{"id":9027,"date":"2023-12-26T02:40:25","date_gmt":"2023-12-25T23:10:25","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2023-12-26T02:40:25","modified_gmt":"2023-12-25T23:10:25","slug":"%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%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\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u0631\u0627\u0647\u0646\u0645\u0627\u06cc Heaps \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 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href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%88%db%8c%da%98%da%af%db%8c_%d9%87%d8%a7_%d9%88_%d8%ae%d9%88%d8%a7%d8%b5_%d9%87%db%8c%d9%be_%d9%87%d8%a7\" >\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627 \u0648 \u062e\u0648\u0627\u0635 \u0647\u06cc\u067e \u0647\u0627<\/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\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%d9%86%d9%88%d8%a7%d8%b9_%d9%87%db%8c%d9%be_%d9%87%d8%a7\" >\u0627\u0646\u0648\u0627\u0639 \u0647\u06cc\u067e \u0647\u0627<\/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\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%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_%d9%87%db%8c%d9%be_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86_%e2%80%93_the_heapq_%d9%85%d8%af%d9%88%d9%84\" >\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0647\u06cc\u067e \u067e\u0627\u06cc\u062a\u0648\u0646 &#8211; The heapq \u0645\u062f\u0648\u0644<\/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\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%da%86%da%af%d9%88%d9%86%d9%87_%db%8c%da%a9_%d9%84%db%8c%d8%b3%d8%aa_%d8%b1%d8%a7_%d8%a8%d9%87_%db%8c%da%a9_%d9%be%d8%b4%d8%aa%d9%87_%d8%aa%d8%a8%d8%af%db%8c%d9%84_%da%a9%d9%86%db%8c%d9%85\" >\u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u06cc\u06a9 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href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d8%ad%d9%88%d9%87_%d8%ad%d8%b0%d9%81_%d9%88_%d8%a8%d8%b1%da%af%d8%b1%d8%af%d8%a7%d9%86%d8%af%d9%86_%da%a9%d9%88%da%86%da%a9%d8%aa%d8%b1%db%8c%d9%86_%d8%b9%d9%86%d8%b5%d8%b1_%d8%a7%d8%b2_%d9%87%db%8c%d9%be\" >\u0646\u062d\u0648\u0647 \u062d\u0630\u0641 \u0648 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u062f\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 \u0647\u06cc\u067e<\/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\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%da%86%da%af%d9%88%d9%86%d9%87_%db%8c%da%a9_%d9%85%d9%88%d8%b1%d8%af_%d8%ac%d8%af%db%8c%d8%af_%d8%b1%d8%a7_%d9%81%d8%b4%d8%a7%d8%b1_%d8%af%d9%87%db%8c%d8%af_%d9%88_%da%a9%d9%88%da%86%da%a9%d8%aa%d8%b1%db%8c%d9%86_%d9%85%d9%88%d8%b1%d8%af_%d8%b1%d8%a7_%d9%be%d8%a7%d9%be_%da%a9%d9%86%db%8c%d8%af\" >\u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0645\u0648\u0631\u062f \u062c\u062f\u06cc\u062f \u0631\u0627 \u0641\u0634\u0627\u0631 \u062f\u0647\u06cc\u062f \u0648 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0631\u0627 \u067e\u0627\u067e \u06a9\u0646\u06cc\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" 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href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%db%8c%d8%a7%d9%81%d8%aa%d9%86_%d8%a7%da%a9%d8%b3%d8%aa%d8%b1%db%8c%d9%85_%d9%87%d8%a7%db%8c_%d9%85%d8%aa%d8%b9%d8%af%d8%af_%d8%af%d8%b1_%d9%87%db%8c%d9%be_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u06cc\u0627\u0641\u062a\u0646 \u0627\u06a9\u0633\u062a\u0631\u06cc\u0645 \u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f \u062f\u0631 \u0647\u06cc\u067e \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-12\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%da%86%da%af%d9%88%d9%86%d9%87_%d9%87%d9%be_%d8%b3%d9%81%d8%a7%d8%b1%d8%b4%db%8c_%d8%ae%d9%88%d8%af_%d8%b1%d8%a7_%d8%a8%d8%b3%d8%a7%d8%b2%db%8c%d8%af\" >\u0686\u06af\u0648\u0646\u0647 \u0647\u067e \u0633\u0641\u0627\u0631\u0634\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0633\u0627\u0632\u06cc\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-heaps-%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 class=\"content\"><noscript><\/p>\n<style>.lazyload-placeholder { display: none;  }<\/style>\n<p><\/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>\u0641\u0631\u0648\u062f\u06af\u0627\u0647\u06cc \u0634\u0644\u0648\u063a \u0631\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0647\u0631 \u062f\u0642\u06cc\u0642\u0647 \u067e\u0631\u0648\u0627\u0632\u0647\u0627\u06cc\u06cc \u0627\u0632 \u0622\u0646 \u0628\u0644\u0646\u062f \u0648 \u0641\u0631\u0648\u062f \u0645\u06cc\u200c\u0622\u06cc\u0646\u062f.  \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u06a9\u0646\u062a\u0631\u0644\u200c\u06a9\u0646\u0646\u062f\u0647\u200c\u0647\u0627\u06cc \u062a\u0631\u0627\u0641\u06cc\u06a9 \u0647\u0648\u0627\u06cc\u06cc \u067e\u0631\u0648\u0627\u0632\u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0648\u0631\u06cc\u062a \u0627\u0648\u0644\u0648\u06cc\u062a\u200c\u0628\u0646\u062f\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c heaps \u0628\u0647 \u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u062e\u0627\u0635 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0648 \u067e\u0631\u062f\u0627\u0632\u0634 \u06a9\u0646\u06cc\u0645 \u0648 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u062d\u0627\u0635\u0644 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u00ab\u0641\u0648\u0631\u06cc\u200c\u062a\u0631\u06cc\u0646\u00bb \u06cc\u0627 \u00ab\u0645\u0647\u0645\u200c\u062a\u0631\u06cc\u0646\u00bb \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0647\u0645\u06cc\u0634\u0647 \u062f\u0631 \u0628\u0627\u0644\u0627\u06cc \u0635\u0641\u062d\u0647 \u0642\u0627\u0628\u0644 \u062f\u0633\u062a\u0631\u0633\u06cc \u0647\u0633\u062a\u0646\u062f.<\/p>\n<blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0645\u0627 \u0633\u0641\u0631\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0627\u0646\u0628\u0648\u0647\u06cc \u0627\u0632 \u0632\u0645\u06cc\u0646 \u0622\u063a\u0627\u0632 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0645\u0627 \u0628\u0627 \u0627\u0628\u0647\u0627\u0645 \u0632\u062f\u0627\u06cc\u06cc \u0627\u0632 \u0686\u06cc\u0633\u062a\u06cc \u067e\u0634\u062a\u0647 \u0647\u0627 \u0648 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0630\u0627\u062a\u06cc \u0622\u0646\u0647\u0627 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u0632 \u0622\u0646\u062c\u0627\u060c \u0645\u0627 \u0628\u0647 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u067e\u0634\u062a\u0647\u200c\u0647\u0627 \u062a\u0648\u0633\u0637 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0645\u06cc\u200c\u067e\u0631\u062f\u0627\u0632\u06cc\u0645 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644\u060c \u0648 \u0645\u062c\u0645\u0648\u0639\u0647 \u063a\u0646\u06cc \u0627\u0632 \u0642\u0627\u0628\u0644\u06cc\u062a \u0647\u0627\u06cc \u0622\u0646 \u0631\u0627 \u06a9\u0634\u0641 \u06a9\u0646\u06cc\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0627\u06af\u0631 \u062a\u0627 \u0628\u0647 \u062d\u0627\u0644 \u0628\u0647 \u0627\u06cc\u0646 \u0641\u06a9\u0631 \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u067e\u0648\u06cc\u0627 \u0631\u0627 \u06a9\u0647 \u0627\u063a\u0644\u0628 \u0628\u0647 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 (\u06cc\u0627 \u067e\u0627\u06cc\u06cc\u0646\u200c\u062a\u0631\u06cc\u0646) \u0627\u0648\u0644\u0648\u06cc\u062a \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a\u060c \u0628\u0647\u200c\u0637\u0648\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u062f\u06cc\u0631\u06cc\u062a \u06a9\u0646\u06cc\u062f\u060c \u062f\u0631 \u0627\u0646\u062a\u0638\u0627\u0631 \u0634\u0645\u0627 \u0647\u0633\u062a\u06cc\u062f.