>n-2<\/em> \u0645\u0627\u0646\u0646\u062f <em>\u0645\u0646<\/em> \u0628\u0631\u0627\u0628\u0631 2 \u0627\u0633\u062a \u0648 \u063a\u06cc\u0631\u0647.<\/p>\n<p>\u0645\u06cc\u0632\u0627\u0646 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u0633\u062a <code>(n - 1) + (n - 2) + ... + 1<\/code>\u060c \u06a9\u0647 \u0628\u0647 Selection Sort \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \\(O(n^2)\\) \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<h3 id=\"insertionsort\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%b1%d8%ac\"><\/span>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u0627\u0646\u0646\u062f Selection Sort\u060c \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u0642\u0633\u0645\u062a \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0648 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f.  \u0631\u0648\u06cc \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f \u0648 \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u0645\u0634\u0627\u0647\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0635\u062d\u06cc\u062d \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<h4 id=\"howdoesinsertionsortwork\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061f<\/h4>\n<p>\u0645\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0633\u067e\u0633 \u0628\u0647 \u0639\u0646\u0635\u0631 \u0628\u0639\u062f\u06cc \u0645\u06cc \u0631\u0648\u06cc\u0645\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0635\u062f\u0627 \u06a9\u0646\u06cc\u0645 <code>x<\/code>.  \u0627\u06af\u0631 <code>x<\/code> \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0647\u0645\u0627\u0646 \u0635\u0648\u0631\u062a \u0628\u0627\u0642\u06cc \u0645\u06cc \u06af\u0630\u0627\u0631\u06cc\u0645.  \u0627\u06af\u0631 <code>x<\/code> \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0633\u062a\u060c \u0645\u0642\u062f\u0627\u0631 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644 \u0631\u0627 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u062f\u0648\u0645 \u06a9\u067e\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644 \u0631\u0627 \u0631\u0648\u06cc \u0622\u0646 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645 <code>x<\/code>.<\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0639\u0646\u0627\u0635\u0631 \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0645\u06cc \u0631\u0648\u06cc\u0645\u060c \u0628\u0647 \u0637\u0648\u0631 \u0645\u062f\u0627\u0648\u0645 \u0639\u0646\u0627\u0635\u0631 \u0628\u0632\u0631\u06af\u062a\u0631 \u0631\u0627 \u062f\u0631 \u0642\u0633\u0645\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0647 \u0633\u0645\u062a \u0628\u0627\u0644\u0627 \u062d\u0631\u06a9\u062a \u0645\u06cc \u062f\u0647\u06cc\u0645 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0639\u0646\u0635\u0631\u06cc \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 <code>x<\/code> \u06cc\u0627 \u0628\u0647 \u0627\u0646\u062a\u0647\u0627\u06cc \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0631\u0633\u06cc\u062f \u0648 \u0633\u067e\u0633 \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u062f <code>x<\/code> \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0635\u062d\u06cc\u062d \u062e\u0648\u062f<\/p>\n<h4 id=\"howtoimplementinsertionsortinpython\">\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h4>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">insertion_sort<\/span>(<span class=\"hljs-params\">nums<\/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\">1<\/span>, <span class=\"hljs-built_in\">len<\/span>(nums)):\n        item_to_insert = nums(i)\n        \n        j = i - <span class=\"hljs-number\">1<\/span>\n        \n        \n        <span class=\"hljs-keyword\">while<\/span> j &gt;= <span class=\"hljs-number\">0<\/span> <span class=\"hljs-keyword\">and<\/span> nums(j) &gt; item_to_insert:\n            nums(j + <span class=\"hljs-number\">1<\/span>) = nums(j)\n            j -= <span class=\"hljs-number\">1<\/span>\n        \n        nums(j + <span class=\"hljs-number\">1<\/span>) = item_to_insert\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">28<\/span>, <span class=\"hljs-number\">6<\/span>)\ninsertion_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<h4 id=\"timecomplexityoftheinsertionsort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c<\/h4>\n<p>\u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a\u060c \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0639\u06a9\u0648\u0633 \u0645\u0631\u062a\u0628 \u0645\u06cc \u0634\u0648\u062f.  \u0628\u06cc\u0631\u0648\u0646\u06cc <code>for loop<\/code> \u062f\u0631 \u062a\u0627\u0628\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c \u0647\u0645\u06cc\u0634\u0647 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f <em>n-1<\/em> \u0628\u0627\u0631.<\/p>\n<p>\u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a\u060c \u062f\u0631\u0648\u0646\u06cc <code>for loop<\/code> \u062e\u0648\u0627\u0647\u062f \u0634\u062f swap \u06cc\u06a9 \u0628\u0627\u0631\u060c \u067e\u0633 swap \u062f\u0648\u060c \u0648 \u063a\u06cc\u0631\u0647.  \u0633\u067e\u0633 \u062a\u0639\u062f\u0627\u062f \u0645\u0628\u0627\u062f\u0644\u0647 \u0647\u0627 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>1 + 2 + ... + (n - 3) + (n - 2) + (n - 1)<\/code> \u06a9\u0647 \u0628\u0647 Insertion Sort \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \\(O(n^2)\\) \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<h3 id=\"heapsort\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d9%be%d8%b4%d8%aa%d9%87\"><\/span>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u067e\u0634\u062a\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0645\u062d\u0628\u0648\u0628\u060c \u0645\u0627\u0646\u0646\u062f \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc Insertion \u0648 Selection\u060c \u0641\u0647\u0631\u0633\u062a \u0631\u0627 \u0628\u0647 \u0628\u062e\u0634\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0634\u062f\u0647 \u0648 \u0645\u0631\u062a\u0628\u200c\u0646\u0634\u062f\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f.  \u0628\u062e\u0634 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 Heap \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"howdoesheapsortwork\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0647\u06cc\u067e \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061f<\/h4>\n<p>\u0645\u0627 \u0628\u0627 \u062a\u0628\u062f\u06cc\u0644 \u0644\u06cc\u0633\u062a \u0628\u0647 \u06cc\u06a9 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <strong>\u0645\u0627\u06a9\u0633 \u0647\u06cc\u067e<\/strong> &#8211; \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u0646\u0631\u06cc \u06a9\u0647 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0622\u0646 \u0627\u0633\u062a root node.  \u0633\u067e\u0633 \u0622\u0646 \u0645\u0648\u0631\u062f \u0631\u0627 \u062f\u0631 \u0627\u0646\u062a\u0647\u0627\u06cc \u0644\u06cc\u0633\u062a \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645.  \u0633\u067e\u0633 \u0645\u0627 \u062e\u0648\u062f \u0631\u0627 \u0628\u0627\u0632\u0633\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0645\u0627\u06a9\u0633 \u0647\u06cc\u067e<\/em> \u06a9\u0647 \u0627\u06a9\u0646\u0648\u0646 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631 \u062f\u0627\u0631\u062f \u0648 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u062c\u062f\u06cc\u062f \u0631\u0627 \u0642\u0628\u0644 \u0627\u0632 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0644\u06cc\u0633\u062a \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0645\u0627 \u0627\u06cc\u0646 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645 process \u0633\u0627\u062e\u062a \u067e\u0634\u062a\u0647 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0647\u0645\u0647 \u06af\u0631\u0647 \u0647\u0627 \u062d\u0630\u0641 \u0634\u0648\u0646\u062f.<\/p>\n<h4 id=\"howtoimplementheapsortinpython\">\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0647\u06cc\u067e \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h4>\n<p>\u0645\u0627 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u06a9\u0645\u06a9\u06cc \u0627\u06cc\u062c\u0627\u062f \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <code>heapify<\/code> \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">heapify<\/span>(<span class=\"hljs-params\">nums, heap_size, root_index<\/span>):<\/span>\n    \n    largest = root_index\n    left_child = (<span class=\"hljs-number\">2<\/span> * root_index) + <span class=\"hljs-number\">1<\/span>\n    right_child = (<span class=\"hljs-number\">2<\/span> * root_index) + <span class=\"hljs-number\">2<\/span>\n\n    \n    \n    <span class=\"hljs-keyword\">if<\/span> left_child &lt; heap_size <span class=\"hljs-keyword\">and<\/span> nums(left_child) &gt; nums(largest):\n        largest = left_child\n\n    \n    <span class=\"hljs-keyword\">if<\/span> right_child &lt; heap_size <span class=\"hljs-keyword\">and<\/span> nums(right_child) &gt; nums(largest):\n        largest = right_child\n\n    \n    <span class=\"hljs-keyword\">if<\/span> largest != root_index:\n        nums(root_index), nums(largest) = nums(largest), nums(root_index)\n        \n        heapify(nums, heap_size, largest)\n\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">heap_sort<\/span>(<span class=\"hljs-params\">nums<\/span>):<\/span>\n    n = <span class=\"hljs-built_in\">len<\/span>(nums)\n\n    \n    \n    \n    \n    \n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(n, -<span class=\"hljs-number\">1<\/span>, -<span class=\"hljs-number\">1<\/span>):\n        heapify(nums, n, i)\n\n    \n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(n - <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, -<span class=\"hljs-number\">1<\/span>):\n        nums(i), nums(<span class=\"hljs-number\">0<\/span>) = nums(<span class=\"hljs-number\">0<\/span>), nums(i)\n        heapify(nums, i, <span class=\"hljs-number\">0<\/span>)\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">35<\/span>, <span class=\"hljs-number\">12<\/span>, <span class=\"hljs-number\">43<\/span>, <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">51<\/span>)\nheap_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<h4 id=\"timecomplexityoftheheapsort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0647\u06cc\u067e<\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0628\u0647 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0622\u0646 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 <code>heapify<\/code> \u062a\u0627\u0628\u0639.  \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a\u060c \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0647\u0631\u06af\u0632 \u0627\u06cc\u0646 \u0646\u06cc\u0633\u062a root \u0639\u0646\u0635\u0631\u060c \u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u06cc\u06a9 \u062a\u0645\u0627\u0633 \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0628\u0647 <code>heapify<\/code>.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062a\u0645\u0627\u0633 \u0647\u0627\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0633\u06cc\u0627\u0631 \u06af\u0631\u0627\u0646 \u0628\u0647 \u0646\u0638\u0631 \u0628\u0631\u0633\u0646\u062f\u060c \u0628\u0647 \u06cc\u0627\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0627 \u0628\u0627 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u0646\u0631\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u062f\u0631\u062e\u062a \u062f\u0648\u062f\u0648\u06cc\u06cc \u0631\u0627 \u0628\u0627 3 \u0639\u0646\u0635\u0631 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f\u060c \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0646 2 \u0627\u0633\u062a. \u062d\u0627\u0644\u0627 \u062f\u0631\u062e\u062a \u062f\u0648\u062f\u0648\u06cc\u06cc \u0631\u0627 \u0628\u0627 7 \u0639\u0646\u0635\u0631 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f\u060c \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0646 3 \u0627\u0633\u062a. \u062f\u0631\u062e\u062a \u0628\u0647 \u0635\u0648\u0631\u062a \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0631\u0634\u062f \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 <em>n<\/em>.  \u0627\u06cc\u0646 <code>heapify<\/code> \u062a\u0627\u0628\u0639 \u0622\u0646 \u062f\u0631\u062e\u062a \u0631\u0627 \u062f\u0631 \u0632\u0645\u0627\u0646 \\(O(log(n))\\) \u0637\u06cc \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0627\u06cc\u0646 <code>heap_sort<\/code> \u062a\u0627\u0628\u0639 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \\(n\\) \u0628\u0627\u0631\u0647\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u06a9\u0644\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0647\u06cc\u067e \\(O(nlog(n))\\) \u0627\u0633\u062a.<\/p>\n<h3 id=\"mergesort\"><span class=\"ez-toc-section\" id=\"%d8%a7%d8%af%d8%ba%d8%a7%d9%85_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c\"><\/span>\u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u0642\u0633\u06cc\u0645 \u0648 \u063a\u0644\u0628\u0647 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u0646\u0635\u0641 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0641\u0642\u0637 \u062f\u0627\u0631\u0627\u06cc \u0639\u0646\u0627\u0635\u0631 \u0645\u0646\u0641\u0631\u062f \u0628\u0627\u0634\u062f\u060c \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0631 2 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0639\u0646\u0627\u0635\u0631 \u0645\u062c\u0627\u0648\u0631 \u0628\u0647 \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u0646\u062f\u060c \u0633\u067e\u0633 \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u062f\u063a\u0627\u0645 \u0634\u062f\u0647 \u0648 \u0628\u0627 \u062c\u0641\u062a \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0646\u06cc\u0632 \u0645\u0631\u062a\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u0627\u06cc\u0646 process \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc \u06cc\u0627\u0628\u062f \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0627 \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0644\u06cc\u0633\u062a \u0648\u0631\u0648\u062f\u06cc \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645.<\/p>\n<h4 id=\"howdoesmergesortwork\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061f<\/h4>\n<p>\u0645\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u0646\u0635\u0641 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0644\u06cc\u0633\u062a \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06cc\u06a9 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645.  \u0633\u067e\u0633 \u0647\u0631 \u0646\u06cc\u0645\u0647 \u0631\u0627 \u06a9\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0634\u062f\u0647 \u0628\u0648\u062f \u0628\u0627 \u0647\u0645 \u0627\u062f\u063a\u0627\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0642\u0633\u0645\u062a \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645 process.