<\/p>\n<\/blockquote>\n<h3 id=\"whatisaheap\"><span class=\"ez-toc-section\" id=\"%d9%87%db%8c%d9%be_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>\u0647\u06cc\u067e \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u0648\u0644\u06cc\u0646 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0642\u0628\u0644 \u0627\u0632 \u0641\u0631\u0648 \u0631\u0641\u062a\u0646 \u062f\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0634\u062a\u0647 \u0647\u0627 \u0628\u062f\u0627\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a <em>\u067e\u0634\u062a\u0647 \u0686\u06cc\u0633\u062a<\/em>.  \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0646\u06cc\u0631\u0648\u06af\u0627\u0647 \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u062f\u0631\u062e\u062a \u0628\u0631\u062c\u0633\u062a\u0647 \u0627\u0633\u062a\u060c \u0628\u0647 \u0648\u06cc\u0698\u0647 \u062f\u0631 <strong>\u062d\u0641\u0638 \u0646\u0638\u0645 \u0648 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628<\/strong>.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u0686\u0634\u0645\u0627\u0646 \u0622\u0645\u0648\u0632\u0634 \u0646\u062f\u06cc\u062f\u0647 \u0634\u0628\u06cc\u0647 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u062f\u0648\u062a\u0627\u06cc\u06cc \u0628\u0627\u0634\u062f\u060c \u062a\u0641\u0627\u0648\u062a \u0647\u0627\u06cc \u0638\u0631\u06cc\u0641 \u062f\u0631 \u0633\u0627\u062e\u062a\u0627\u0631 \u0648 \u0642\u0648\u0627\u0646\u06cc\u0646 \u062d\u0627\u06a9\u0645 \u0628\u0631 \u0622\u0646 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u062e\u0635 \u0622\u0646 \u0631\u0627 \u0645\u062a\u0645\u0627\u06cc\u0632 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u06cc\u06a9\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u0646\u062f\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0645\u0627\u0647\u06cc\u062a \u0622\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0627\u0633\u062a <em><strong>\u062f\u0631\u062e\u062a \u062f\u0648\u062f\u0648\u06cc\u06cc \u06a9\u0627\u0645\u0644<\/strong><\/em>.  \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0647\u0631 \u0633\u0637\u062d \u062f\u0631\u062e\u062a\u060c \u0628\u0647 \u062c\u0632 \u0622\u062e\u0631\u06cc\u0646 \u0633\u0637\u062d\u060c \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u067e\u0631 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u062f\u0631 \u0627\u06cc\u0646 \u0622\u062e\u0631\u06cc\u0646 \u0633\u0637\u062d\u060c \u06af\u0631\u0647 \u0647\u0627 \u0627\u0632 \u0686\u067e \u0628\u0647 \u0631\u0627\u0633\u062a \u067e\u0631 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u0686\u0646\u06cc\u0646 \u0633\u0627\u062e\u062a\u0627\u0631\u06cc \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u067e\u0634\u062a\u0647\u200c\u0647\u0627 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647\u200c\u0637\u0648\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627 \u06cc\u0627 \u0641\u0647\u0631\u0633\u062a\u200c\u0647\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u0648 \u062f\u0633\u062a\u06a9\u0627\u0631\u06cc \u06a9\u0631\u062f\u060c \u0628\u0627 \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0631 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0646\u0639\u06a9\u0633 \u06a9\u0646\u0646\u062f\u0647 \u0645\u062d\u0644 \u0642\u0631\u0627\u0631\u06af\u06cc\u0631\u06cc \u0622\u0646 \u062f\u0631 \u062f\u0631\u062e\u062a.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3.stackabuse.com\/media\/articles\/guide-to-heaps-in-python-1.png\" alt=\"guide-to-heaps-in-python-01.png\" title=\"\"><\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062c\u0648\u0647\u0631 \u0648\u0627\u0642\u0639\u06cc \u06cc\u06a9 \u062a\u0648\u062f\u0647 \u062f\u0631 \u0622\u0646 \u0646\u0647\u0641\u062a\u0647 \u0627\u0633\u062a <em><strong>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<\/strong><\/em>.  \u062f\u0631 \u06cc\u06a9 <em>\u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u0634\u062a\u0647<\/em>\u060c \u0645\u0642\u062f\u0627\u0631 \u0647\u0631 \u06af\u0631\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u062e\u0648\u062f \u0641\u0631\u0627\u062a\u0631 \u0645\u06cc \u0631\u0648\u062f \u06cc\u0627 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0648 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0631\u0627 \u062f\u0631\u0633\u062a \u062f\u0631 \u0631\u06cc\u0634\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.  \u0627\u0632 \u0633\u0648\u06cc \u062f\u06cc\u06af\u0631\u060c \u0627\u0644\u0641 <em>\u067e\u0634\u062a\u0647 \u062f\u0642\u06cc\u0642\u0647<\/em> \u0628\u0631 \u0627\u0633\u0627\u0633 \u0627\u0635\u0644 \u0645\u062e\u0627\u0644\u0641 \u0639\u0645\u0644 \u0645\u06cc \u06a9\u0646\u062f: \u0645\u0642\u062f\u0627\u0631 \u0647\u0631 \u06af\u0631\u0647 \u06cc\u0627 \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u0622\u0646 \u0627\u0633\u062a\u060c \u0648 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0631\u06cc\u0634\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u062f.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3.stackabuse.com\/media\/articles\/guide-to-heaps-in-python-2.png\" alt=\"guide-to-heaps-in-python-02.png\" title=\"\"><\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u0635\u06cc\u0647:<\/strong> \u0634\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f <em>\u0647\u0631\u0645 \u0627\u0639\u062f\u0627\u062f<\/em>.  \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0632 \u067e\u0627\u06cc\u0647 \u0628\u0647 \u0642\u0644\u0647 \u0635\u0639\u0648\u062f \u0645\u06cc \u06a9\u0646\u06cc\u062f\u060c \u0627\u0639\u062f\u0627\u062f \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f \u0648 \u0628\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u0642\u062f\u0627\u0631 \u062f\u0631 \u0627\u0648\u062c \u0645\u06cc \u0631\u0633\u062f.  \u062f\u0631 \u0645\u0642\u0627\u0628\u0644\u060c \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u06a9\u0648\u0686\u06a9 \u0628\u0627 \u062d\u062f\u0627\u0642\u0644 \u0645\u0642\u062f\u0627\u0631 \u062f\u0631 \u0627\u0648\u062c \u062e\u0648\u062f \u0634\u0631\u0648\u0639 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0647 \u0628\u0627 \u062d\u0631\u06a9\u062a \u0628\u0647 \u0633\u0645\u062a \u067e\u0627\u06cc\u06cc\u0646 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u06cc\u0627\u0628\u0646\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u067e\u06cc\u0634\u0631\u0641\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0639\u0645\u06cc\u0642 \u062a\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0627\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0630\u0627\u062a\u06cc heap \u0647\u0627 \u0639\u0645\u0644\u06cc\u0627\u062a \u06a9\u0627\u0631\u0622\u0645\u062f \u0631\u0627 \u0645\u0645\u06a9\u0646 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0686\u06af\u0648\u0646\u0647 \u067e\u0627\u06cc\u062a\u0648\u0646 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644 \u0628\u0647 \u0637\u0648\u0631 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0627\u0646\u0628\u0648\u0647\u06cc \u0631\u0627 \u062f\u0631 \u062a\u0644\u0627\u0634 \u0647\u0627\u06cc \u06a9\u062f\u0646\u0648\u06cc\u0633\u06cc \u0645\u0627 \u0627\u062f\u063a\u0627\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h3 id=\"characteristicsandpropertiesofheaps\"><span class=\"ez-toc-section\" id=\"%d9%88%db%8c%da%98%da%af%db%8c_%d9%87%d8%a7_%d9%88_%d8%ae%d9%88%d8%a7%d8%b5_%d9%87%db%8c%d9%be_%d9%87%d8%a7\"><\/span>\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627 \u0648 \u062e\u0648\u0627\u0635 \u0647\u06cc\u067e \u0647\u0627<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Heap \u0647\u0627 \u0628\u0627 \u0633\u0627\u062e\u062a\u0627\u0631 \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f \u0648 \u0627\u0635\u0648\u0644 \u0646\u0638\u0645 \u062f\u0647\u06cc \u062e\u0648\u062f\u060c \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627 \u0648 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0645\u062a\u0645\u0627\u06cc\u0632 \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u0646\u062f \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0627\u0648\u0644 \u0648 \u0645\u0647\u0645\u062a\u0631 \u0627\u0632 \u0647\u0645\u0647\u060c \u067e\u0634\u062a\u0647 \u0647\u0627 \u0647\u0633\u062a\u0646\u062f <strong>\u0630\u0627\u062a\u0627 \u06a9\u0627\u0631\u0622\u0645\u062f<\/strong>.  \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631\u062e\u062a\u06cc \u0622\u0646\u0647\u0627\u060c \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0641\u0631\u0645\u062a \u062f\u0631\u062e\u062a \u062f\u0648\u062f\u0648\u06cc\u06cc \u06a9\u0627\u0645\u0644\u060c \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0639\u0645\u0644\u06cc\u0627\u062a\u06cc \u0645\u0627\u0646\u0646\u062f \u062f\u0631\u062c \u0648 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0639\u0646\u0627\u0635\u0631 \u0627\u0648\u0644\u0648\u06cc\u062a (\u062d\u062f\u0627\u06a9\u062b\u0631 \u06cc\u0627 \u062d\u062f\u0627\u0642\u0644) \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f. <em>O (log n)<\/em>.  \u0627\u06cc\u0646 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627 \u0648 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062f\u0633\u062a\u0631\u0633\u06cc \u0645\u06a9\u0631\u0631 \u0628\u0647 \u0639\u0646\u0627\u0635\u0631 \u0627\u0648\u0644\u0648\u06cc\u062a \u062f\u0627\u0631\u0646\u062f\u060c \u0627\u0645\u062a\u06cc\u0627\u0632\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u06cc\u06a9\u06cc \u062f\u06cc\u06af\u0631 \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u06a9\u067e\u0647 \u0647\u0627 \u0622\u0646\u0647\u0627 \u0627\u0633\u062a <strong>\u06a9\u0627\u0631\u0627\u06cc\u06cc \u062d\u0627\u0641\u0638\u0647<\/strong>.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u067e\u200c\u0647\u0627 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627 \u06cc\u0627 \u0644\u06cc\u0633\u062a\u200c\u0647\u0627 \u0628\u062f\u0648\u0646 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u0634\u0627\u0631\u0647\u200c\u06af\u0631\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0628\u0647 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0641\u0631\u0632\u0646\u062f \u06cc\u0627 \u0648\u0627\u0644\u062f \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u060c \u062f\u0631 \u0641\u0636\u0627 \u0635\u0631\u0641\u0647\u200c\u062c\u0648\u06cc\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f.  \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0631 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0637\u0627\u0628\u0642 \u0628\u0627 \u0642\u0631\u0627\u0631\u06af\u06cc\u0631\u06cc \u0622\u0646 \u062f\u0631 \u062f\u0631\u062e\u062a \u0627\u0633\u062a \u06a9\u0647 \u0627\u0645\u06a9\u0627\u0646 \u067e\u06cc\u0645\u0627\u06cc\u0634 \u0648 \u062f\u0633\u062a\u06a9\u0627\u0631\u06cc \u0642\u0627\u0628\u0644 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0648 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u062e\u0627\u0635\u06cc\u062a \u0633\u0641\u0627\u0631\u0634 \u062f\u0647\u06cc \u0647\u067e \u0647\u0627\u060c \u0686\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a max heap \u06cc\u0627 min heap\u060c \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0631\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f <strong>\u0631\u06cc\u0634\u0647 \u0647\u0645\u06cc\u0634\u0647 \u0639\u0646\u0635\u0631 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0627\u0648\u0644\u0648\u06cc\u062a \u0631\u0627 \u062f\u0627\u0631\u062f<\/strong>.  \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u062b\u0627\u0628\u062a \u0686\u06cc\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0645\u06a9\u0627\u0646 \u062f\u0633\u062a\u0631\u0633\u06cc \u0633\u0631\u06cc\u0639 \u0628\u0647 \u0639\u0646\u0635\u0631 \u0628\u0627 \u0627\u0648\u0644\u0648\u06cc\u062a \u0631\u0627 \u0628\u062f\u0648\u0646 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062c\u0633\u062a\u062c\u0648 \u062f\u0631 \u06a9\u0644 \u0633\u0627\u062e\u062a\u0627\u0631 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u067e\u0634\u062a\u0647 \u0647\u0627 \u0647\u0633\u062a\u0646\u062f <strong>\u0647\u0645\u0647 \u06a9\u0627\u0631\u0647<\/strong>.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0647\u067e \u0647\u0627\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc (\u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0631 \u0648\u0627\u0644\u062f\u06cc\u0646 \u062d\u062f\u0627\u06a9\u062b\u0631 \u062f\u0648 \u0641\u0631\u0632\u0646\u062f \u062f\u0627\u0631\u0646\u062f) \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0647\u0633\u062a\u0646\u062f\u060c \u0647\u067e \u0647\u0627 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0628\u06cc\u0634 \u0627\u0632 \u062f\u0648 \u0641\u0631\u0632\u0646\u062f \u062a\u0639\u0645\u06cc\u0645 \u062f\u0627\u062f\u060c \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. <em>\u067e\u0634\u062a\u0647 \u0647\u0627\u06cc d-ary<\/em>.  \u0627\u06cc\u0646 \u0627\u0646\u0639\u0637\u0627\u0641 \u067e\u0630\u06cc\u0631\u06cc \u0627\u0645\u06a9\u0627\u0646 \u062a\u0646\u0638\u06cc\u0645 \u062f\u0642\u06cc\u0642 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0648\u0627\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0627\u0635 \u0648 \u0627\u0644\u0632\u0627\u0645\u0627\u062a \u0639\u0645\u0644\u06a9\u0631\u062f \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u067e\u0634\u062a\u0647 \u0647\u0627 \u0647\u0633\u062a\u0646\u062f <strong>\u062e\u0648\u062f \u062a\u0646\u0638\u06cc\u0645<\/strong>.  \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u0639\u0646\u0627\u0635\u0631 \u0627\u0636\u0627\u0641\u0647 \u06cc\u0627 \u062d\u0630\u0641 \u0634\u0648\u0646\u062f\u060c \u0633\u0627\u062e\u062a\u0627\u0631 \u062e\u0648\u062f \u0631\u0627 \u0645\u062c\u062f\u062f\u0627\u064b \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u062e\u0648\u0627\u0635 \u062e\u0648\u062f \u0631\u0627 \u062d\u0641\u0638 \u06a9\u0646\u062f.  \u0627\u06cc\u0646 \u062a\u0639\u0627\u062f\u0644 \u067e\u0648\u06cc\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0647\u06cc\u067e \u0647\u0645\u06cc\u0634\u0647 \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u0635\u0644\u06cc \u062e\u0648\u062f \u0628\u0647\u06cc\u0646\u0647 \u0645\u06cc \u0645\u0627\u0646\u062f.<\/p>\n<p>\u0628\u0627 \u06a9\u0627\u0648\u0634 \u0639\u0645\u06cc\u0642\u200c\u062a\u0631 \u062f\u0631 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0648 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0639\u0645\u0644\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0648\u0627\u0642\u0639\u06cc heaps \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0645\u0627 \u0622\u0634\u06a9\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n<h3 id=\"typesofheaps\"><span class=\"ez-toc-section\" id=\"%d8%a7%d9%86%d9%88%d8%a7%d8%b9_%d9%87%db%8c%d9%be_%d9%87%d8%a7\"><\/span>\u0627\u0646\u0648\u0627\u0639 \u0647\u06cc\u067e \u0647\u0627<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0647\u0645\u0647 \u062a\u0648\u062f\u0647 \u0647\u0627 \u06cc\u06a9\u0633\u0627\u0646 \u0627\u06cc\u062c\u0627\u062f \u0646\u0645\u06cc \u0634\u0648\u0646\u062f.  \u0628\u0633\u062a\u0647 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0648 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0633\u0627\u062e\u062a\u0627\u0631\u06cc\u060c \u0647\u067e \u0647\u0627 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u06cc \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0631\u062f \u06a9\u0647 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627 \u0648 \u0645\u0632\u0627\u06cc\u0627\u06cc \u062e\u0627\u0635 \u062e\u0648\u062f \u0631\u0627 \u062f\u0627\u0631\u0646\u062f.  \u062f\u0648 \u062f\u0633\u062a\u0647 \u0627\u0635\u0644\u06cc \u0647\u0633\u062a\u0646\u062f <em>\u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u0634\u062a\u0647<\/em> \u0648 <em>\u067e\u0634\u062a\u0647 \u062f\u0642\u06cc\u0642\u0647<\/em>.<\/p>\n<p>\u0645\u062a\u0645\u0627\u06cc\u0632\u062a\u0631\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u0627\u0644\u0641 <strong>\u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u0634\u062a\u0647<\/strong> \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0647\u0631 \u06af\u0631\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u06cc\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u0622\u0646 \u0627\u0633\u062a.  \u0627\u06cc\u0646 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u062f\u0631 \u067e\u0634\u062a\u0647 \u0647\u0645\u06cc\u0634\u0647 \u062f\u0631 \u0631\u06cc\u0634\u0647 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f.  \u0686\u0646\u06cc\u0646 \u0633\u0627\u062e\u062a\u0627\u0631\u06cc \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0632\u0645\u0627\u0646\u06cc \u0645\u0641\u06cc\u062f \u0627\u0633\u062a \u06a9\u0647 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062f\u0633\u062a\u0631\u0633\u06cc \u0645\u06a9\u0631\u0631 \u0628\u0647 \u0639\u0646\u0635\u0631 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0645\u0627\u0646\u0646\u062f \u0627\u062c\u0631\u0627\u06cc \u0635\u0641 \u0647\u0627\u06cc \u0627\u0648\u0644\u0648\u06cc\u062a \u062f\u0627\u0631 \u062e\u0627\u0635.<\/p>\n<p>\u0647\u0645\u062a\u0627\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u0647\u06cc\u067e\u060c a <strong>\u067e\u0634\u062a\u0647 \u062f\u0642\u06cc\u0642\u0647<\/strong> \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0647\u0631 \u06af\u0631\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0631\u0632\u0646\u062f\u0627\u0646 \u0622\u0646 \u0628\u0627\u0634\u062f.  \u0627\u06cc\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u067e\u0634\u062a\u0647 \u0631\u0627 \u062f\u0631 \u0631\u06cc\u0634\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.  \u062a\u0648\u062f\u0647\u200c\u0647\u0627\u06cc \u062d\u062f\u0627\u0642\u0644 \u062f\u0631 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 \u0627\u0647\u0645\u06cc\u062a \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a\u060c \u0645\u0627\u0646\u0646\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0627 \u067e\u0631\u062f\u0627\u0632\u0634 \u0628\u0644\u0627\u062f\u0631\u0646\u06af \u062f\u0627\u062f\u0647 \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u0646\u062f\u060c \u0628\u0633\u06cc\u0627\u0631 \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0647\u0627\u06cc \u0627\u0648\u0644\u06cc\u0647\u060c \u0647\u067e \u0647\u0627 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0627\u06a9\u062a\u0648\u0631 \u0627\u0646\u0634\u0639\u0627\u0628 \u0622\u0646\u0647\u0627 \u0646\u06cc\u0632 \u0645\u062a\u0645\u0627\u06cc\u0632 \u06a9\u0631\u062f:<\/p>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u067e\u0634\u062a\u0647 \u0647\u0627\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0647\u0633\u062a\u0646\u062f\u060c \u0628\u0627 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0648\u0627\u0644\u062f\u06cc\u0646 \u062d\u062f\u0627\u06a9\u062b\u0631 \u062f\u0648 \u0641\u0631\u0632\u0646\u062f\u060c \u0645\u0641\u0647\u0648\u0645 \u0647\u067e \u0647\u0627 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u06af\u0631\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u06cc\u0634 \u0627\u0632 \u062f\u0648 \u0641\u0631\u0632\u0646\u062f \u062f\u0627\u0631\u0646\u062f \u062a\u0639\u0645\u06cc\u0645 \u062f\u0627\u062f.  \u062f\u0631 \u06cc\u06a9 <strong>\u067e\u0634\u062a\u0647 d-ary<\/strong>\u060c \u0647\u0631 \u06af\u0631\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u062f\u0627\u0631\u062f <code>d<\/code> \u0641\u0631\u0632\u0646\u062f\u0627\u0646.  \u0627\u06cc\u0646 \u062a\u0646\u0648\u0639 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc \u062e\u0627\u0635\u060c \u0645\u0627\u0646\u0646\u062f \u06a9\u0627\u0647\u0634 \u0627\u0631\u062a\u0641\u0627\u0639 \u062f\u0631\u062e\u062a \u0628\u0631\u0627\u06cc \u0633\u0631\u0639\u062a \u0628\u062e\u0634\u06cc\u062f\u0646 \u0628\u0647 \u0639\u0645\u0644\u06cc\u0627\u062a \u062e\u0627\u0635\u060c \u0628\u0647\u06cc\u0646\u0647 \u06a9\u0631\u062f.<\/p>\n<p><strong>\u062f\u0648\u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u06cc\u067e<\/strong> \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u062f\u0631\u062e\u062a\u0627\u0646 \u062f\u0648 \u062c\u0645\u0644\u0647 \u0627\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u067e\u0634\u062a\u0647 \u0647\u0627\u06cc \u062f\u0648\u062c\u0645\u0644\u0647 \u0627\u06cc \u062f\u0631 \u0627\u062c\u0631\u0627\u06cc \u0635\u0641 \u0647\u0627\u06cc \u0627\u0648\u0644\u0648\u06cc\u062a \u062f\u0627\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u062f\u063a\u0627\u0645 \u06a9\u0627\u0631\u0622\u0645\u062f \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u0646\u062f.<\/p>\n<p>\u0646\u0627\u0645 \u0622\u0646 \u0627\u0632 \u062f\u0646\u0628\u0627\u0644\u0647 \u0645\u0639\u0631\u0648\u0641 \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc\u060c the <strong>\u067e\u0634\u062a\u0647 \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc<\/strong> \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627\u06cc \u0627\u0633\u062a\u0647\u0644\u0627\u06a9 \u0628\u0647\u062a\u0631\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0639\u0645\u0644\u06cc\u0627\u062a \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 \u067e\u0634\u062a\u0647 \u0647\u0627\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u06cc\u0627 \u062f\u0648 \u062c\u0645\u0644\u0647 \u0627\u06cc \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f.  \u0622\u0646\u0647\u0627 \u0628\u0647 \u0648\u06cc\u0698\u0647 \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u0634\u0628\u06a9\u0647 \u0645\u0641\u06cc\u062f \u0647\u0633\u062a\u0646\u062f.<\/p>\n<h3 id=\"pythonsheapimplementationtheheapqmodule\"><span class=\"ez-toc-section\" id=\"%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d9%87%db%8c%d9%be_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86_%e2%80%93_the_heapq_%d9%85%d8%af%d9%88%d9%84\"><\/span>\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0647\u06cc\u067e \u067e\u0627\u06cc\u062a\u0648\u0646 &#8211; The <em>heapq<\/em> \u0645\u062f\u0648\u0644<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u067e\u0627\u06cc\u062a\u0648\u0646 \u06cc\u06a9 \u0645\u0627\u0698\u0648\u0644 \u062f\u0627\u062e\u0644\u06cc \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a \u067e\u0634\u062a\u0647 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f &#8211; the <code>heapq<\/code> \u0645\u062f\u0648\u0644.  \u0627\u06cc\u0646 \u0645\u0627\u0698\u0648\u0644 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 heap \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0628\u0647 \u062a\u0648\u0633\u0639\u0647 \u062f\u0647\u0646\u062f\u06af\u0627\u0646 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u0644\u06cc\u0633\u062a \u0647\u0627 \u0631\u0627 \u0628\u0647 heap \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u0647 \u0648 \u0628\u062f\u0648\u0646 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc\u060c \u0639\u0645\u0644\u06cc\u0627\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 heap \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u0646\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u062a\u0641\u0627\u0648\u062a\u200c\u0647\u0627\u06cc \u0638\u0631\u06cc\u0641 \u0627\u06cc\u0646 \u0645\u0627\u0698\u0648\u0644 \u0648 \u0627\u06cc\u0646\u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0642\u062f\u0631\u062a \u067e\u0634\u062a\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0634\u0645\u0627 \u0628\u0647 \u0627\u0631\u0645\u063a\u0627\u0646 \u0645\u06cc\u200c\u0622\u0648\u0631\u062f\u060c \u0628\u067e\u0631\u062f\u0627\u0632\u06cc\u0645.<\/p>\n<p>\u0631\u0627 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644 \u06cc\u06a9 \u0646\u0648\u0639 \u062f\u0627\u062f\u0647 \u067e\u0634\u062a\u0647 \u0645\u062a\u0645\u0627\u06cc\u0632 \u0627\u0631\u0627\u0626\u0647 \u0646\u0645\u06cc \u062f\u0647\u062f.  \u062f\u0631 \u0639\u0648\u0636\u060c \u062a\u0648\u0627\u0628\u0639\u06cc \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0631\u0648\u06cc \u0644\u06cc\u0633\u062a\u200c\u0647\u0627\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0645\u0639\u0645\u0648\u0644\u06cc \u06a9\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c \u0622\u0646\u0647\u0627 \u0631\u0627 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0647\u200c\u0639\u0646\u0648\u0627\u0646 \u0622\u0646\u200c\u0647\u0627 \u0631\u0641\u062a\u0627\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f <em>\u067e\u0634\u062a\u0647 \u0647\u0627\u06cc \u062f\u0648\u062a\u0627\u06cc\u06cc<\/em>.<\/p>\n<blockquote>\n<p>\u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0647\u0645 \u0627\u0632 \u0646\u0638\u0631 \u062d\u0627\u0641\u0638\u0647 \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a \u0648 \u0647\u0645 \u0628\u0647 \u0637\u0648\u0631 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0628\u0627 \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0645\u0648\u062c\u0648\u062f \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u062f\u063a\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<\/blockquote>\n<p>\u06cc\u0639\u0646\u06cc \u0647\u0645\u06cc\u0646 <em>\u067e\u0634\u062a\u0647 \u0647\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0644\u06cc\u0633\u062a \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f<\/em> \u06a9\u0647 \u062f\u0631 <code>heapq<\/code>.  \u0632\u06cc\u0628\u0627\u06cc\u06cc \u0627\u06cc\u0646 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0631 \u0633\u0627\u062f\u06af\u06cc \u0622\u0646 \u0627\u0633\u062a &#8211; \u0633\u06cc\u0633\u062a\u0645 \u0641\u0647\u0631\u0633\u062a \u0641\u0647\u0631\u0633\u062a \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0635\u0641\u0631 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u0646\u0631\u06cc \u0636\u0645\u0646\u06cc \u0639\u0645\u0644 \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u0631\u0627\u06cc \u0647\u0631 \u0639\u0646\u0635\u0631 \u0645\u0639\u06cc\u0646 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a <code>i<\/code>\u060c \u0622\u0646:<\/p>\n<ul>\n<li>\u06a9\u0648\u062f\u06a9 \u0686\u067e \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0627\u0633\u062a <code>2*i + 1<\/code><\/li>\n<li>\u06a9\u0648\u062f\u06a9 \u0631\u0627\u0633\u062a \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0627\u0633\u062a <code>2*i + 2<\/code><\/li>\n<li>\u06af\u0631\u0647 \u0648\u0627\u0644\u062f \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0627\u0633\u062a <code>(i-1)\/\/2<\/code><\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/s3.stackabuse.com\/media\/articles\/guide-to-heaps-in-python-3.png\" alt=\"guide-to-heaps-in-python-03.png\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0633\u0627\u062e\u062a\u0627\u0631 \u0636\u0645\u0646\u06cc \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u0646\u0631\u06cc \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u06af\u0631\u0647 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0646\u06cc\u0633\u062a\u060c \u0639\u0645\u0644\u06cc\u0627\u062a \u0631\u0627 \u0633\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062d\u0627\u0641\u0638\u0647 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0645\u06cc \u0631\u0633\u0627\u0646\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0641\u0636\u0627:<\/strong> Heap \u0647\u0627 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0631\u062e\u062a \u0647\u0627\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u06cc \u0634\u0648\u0646\u062f\u060c \u0627\u0645\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0630\u062e\u06cc\u0631\u0647 \u0627\u0634\u0627\u0631\u0647 \u06af\u0631\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0628\u0631\u0627\u06cc \u06af\u0631\u0647 \u0647\u0627\u06cc \u0641\u0631\u0632\u0646\u062f \u0646\u062f\u0627\u0631\u0646\u062f.  \u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u0645\u06cc \u0634\u0648\u062f \u0622\u0646\u0647\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0627 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0641\u0636\u0627\u06cc\u06cc <em>\u0628\u0631)<\/em> \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u0633\u0627\u0632\u06cc n \u0639\u0646\u0635\u0631<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0630\u06a9\u0631 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 <code>heapq<\/code> \u0645\u062f\u0648\u0644 <strong>\u0628\u0647 \u0635\u0648\u0631\u062a \u067e\u06cc\u0634\u200c\u0641\u0631\u0636 \u062a\u0639\u062f\u0627\u062f min heap \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f<\/strong>.  \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0647\u0645\u06cc\u0634\u0647 \u062f\u0631 \u0631\u06cc\u0634\u0647 (\u06cc\u0627 \u0627\u0648\u0644\u06cc\u0646 \u0645\u0648\u0642\u0639\u06cc\u062a \u062f\u0631 \u0644\u06cc\u0633\u062a) \u0627\u0633\u062a.  \u0627\u06af\u0631 \u0628\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u062f\u060c \u0628\u0627\u06cc\u062f \u062a\u0631\u062a\u06cc\u0628 \u0631\u0627 \u0628\u0627 \u0636\u0631\u0628 \u0639\u0646\u0627\u0635\u0631 \u062f\u0631 \u0628\u0631\u0639\u06a9\u0633 \u06a9\u0646\u06cc\u062f <code>-1<\/code> \u06cc\u0627 \u0627\u0632 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u067e\u0627\u06cc\u062a\u0648\u0646 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0628\u0647 \u062a\u0648\u0633\u0639\u0647 \u062f\u0647\u0646\u062f\u06af\u0627\u0646 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u0639\u0645\u0644\u06cc\u0627\u062a \u067e\u0634\u062a\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u062f\u0631 \u0644\u06cc\u0633\u062a \u0647\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u0646\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/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 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644 \u062f\u0631 \u0628\u0631\u0646\u0627\u0645\u0647 \u062e\u0648\u062f\u060c \u0628\u0627\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0633\u0627\u062f\u0647 \u0648\u0627\u0631\u062f \u06a9\u0646\u06cc\u062f  <code>import heapq<\/code>.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u062f\u0631 \u0628\u062e\u0634\u200c\u0647\u0627\u06cc \u0628\u0639\u062f\u06cc\u060c \u0628\u0647 \u0639\u0645\u0642 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a\u200c\u0647\u0627\u06cc \u0627\u0633\u0627\u0633\u06cc \u0645\u06cc\u200c\u067e\u0631\u062f\u0627\u0632\u06cc\u0645\u060c \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u0648 \u0645\u0648\u0627\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n<h3 id=\"howtotransformalistintoaheap\"><span class=\"ez-toc-section\" id=\"%da%86%da%af%d9%88%d9%86%d9%87_%db%8c%da%a9_%d9%84%db%8c%d8%b3%d8%aa_%d8%b1%d8%a7_%d8%a8%d9%87_%db%8c%da%a9_%d9%be%d8%b4%d8%aa%d9%87_%d8%aa%d8%a8%d8%af%db%8c%d9%84_%da%a9%d9%86%db%8c%d9%85\"><\/span>\u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u06cc\u0645<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>heapify()<\/code> \u062a\u0627\u0628\u0639 \u0646\u0642\u0637\u0647 \u0634\u0631\u0648\u0639 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u06a9\u0627\u0631\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u067e\u0634\u062a\u0647 \u0627\u0633\u062a.  \u06cc\u06a9 \u062a\u06a9\u0631\u0627\u0631 (\u0645\u0639\u0645\u0648\u0644\u0627\u064b \u06cc\u06a9 \u0644\u06cc\u0633\u062a) \u0645\u06cc \u06af\u06cc\u0631\u062f \u0648 \u0639\u0646\u0627\u0635\u0631 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u062c\u0627\u06cc \u062e\u0648\u062f \u0645\u062c\u062f\u062f\u0627\u064b \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u06a9\u0648\u0686\u06a9 \u0631\u0627 \u0628\u0631\u0622\u0648\u0631\u062f\u0647 \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\ndata = (<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">6<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>)\nheapq.heapify(data)\n<span class=\"hljs-built_in\">print<\/span>(data)\n<\/code><\/pre>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u062f\u0648\u0628\u0627\u0631\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062d\u062f\u0627\u0642\u0644 \u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">(1, 1, 2, 3, 3, 9, 4, 6, 5, 5, 5)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong> \u062a\u0628\u062f\u06cc\u0644 \u06cc\u06a9 \u0644\u06cc\u0633\u062a \u0646\u0627\u0645\u0631\u062a\u0628 \u0628\u0647 \u067e\u0634\u062a\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>heapify<\/code> \u062a\u0627\u0628\u0639 \u06cc\u06a9 \u0627\u0633\u062a <em>\u0628\u0631)<\/em> \u0639\u0645\u0644.  \u0627\u06cc\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062e\u0644\u0627\u0641 \u0648\u0627\u0642\u0639 \u0628\u0647 \u0646\u0638\u0631 \u0628\u0631\u0633\u062f\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0627\u0646\u062a\u0638\u0627\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f <em>O(nlogn)<\/em>\u060c \u0627\u0645\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631\u062e\u062a\u06cc\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0632\u0645\u0627\u0646 \u062e\u0637\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"howtoaddanelementtotheheap\"><span class=\"ez-toc-section\" id=\"%da%86%da%af%d9%88%d9%86%d9%87_%db%8c%da%a9_%d8%b9%d9%86%d8%b5%d8%b1_%d8%b1%d8%a7_%d8%a8%d9%87_heap_%d8%a7%d8%b6%d8%a7%d9%81%d9%87_%da%a9%d9%86%db%8c%d9%85\"><\/span>\u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0647 Heap \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>heappush()<\/code> \u062a\u0627\u0628\u0639 \u0628\u0647 \u0634\u0645\u0627 \u0627\u06cc\u0646 \u0627\u0645\u06a9\u0627\u0646 \u0631\u0627 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062c\u062f\u06cc\u062f \u0631\u0627 \u062f\u0631 \u067e\u0634\u062a\u0647 \u0648\u0627\u0631\u062f \u06a9\u0646\u06cc\u062f \u0648 \u062f\u0631 \u0639\u06cc\u0646 \u062d\u0627\u0644 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u067e\u0634\u062a\u0647 \u0631\u0627 \u062d\u0641\u0638 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\nheap = ()\nheapq.heappush(heap, <span class=\"hljs-number\">5<\/span>)\nheapq.heappush(heap, <span class=\"hljs-number\">3<\/span>)\nheapq.heappush(heap, <span class=\"hljs-number\">7<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(heap)\n<\/code><\/pre>\n<p>\u0628\u0627 \u0627\u062c\u0631\u0627\u06cc \u06a9\u062f\u060c \u0644\u06cc\u0633\u062a\u06cc \u0627\u0632 \u0639\u0646\u0627\u0635\u0631\u06cc \u06a9\u0647 \u0648\u06cc\u0698\u06af\u06cc min heap \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u0646\u062f \u0628\u0647 \u0634\u0645\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\">(3, 5, 7)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong> \u0639\u0645\u0644\u06cc\u0627\u062a \u062f\u0631\u062c \u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647\u060c \u06a9\u0647 \u0634\u0627\u0645\u0644 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0646 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062c\u062f\u06cc\u062f \u062f\u0631 \u067e\u0634\u062a\u0647 \u0628\u0627 \u062d\u0641\u0638 \u0648\u06cc\u0698\u06af\u06cc heap \u0627\u0633\u062a\u060c \u062f\u0627\u0631\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a. <em>O(logn)<\/em>.  \u0627\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a\u060c \u0627\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0627\u0632 \u0628\u0631\u06af \u0628\u0647 \u0631\u06cc\u0634\u0647 \u0633\u0641\u0631 \u06a9\u0646\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"howtoremoveandreturnthesmallestelementfromtheheap\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%ad%d9%88%d9%87_%d8%ad%d8%b0%d9%81_%d9%88_%d8%a8%d8%b1%da%af%d8%b1%d8%af%d8%a7%d9%86%d8%af%d9%86_%da%a9%d9%88%da%86%da%a9%d8%aa%d8%b1%db%8c%d9%86_%d8%b9%d9%86%d8%b5%d8%b1_%d8%a7%d8%b2_%d9%87%db%8c%d9%be\"><\/span>\u0646\u062d\u0648\u0647 \u062d\u0630\u0641 \u0648 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u062f\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 \u0647\u06cc\u067e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>heappop()<\/code> \u062a\u0627\u0628\u0639 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0627\u0632 \u067e\u0634\u062a\u0647 (\u0631\u06cc\u0634\u0647 \u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u06a9\u0648\u0686\u06a9) \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0648 \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f.  \u067e\u0633 \u0627\u0632 \u062d\u0630\u0641\u060c \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0644\u06cc\u0633\u062a \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0645\u0639\u062a\u0628\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\nheap = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">9<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(heapq.heappop(heap))\n<span class=\"hljs-built_in\">print<\/span>(heap)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0631\u0627 <code>heappop()<\/code> \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647 \u067e\u0631\u062f\u0627\u0632\u0634 \u0639\u0646\u0627\u0635\u0631 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0635\u0639\u0648\u062f\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u0646\u062f\u060c \u0645\u0627\u0646\u0646\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0647\u06cc\u067e\u060c \u06cc\u0627 \u0647\u0646\u06af\u0627\u0645 \u0627\u062c\u0631\u0627\u06cc \u0635\u0641\u200c\u0647\u0627\u06cc \u0627\u0648\u0644\u0648\u06cc\u062a\u06cc \u06a9\u0647 \u0648\u0638\u0627\u06cc\u0641 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0648\u0631\u06cc\u062a \u0622\u0646\u0647\u0627 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u0628\u0633\u06cc\u0627\u0631 \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u0627\u0633\u062a.