<\/p>\n<p>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0628\u0627 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0627\u0635\u0631 \u0647\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0647\u0631 \u0644\u06cc\u0633\u062a \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06af\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0648\u0644 \u0628\u0627 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0645\u062a\u0631\u06cc \u0634\u0631\u0648\u0639 \u0634\u0648\u062f\u060c \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0633\u067e\u0633 \u062f\u0648\u0645\u06cc\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0648\u0644 \u0631\u0627 \u0628\u0627 \u0627\u0648\u0644\u06cc\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0646\u06cc\u0645\u0647 \u062f\u0648\u0645 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0647\u0631 \u0628\u0627\u0631 \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u06cc \u0631\u0627 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u06cc \u0646\u06cc\u0645\u0647 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0634\u0627\u062e\u0635 \u0645\u0648\u0631\u062f\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0627 \u06cc\u06a9 \u0645\u0648\u0631\u062f \u0645\u0642\u0627\u06cc\u0633\u0647 \u0634\u0648\u062f \u0631\u0627 \u062c\u0627\u0628\u0647\u200c\u062c\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"howtoimplementmergesortinpython\">\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Merge Sort \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h4>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge<\/span>(<span class=\"hljs-params\">left_list, right_list<\/span>):<\/span>\n    sorted_list = ()\n    left_list_index = right_list_index = <span class=\"hljs-number\">0<\/span>\n\n    \n    left_list_length, right_list_length = <span class=\"hljs-built_in\">len<\/span>(left_list), <span class=\"hljs-built_in\">len<\/span>(right_list)\n\n    <span class=\"hljs-keyword\">for<\/span> _ <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(left_list_length + right_list_length):\n        <span class=\"hljs-keyword\">if<\/span> left_list_index &lt; left_list_length <span class=\"hljs-keyword\">and<\/span> right_list_index &lt; right_list_length:\n            \n            \n            \n            <span class=\"hljs-keyword\">if<\/span> left_list(left_list_index) &lt;= right_list(right_list_index):\n                sorted_list.append(left_list(left_list_index))\n                left_list_index += <span class=\"hljs-number\">1<\/span>\n            \n            \n            <span class=\"hljs-keyword\">else<\/span>:\n                sorted_list.append(right_list(right_list_index))\n                right_list_index += <span class=\"hljs-number\">1<\/span>\n\n        \n        \n        <span class=\"hljs-keyword\">elif<\/span> left_list_index == left_list_length:\n            sorted_list.append(right_list(right_list_index))\n            right_list_index += <span class=\"hljs-number\">1<\/span>\n        \n        \n        <span class=\"hljs-keyword\">elif<\/span> right_list_index == right_list_length:\n            sorted_list.append(left_list(left_list_index))\n            left_list_index += <span class=\"hljs-number\">1<\/span>\n\n    <span class=\"hljs-keyword\">return<\/span> sorted_list\n\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge_sort<\/span>(<span class=\"hljs-params\">nums<\/span>):<\/span>\n    \n    <span class=\"hljs-keyword\">if<\/span> <span class=\"hljs-built_in\">len<\/span>(nums) &lt;= <span class=\"hljs-number\">1<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> nums\n\n    \n    mid = <span class=\"hljs-built_in\">len<\/span>(nums) \/\/ <span class=\"hljs-number\">2<\/span>\n\n    \n    left_list = merge_sort(nums(:mid))\n    right_list = merge_sort(nums(mid:))\n\n    \n    <span class=\"hljs-keyword\">return<\/span> merge(left_list, right_list)\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">120<\/span>, <span class=\"hljs-number\">45<\/span>, <span class=\"hljs-number\">68<\/span>, <span class=\"hljs-number\">250<\/span>, <span class=\"hljs-number\">176<\/span>)\nrandom_list_of_nums = merge_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 <code>merge_sort()<\/code> \u062a\u0627\u0628\u0639\u060c \u0628\u0631\u062e\u0644\u0627\u0641 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0642\u0628\u0644\u06cc\u060c \u0628\u0647 \u062c\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0641\u0647\u0631\u0633\u062a \u0645\u0648\u062c\u0648\u062f\u060c \u0641\u0647\u0631\u0633\u062a \u062c\u062f\u06cc\u062f\u06cc \u0631\u0627 \u06a9\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0628\u0631\u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u062f.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0628\u0647 \u0641\u0636\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u062c\u062f\u06cc\u062f \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0644\u06cc\u0633\u062a \u0648\u0631\u0648\u062f\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/p>\n<h4 id=\"timecomplexityofthemergesort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645<\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 <code>merge<\/code> \u062a\u0627\u0628\u0639.  \u062f\u0648 \u0644\u06cc\u0633\u062a \u0645\u06cc \u06af\u06cc\u0631\u062f \u0648 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f <em>n<\/em> \u0628\u0627\u0631\u0647\u0627\u060c \u06a9\u062c\u0627 <em>n<\/em> \u0627\u0646\u062f\u0627\u0632\u0647 \u0648\u0631\u0648\u062f\u06cc \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0622\u0646\u0647\u0627 \u0627\u0633\u062a.