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0648 \u0644\u06cc\u0633\u062a \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">1\n(3, 7, 5, 9)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646\u062c\u0627\u060c <code>1<\/code> \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0627\u0632 <code>heap<\/code>\u060c \u0648 \u0644\u06cc\u0633\u062a \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 \u0648\u06cc\u0698\u06af\u06cc heap \u0631\u0627 \u062d\u062a\u06cc \u067e\u0633 \u0627\u0632 \u062d\u0630\u0641 \u0645\u0627 \u062d\u0641\u0638 \u06a9\u0631\u062f\u0647 \u0627\u0633\u062a <code>1<\/code>.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong> \u062d\u0630\u0641 \u0639\u0646\u0635\u0631 \u0631\u06cc\u0634\u0647 (\u06a9\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u06a9\u0648\u0686\u06a9 \u06cc\u0627 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0627\u0633\u062a) \u0648 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0645\u062c\u062f\u062f \u067e\u0634\u062a\u0647 \u0646\u06cc\u0632 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f. <em>O(logn)<\/em> \u0632\u0645\u0627\u0646.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"howtopushanewitemandpopthesmallestitem\"><span class=\"ez-toc-section\" id=\"%da%86%da%af%d9%88%d9%86%d9%87_%db%8c%da%a9_%d9%85%d9%88%d8%b1%d8%af_%d8%ac%d8%af%db%8c%d8%af_%d8%b1%d8%a7_%d9%81%d8%b4%d8%a7%d8%b1_%d8%af%d9%87%db%8c%d8%af_%d9%88_%da%a9%d9%88%da%86%da%a9%d8%aa%d8%b1%db%8c%d9%86_%d9%85%d9%88%d8%b1%d8%af_%d8%b1%d8%a7_%d9%be%d8%a7%d9%be_%da%a9%d9%86%db%8c%d8%af\"><\/span>\u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0645\u0648\u0631\u062f \u062c\u062f\u06cc\u062f \u0631\u0627 \u0641\u0634\u0627\u0631 \u062f\u0647\u06cc\u062f \u0648 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0631\u0627 \u067e\u0627\u067e \u06a9\u0646\u06cc\u062f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>heappushpop()<\/code> \u062a\u0627\u0628\u0639 \u06cc\u06a9 \u0639\u0645\u0644\u06cc\u0627\u062a \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0622\u06cc\u062a\u0645 \u062c\u062f\u06cc\u062f \u0631\u0627 \u0631\u0648\u06cc \u067e\u0634\u062a\u0647 \u0647\u0644 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0633\u067e\u0633 \u0638\u0627\u0647\u0631 \u0645\u06cc \u0634\u0648\u062f \u0648 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0622\u06cc\u062a\u0645 \u0631\u0627 \u0627\u0632 \u067e\u0634\u062a\u0647 \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\nheap = (<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">9<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(heapq.heappushpop(heap, <span class=\"hljs-number\">4<\/span>)) \n<span class=\"hljs-built_in\">print<\/span>(heap)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u062e\u0631\u0648\u062c\u06cc \u062e\u0648\u0627\u0647\u062f \u0634\u062f <code>3<\/code>\u060c \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631\u060c \u0648 \u0686\u0627\u067e \u062c\u062f\u06cc\u062f <code>heap<\/code> \u0644\u06cc\u0633\u062a\u06cc \u06a9\u0647 \u0627\u06a9\u0646\u0648\u0646 \u0634\u0627\u0645\u0644 \u0645\u06cc \u0634\u0648\u062f <code>4<\/code> \u062f\u0631 \u062d\u06cc\u0646 \u062d\u0641\u0638 \u062e\u0627\u0635\u06cc\u062a heap:<\/p>\n<pre><code class=\"hljs\">3\n(4, 5, 7, 9)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/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\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>heappushpop()<\/code> \u0639\u0645\u0644\u06a9\u0631\u062f \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631 \u0627\u0632 \u0627\u0646\u062c\u0627\u0645 \u0639\u0645\u0644\u06cc\u0627\u062a \u0647\u0644 \u062f\u0627\u062f\u0646 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062c\u062f\u06cc\u062f \u0648 \u0628\u06cc\u0631\u0648\u0646 \u0632\u062f\u0646 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0628\u0647 \u0637\u0648\u0631 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0627\u0633\u062a.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"howtoreplacethesmallestitemandpushanewitem\"><span class=\"ez-toc-section\" id=\"%da%86%da%af%d9%88%d9%86%d9%87_%da%a9%d9%88%da%86%da%a9%d8%aa%d8%b1%db%8c%d9%86_%d9%85%d9%88%d8%b1%d8%af_%d8%b1%d8%a7_%d8%ac%d8%a7%db%8c%da%af%d8%b2%db%8c%d9%86_%da%a9%d9%86%db%8c%d9%85_%d9%88_%db%8c%da%a9_%d9%85%d9%88%d8%b1%d8%af_%d8%ac%d8%af%db%8c%d8%af_%d8%b1%d8%a7_%d9%81%d8%b4%d8%a7%d8%b1_%d8%af%d9%87%db%8c%d9%85\"><\/span>\u0686\u06af\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0631\u0627 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u06a9 \u0645\u0648\u0631\u062f \u062c\u062f\u06cc\u062f \u0631\u0627 \u0641\u0634\u0627\u0631 \u062f\u0647\u06cc\u0645<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>heapreplace()<\/code> \u062a\u0627\u0628\u0639 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0627\u0632 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062c\u062f\u06cc\u062f \u0631\u0627 \u0631\u0648\u06cc \u067e\u0634\u062a\u0647 \u0647\u0644 \u0645\u06cc \u062f\u0647\u062f\u060c \u0647\u0645\u0647 \u062f\u0631 \u06cc\u06a9 \u0639\u0645\u0644\u06cc\u0627\u062a \u06a9\u0627\u0631\u0622\u0645\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\nheap = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">9<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(heapq.heapreplace(heap, <span class=\"hljs-number\">4<\/span>))\n<span class=\"hljs-built_in\">print<\/span>(heap)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0686\u0627\u067e \u0645\u06cc \u06a9\u0646\u062f <code>1<\/code>\u060c \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631\u060c \u0648 \u0644\u06cc\u0633\u062a \u0627\u06a9\u0646\u0648\u0646 \u0634\u0627\u0645\u0644 4 \u0627\u0633\u062a \u0648 \u0648\u06cc\u0698\u06af\u06cc heap \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\">1\n(4, 5, 7, 9)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\">\n                            <img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2023\/12\/icon-information-circle-solid.svg.svg+xml\" class=\"icon\" aria-hidden=\"true\" alt=\"\" title=\"\">\n                        <\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f<\/strong>: <code>heapreplace()<\/code> \u062f\u0631 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc \u067e\u062e\u0634 \u062c\u0631\u06cc\u0627\u0646\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0641\u0639\u0644\u06cc \u0631\u0627 \u0628\u0627 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u062c\u062f\u06cc\u062f \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u06a9\u0646\u06cc\u062f \u0645\u0641\u06cc\u062f \u0627\u0633\u062a\u060c \u0645\u0627\u0646\u0646\u062f \u0639\u0645\u0644\u06cc\u0627\u062a \u067e\u0646\u062c\u0631\u0647 \u0686\u0631\u062e\u0634\u06cc \u06cc\u0627 \u0648\u0638\u0627\u06cc\u0641 \u067e\u0631\u062f\u0627\u0632\u0634 \u062f\u0627\u062f\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648\u0627\u0642\u0639\u06cc.