<\/p>\n<p>\u0627\u06cc\u0646 <code>merge_sort<\/code> \u062a\u0627\u0628\u0639 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 2 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0628\u0647 \u0635\u0648\u0631\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0641\u0631\u0639\u06cc \u0631\u0627 \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u062f.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0648\u0631\u0648\u062f\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0646\u06cc\u0645\u06cc \u0627\u0632 \u0622\u0646\u0686\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0645\u0627\u0646\u0646\u062f \u062f\u0631\u062e\u062a\u0627\u0646 \u062f\u0648\u062f\u0648\u06cc\u06cc \u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u062f\u0631\u06cc\u0627\u0641\u062a \u0622\u0646 \u0628\u0627\u0634\u062f process \u0631\u0634\u062f \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0628\u0647 <em>n<\/em>.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u06a9\u0644\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Merge Sort \\(O(nlog(n))\\) \u0627\u0633\u062a.<\/p>\n<h3 id=\"quicksort\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%b3%d8%b1%db%8c%d8%b9\"><\/span>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0646 \u0648 \u063a\u0644\u0628\u0647 \u06a9\u0646\u060c \u0645\u062a\u062f\u0627\u0648\u0644 \u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0622\u0646 \u067e\u0631\u062f\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u067e\u06cc\u06a9\u0631\u0628\u0646\u062f\u06cc \u0634\u0648\u062f\u060c \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a \u0648 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0641\u0636\u0627\u06cc \u0627\u0636\u0627\u0641\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Merge Sort \u0646\u062f\u0627\u0631\u062f.  \u0645\u0627 \u0644\u06cc\u0633\u062a \u0631\u0627 \u062d\u0648\u0644 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0645\u062d\u0648\u0631\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0627\u0637\u0631\u0627\u0641 \u0645\u062d\u0648\u0631 \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"howdoesquicksortwork\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061f<\/h4>\n<p>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0628\u0627 \u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0628\u0646\u062f\u06cc \u0644\u06cc\u0633\u062a \u0634\u0631\u0648\u0639 \u0645\u06cc \u0634\u0648\u062f &#8211; \u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0627\u0632 \u0644\u06cc\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0622\u0646 \u0642\u0631\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u06af\u0631\u0641\u062a.  \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 Pivot \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u0645\u062d\u0648\u0631 \u0628\u0647 \u0633\u0645\u062a \u0686\u067e \u0622\u0646 \u0645\u0646\u062a\u0642\u0644 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0628\u0632\u0631\u06af\u062a\u0631 \u0628\u0647 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0622\u0646 \u0645\u0646\u062a\u0642\u0644 \u0645\u06cc \u0634\u0648\u0646\u062f.<\/p>\n<p>\u0628\u0627 \u062f\u0627\u0646\u0633\u062a\u0646 \u0627\u06cc\u0646\u06a9\u0647 pivot \u062f\u0631 \u062c\u0627\u06cc \u0645\u0646\u0627\u0633\u0628 \u062e\u0648\u062f \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f\u060c \u0628\u0647 \u0635\u0648\u0631\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0637\u0631\u0627\u0641 \u0645\u062d\u0648\u0631 \u0631\u0627 \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u06a9\u0644 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u0648\u062f.<\/p>\n<h4 id=\"howtoimplementquicksortinpython\">\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/h4>\n<pre><code class=\"hljs\">\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">partition<\/span>(<span class=\"hljs-params\">nums, low, high<\/span>):<\/span>\n    \n    \n    \n    \n    pivot = nums((low + high) \/\/ <span class=\"hljs-number\">2<\/span>)\n    i = low - <span class=\"hljs-number\">1<\/span>\n    j = high + <span class=\"hljs-number\">1<\/span>\n    <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n        i += <span class=\"hljs-number\">1<\/span>\n        <span class=\"hljs-keyword\">while<\/span> nums(i) &lt; pivot:\n            i += <span class=\"hljs-number\">1<\/span>\n\n        j -= <span class=\"hljs-number\">1<\/span>\n        <span class=\"hljs-keyword\">while<\/span> nums(j) &gt; pivot:\n            j -= <span class=\"hljs-number\">1<\/span>\n\n        <span class=\"hljs-keyword\">if<\/span> i &gt;= j:\n            <span class=\"hljs-keyword\">return<\/span> j\n\n        \n        \n        nums(i), nums(j) = nums(j), nums(i)\n\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">quick_sort<\/span>(<span class=\"hljs-params\">nums<\/span>):<\/span>\n    \n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">_quick_sort<\/span>(<span class=\"hljs-params\">items, low, high<\/span>):<\/span>\n        <span class=\"hljs-keyword\">if<\/span> low &lt; high:\n            \n            split_index = partition(items, low, high)\n            _quick_sort(items, low, split_index)\n            _quick_sort(items, split_index + <span class=\"hljs-number\">1<\/span>, high)\n\n    _quick_sort(nums, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-built_in\">len<\/span>(nums) - <span class=\"hljs-number\">1<\/span>)\n\n\n\nrandom_list_of_nums = (<span class=\"hljs-number\">22<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">18<\/span>, <span class=\"hljs-number\">99<\/span>)\nquick_sort(random_list_of_nums)\n<span class=\"hljs-built_in\">print<\/span>(random_list_of_nums)\n\n\n<\/code><\/pre>\n<h4 id=\"timecomplexityofthequicksort\">\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639<\/h4>\n<p>\u0628\u062f\u062a\u0631\u06cc\u0646 \u0633\u0646\u0627\u0631\u06cc\u0648 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u06cc\u0627 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0647\u0645\u06cc\u0634\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062d\u0648\u0631 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u0627\u06cc\u062c\u0627\u062f \u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u06cc \u0634\u0648\u062f <em>n-1<\/em>\u060c \u0628\u0627\u0639\u062b \u062a\u0645\u0627\u0633 \u0647\u0627\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0645\u06cc \u0634\u0648\u062f <em>n-1<\/em> \u0628\u0627\u0631.  \u0627\u06cc\u0646 \u0645\u0627 \u0631\u0627 \u0628\u0647 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a \\(O(n^2)\\) \u0647\u062f\u0627\u06cc\u062a \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u06cc\u06a9 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a \u0648\u062d\u0634\u062a\u0646\u0627\u06a9 \u0627\u0633\u062a\u060c \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0628\u0647 \u0634\u062f\u062a \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u062f \u0632\u06cc\u0631\u0627 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0622\u0646 \u0628\u0633\u06cc\u0627\u0631 \u0633\u0631\u06cc\u0639\u062a\u0631 \u0627\u0633\u062a.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 <code>partition<\/code> \u062a\u0627\u0628\u0639 \u0627\u0632 \u062a\u0648\u062f\u0631\u062a\u0648 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>while<\/code> \u062d\u0644\u0642\u0647\u060c \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u0628\u0627\u062f\u0644\u0647 \u0647\u0627\u06cc \u0622\u0646.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \\(O(n)\\) \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0628\u0627 \u06cc\u06a9 \u067e\u06cc\u0648\u062a \u062e\u0648\u0628\u060c \u062a\u0627\u0628\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0646\u06cc\u0645 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0628\u0627 \\(n\\) \u0631\u0634\u062f \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \\(O(nlog(n))\\) \u0627\u0633\u062a.<\/p>\n<h3 id=\"pythonsbuiltinsortfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%a7%d8%ae%d9%84%db%8c_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u062a\u0648\u0627\u0628\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0627\u062e\u0644\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0631\u06a9 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0645\u0641\u06cc\u062f \u0627\u0633\u062a\u060c \u062f\u0631 \u0627\u06a9\u062b\u0631 \u067e\u0631\u0648\u0698\u0647\u200c\u0647\u0627\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u062f\u0631 \u0632\u0628\u0627\u0646 \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0647\u0631\u0633\u062a \u062e\u0648\u062f \u0631\u0627 \u0637\u0648\u0631\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0645\u062d\u062a\u0648\u06cc\u0627\u062a \u0622\u0646 \u0628\u0627 \u0641\u0647\u0631\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u0648\u0646\u062f <code>sort()<\/code> \u0631\u0648\u0634:<\/p>\n<pre><code class=\"hljs\">apples_eaten_a_day = (<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>)\napples_eaten_a_day.sort()\n<span class=\"hljs-built_in\">print<\/span>(apples_eaten_a_day) \n<\/code><\/pre>\n<p>\u06cc\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>sorted()<\/code> \u062a\u0627\u0628\u0639 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062c\u062f\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">apples_eaten_a_day_2 = (<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>)\nsorted_apples = <span class=\"hljs-built_in\">sorted<\/span>(apples_eaten_a_day_2)\n<span class=\"hljs-built_in\">print<\/span>(sorted_apples) \n<\/code><\/pre>\n<p>\u0647\u0631 \u062f\u0648 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0635\u0639\u0648\u062f\u06cc \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u0627\u0645\u0627 \u0634\u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0628\u0627 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0631\u062f\u0646 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0646\u0632\u0648\u0644\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u062f <code>reverse<\/code> \u067e\u0631\u0686\u0645 \u0628\u0647 <code>True<\/code>:<\/p>\n<pre><code class=\"hljs\">\napples_eaten_a_day.sort(reverse=<span class=\"hljs-literal\">True<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(apples_eaten_a_day) \n\n\nsorted_apples_desc = <span class=\"hljs-built_in\">sorted<\/span>(apples_eaten_a_day_2, reverse=<span class=\"hljs-literal\">True<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(sorted_apples_desc) \n<\/code><\/pre>\n<p>\u0628\u0631\u062e\u0644\u0627\u0641 \u062a\u0648\u0627\u0628\u0639 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u06a9\u0647 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645\u060c \u0647\u0631 \u062f\u0648\u06cc \u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0641\u0647\u0631\u0633\u062a\u200c\u0647\u0627\u06cc \u062a\u0627\u067e\u0644 \u0648 \u06a9\u0644\u0627\u0633\u200c\u0647\u0627 \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u0646\u062f.  \u0627\u06cc\u0646 <code>sorted()<\/code> \u062a\u0627\u0628\u0639 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0647\u0631 \u0634\u06cc \u0642\u0627\u0628\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u062f \u0648 \u0634\u0627\u0645\u0644 \u0644\u06cc\u0633\u062a \u0647\u0627\u060c \u0631\u0634\u062a\u0647 \u0647\u0627\u060c \u062a\u0627\u067e\u0644 \u0647\u0627\u060c \u062f\u06cc\u06a9\u0634\u0646\u0631\u06cc \u0647\u0627\u060c \u0645\u062c\u0645\u0648\u0639\u0647 \u0647\u0627 \u0648 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u0646\u062f\u0647 \u0647\u0627\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u062f.<\/p>\n<blockquote>\n<p>\u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc \u06a9\u0646\u0646\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Timsort\">\u062a\u06cc\u0645 \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646<\/a> \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u0627\u0644\u0647\u0627\u0645 \u06af\u0631\u0641\u062a\u0647 \u0627\u0632 Merge Sort \u0648 Insertion Sort.<\/p>\n<\/blockquote>\n<h3 id=\"speedcomparisons\"><span class=\"ez-toc-section\" id=\"%d9%85%d9%82%d8%a7%db%8c%d8%b3%d9%87_%d8%b3%d8%b1%d8%b9%d8%aa\"><\/span>\u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0631\u0639\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0627\u06cc\u062f\u0647 \u0627\u06cc \u0627\u0632 \u0633\u0631\u0639\u062a \u0639\u0645\u0644\u06a9\u0631\u062f \u0622\u0646\u0647\u0627 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u0644\u06cc\u0633\u062a\u06cc \u0627\u0632 5000 \u0639\u062f\u062f \u0628\u06cc\u0646 0 \u062a\u0627 1000 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u0633\u067e\u0633 \u0632\u0645\u0627\u0646 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062a\u06a9\u0645\u06cc\u0644 \u0647\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0686\u0642\u062f\u0631 \u0637\u0648\u0644 \u0645\u06cc \u06a9\u0634\u062f.  \u0627\u06cc\u0646 \u06a9\u0627\u0631 10 \u0628\u0627\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0627 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0627\u0644\u06af\u0648\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u0648\u062f\u060c \u0632\u0645\u0627\u0646 \u0628\u0631 \u062d\u0633\u0628 \u062b\u0627\u0646\u06cc\u0647 \u0627\u0633\u062a:<\/p>\n<table class=\"table table-striped\" style=\"font-size:15px;overflow-x:auto\">\n<thead>\n<tr>\n<th>\u0627\u062c\u0631\u0627 \u06a9\u0646<\/th>\n<th>\u062d\u0628\u0627\u0628<\/th>\n<th>\u0627\u0646\u062a\u062e\u0627\u0628<\/th>\n<th>\u062f\u0631\u062c<\/th>\n<th>\u067e\u0634\u062a\u0647<\/th>\n<th>\u0627\u062f\u063a\u0627\u0645<\/th>\n<th>\u0633\u0631\u06cc\u0639<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>5.53188<\/td>\n<td>1.23152<\/td>\n<td>1.60355<\/td>\n<td>0.04006<\/td>\n<td>0.02619<\/td>\n<td>0.01639<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>4.92176<\/td>\n<td>1.24728<\/td>\n<td>1.59103<\/td>\n<td>0.03999<\/td>\n<td>0.02584<\/td>\n<td>0.01661<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>4.91642<\/td>\n<td>1.22440<\/td>\n<td>1.59362<\/td>\n<td>0.04407<\/td>\n<td>0.02862<\/td>\n<td>0.01646<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>5.15470<\/td>\n<td>1.25053<\/td>\n<td>1.63463<\/td>\n<td>0.04128<\/td>\n<td>0.02882<\/td>\n<td>0.01860<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4.95522<\/td>\n<td>1.28987<\/td>\n<td>1.61759<\/td>\n<td>0.04515<\/td>\n<td>0.03314<\/td>\n<td>0.01885<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>5.04907<\/td>\n<td>1.25466<\/td>\n<td>1.62515<\/td>\n<td>0.04257<\/td>\n<td>0.02595<\/td>\n<td>0.01628<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>5.05591<\/td>\n<td>1.24911<\/td>\n<td>1.61981<\/td>\n<td>0.04028<\/td>\n<td>0.02733<\/td>\n<td>0.01760<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>5.08799<\/td>\n<td>1.25808<\/td>\n<td>1.62603<\/td>\n<td>0.04264<\/td>\n<td>0.02633<\/td>\n<td>0.01705<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>5.03289<\/td>\n<td>1.24915<\/td>\n<td>1.61446<\/td>\n<td>0.04302<\/td>\n<td>0.03293<\/td>\n<td>0.01762<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>5.14292<\/td>\n<td>1.22021<\/td>\n<td>1.57273<\/td>\n<td>0.03966<\/td>\n<td>0.02572<\/td>\n<td>0.01606<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u06cc\u0627\u0646\u06af\u06cc\u0646<\/td>\n<td>5.08488<\/td>\n<td>1.24748<\/td>\n<td>1.60986<\/td>\n<td>0.04187<\/td>\n<td>0.02809<\/td>\n<td>0.01715<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0627\u06af\u0631 \u062e\u0648\u062f\u062a\u0627\u0646 \u062a\u0633\u062a \u0631\u0627 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u06cc\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u062f\u0631\u06cc\u0627\u0641\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f\u060c \u0627\u0645\u0627 \u0627\u0644\u06af\u0648\u0647\u0627\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0628\u0627\u06cc\u062f \u06cc\u06a9\u0633\u0627\u0646 \u06cc\u0627 \u0645\u0634\u0627\u0628\u0647 \u0628\u0627\u0634\u0646\u062f.  \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628\u200c\u0647\u0627 \u06a9\u0646\u062f\u062a\u0631\u06cc\u0646 \u0648 \u0628\u062f\u062a\u0631\u06cc\u0646 \u0639\u0645\u0644\u06a9\u0631\u062f \u062f\u0631 \u0628\u06cc\u0646 \u0647\u0645\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0627\u0633\u062a.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u062f\u0645\u0647 \u0627\u06cc \u0628\u0631\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627 \u0645\u0641\u06cc\u062f \u0627\u0633\u062a\u060c \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0639\u0645\u0644\u06cc \u0645\u0646\u0627\u0633\u0628 \u0646\u06cc\u0633\u062a.<\/p>\n<p>\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u0645 \u06a9\u0647 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0628\u0633\u06cc\u0627\u0631 \u0633\u0631\u06cc\u0639 \u0627\u0633\u062a\u060c \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0627\u0632 Merge Sort \u0648 \u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627 \u0628\u0647 \u0641\u0636\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0646\u06cc\u0627\u0632 \u0646\u062f\u0627\u0631\u062f.  \u0628\u0647 \u06cc\u0627\u062f \u0628\u06cc\u0627\u0648\u0631\u06cc\u062f \u06a9\u0647 \u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0645\u0627 \u0645\u0628\u062a\u0646\u06cc \u0628\u0648\u062f \u0631\u0648\u06cc \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0644\u06cc\u0633\u062a\u060c \u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0646\u062a\u0627\u06cc\u062c \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 Insertion Sort \u0645\u0642\u0627\u06cc\u0633\u0647\u200c\u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0645\u062a\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 Selection Sort \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u062f\u060c \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc\u200c\u0647\u0627 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0627\u062c\u0631\u0627\u0647\u0627\u060c Selection Sort \u06a9\u0645\u06cc \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0627\u0633\u062a.<\/p>\n<p>Insertion Sorts \u0645\u0628\u0627\u062f\u0644\u0647 \u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 Selection Sort \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f.  \u0627\u06af\u0631 \u0645\u0628\u0627\u062f\u0644\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0632\u0645\u0627\u0646 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0637\u0648\u0644 \u0628\u06a9\u0634\u062f\u060c \u0622\u0646\u06af\u0627\u0647 \u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 &#8220;\u0628\u0631\u0639\u06a9\u0633&#8221; \u0642\u0627\u0628\u0644 \u0642\u0628\u0648\u0644 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\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><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0647\u0646\u06af\u0627\u0645 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0645\u0631\u0627\u0642\u0628 \u0645\u062d\u06cc\u0637 \u0628\u0627\u0634\u06cc\u062f\u060c \u0632\u06cc\u0631\u0627 \u0628\u0631 \u0639\u0645\u0644\u06a9\u0631\u062f \u062a\u0623\u062b\u06cc\u0631 \u0645\u06cc \u06af\u0630\u0627\u0631\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0631\u0627\u0647 \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u0645\u0627 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u0646\u062f \u062a\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 6 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645 &#8211; \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062d\u0628\u0627\u0628\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0627\u0646\u062a\u062e\u0627\u0628\u06cc\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062f\u0631\u062c\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u067e\u0634\u062a\u0647\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 &#8211; \u0648 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0622\u0646\u0647\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646.<\/p>\n<p>\u0645\u06cc\u0632\u0627\u0646 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627 \u0648 \u0645\u0628\u0627\u062f\u0644\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 \u0645\u062d\u06cc\u0637\u06cc \u06a9\u0647 \u06a9\u062f \u0627\u062c\u0631\u0627 \u0645\u06cc \u06a9\u0646\u062f\u060c 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