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"findingmultipleextremesinpythonsheap\"><span class=\"ez-toc-section\" id=\"%db%8c%d8%a7%d9%81%d8%aa%d9%86_%d8%a7%da%a9%d8%b3%d8%aa%d8%b1%db%8c%d9%85_%d9%87%d8%a7%db%8c_%d9%85%d8%aa%d8%b9%d8%af%d8%af_%d8%af%d8%b1_%d9%87%db%8c%d9%be_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u06cc\u0627\u0641\u062a\u0646 \u0627\u06a9\u0633\u062a\u0631\u06cc\u0645 \u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f \u062f\u0631 \u0647\u06cc\u067e \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><code>nlargest(n, iterable(, key))<\/code>  \u0648 <code>nsmallest(n, iterable(, key))<\/code> \u062a\u0648\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u0627\u0628\u06cc \u0686\u0646\u062f\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0628\u0632\u0631\u06af \u06cc\u0627 \u06a9\u0648\u0686\u06a9 \u0627\u0632 \u06cc\u06a9 \u062a\u06a9\u0631\u0627\u0631 \u0634\u0648\u0646\u062f\u0647 \u0637\u0631\u0627\u062d\u06cc \u0634\u062f\u0647 \u0627\u0646\u062f.  \u0622\u0646\u0647\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631 \u0627\u0632 \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 \u06a9\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0634\u0648\u0646\u062f\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0634\u0645\u0627 \u0641\u0642\u0637 \u0628\u0647 \u0686\u0646\u062f \u0645\u0642\u062f\u0627\u0631 \u0634\u062f\u06cc\u062f \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u062f.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0644\u06cc\u0633\u062a \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0627\u0631\u06cc\u062f \u0648 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0633\u0647 \u0645\u0642\u062f\u0627\u0631 \u06a9\u0648\u0686\u06a9 \u0648 \u0633\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u0632\u0631\u06af \u0631\u0627 \u062f\u0631 \u0644\u06cc\u0633\u062a \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">data = (<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">6<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646\u062c\u0627\u060c <code>nlargest()<\/code> \u0648 <code>nsmallest()<\/code> \u062a\u0648\u0627\u0628\u0639 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0645\u0641\u06cc\u062f \u0628\u0627\u0634\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\ndata = (<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">6<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">5<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(heapq.nlargest(<span class=\"hljs-number\">3<\/span>, data))  <span class=\"hljs-comment\"># Outputs (9, 6, 5)<\/span>\n<span class=\"hljs-built_in\">print<\/span>(heapq.nsmallest(<span class=\"hljs-number\">3<\/span>, data))  <span class=\"hljs-comment\"># Outputs (1, 1, 2)<\/span>\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0628\u0647 \u0634\u0645\u0627 \u062f\u0648 \u0644\u06cc\u0633\u062a \u0645\u06cc \u062f\u0647\u062f &#8211; \u06cc\u06a9\u06cc \u0634\u0627\u0645\u0644 \u0633\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u0632\u0631\u06af \u0648 \u062f\u06cc\u06af\u0631\u06cc \u0634\u0627\u0645\u0644 \u0633\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0627\u0632 <code>data<\/code> \u0644\u06cc\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">(9, 6, 5)\n(1, 1, 2)\n<\/code><\/pre>\n<h3 id=\"howtobuildyourcustomheap\"><span class=\"ez-toc-section\" id=\"%da%86%da%af%d9%88%d9%86%d9%87_%d9%87%d9%be_%d8%b3%d9%81%d8%a7%d8%b1%d8%b4%db%8c_%d8%ae%d9%88%d8%af_%d8%b1%d8%a7_%d8%a8%d8%b3%d8%a7%d8%b2%db%8c%d8%af\"><\/span>\u0686\u06af\u0648\u0646\u0647 \u0647\u067e \u0633\u0641\u0627\u0631\u0634\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0633\u0627\u0632\u06cc\u062f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u067e\u0627\u06cc\u062a\u0648\u0646 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0642\u0648\u06cc \u0627\u0632 \u0627\u0628\u0632\u0627\u0631\u0647\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631 \u0628\u0627 heap \u0647\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0631\u0641\u062a\u0627\u0631 \u067e\u06cc\u0634 \u0641\u0631\u0636 min heap \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u06a9\u0627\u0641\u06cc \u0646\u0628\u0627\u0634\u062f.  \u0686\u0647 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u0647\u06cc\u067e \u0628\u0627\u0634\u06cc\u062f \u06cc\u0627 \u0628\u0647 \u0647\u06cc\u067e \u0646\u06cc\u0627\u0632 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0628\u0631 \u0627\u0633\u0627\u0633 \u062a\u0648\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc \u0639\u0645\u0644 \u06a9\u0646\u062f\u060c \u0633\u0627\u062e\u062a \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u067e\u0627\u0633\u062e\u06af\u0648 \u0628\u0627\u0634\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0627\u0646\u0628\u0648\u0647\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0646\u06cc\u0627\u0632\u0647\u0627\u06cc \u062e\u0627\u0635 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u06cc\u0645.<\/p>\n<h4 id=\"implementingamaxheapusingheapq\">\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Max Heap \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>heapq<\/code><\/h4>\n<p>\u0628\u0647 \u0635\u0648\u0631\u062a \u067e\u06cc\u0634 \u0641\u0631\u0636\u060c <code>heapq<\/code> \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f <em>\u06a9\u067e\u0647 \u0647\u0627\u06cc \u062f\u0642\u06cc\u0642\u0647<\/em>.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0627 \u06cc\u06a9 \u062a\u0631\u0641\u0646\u062f \u0633\u0627\u062f\u0647\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u0622\u0646 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06cc\u06a9 max heap \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.  \u0627\u06cc\u062f\u0647 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u0628\u0627 \u0636\u0631\u0628 \u0622\u0646\u0647\u0627 \u062f\u0631 \u0645\u0639\u06a9\u0648\u0633 \u06a9\u0646\u06cc\u0645 <code>-1<\/code> \u0642\u0628\u0644 \u0627\u0632 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 \u0622\u0646\u0647\u0627 \u0628\u0647 \u067e\u0634\u062a\u0647:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\n<span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">MaxHeap<\/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.heap = ()\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">push<\/span>(<span class=\"hljs-params\">self, val<\/span>):<\/span>\n        heapq.heappush(self.heap, -val)\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">pop<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        <span class=\"hljs-keyword\">return<\/span> -heapq.heappop(self.heap)\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">peek<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        <span class=\"hljs-keyword\">return<\/span> -self.heap(<span class=\"hljs-number\">0<\/span>)\n<\/code><\/pre>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f\u060c \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0639\u062f\u062f (\u0627\u0632 \u0646\u0638\u0631 \u0642\u062f\u0631 \u0645\u0637\u0644\u0642) \u0628\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f\u060c \u06a9\u0647 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f <code>heapq<\/code> \u0639\u0645\u0644\u06a9\u0631\u062f\u06cc \u0628\u0631\u0627\u06cc \u062d\u0641\u0638 \u0633\u0627\u062e\u062a\u0627\u0631 \u067e\u0634\u062a\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631.<\/p>\n<h4 id=\"heapswithcustomcomparisonfunctions\">Heaps \u0628\u0627 \u062a\u0648\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc<\/h4>\n<p>\u06af\u0627\u0647\u06cc \u0627\u0648\u0642\u0627\u062a\u060c \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0641\u0642\u0637 \u0628\u0631 \u0627\u0633\u0627\u0633 \u062a\u0631\u062a\u06cc\u0628 \u0637\u0628\u06cc\u0639\u06cc \u0639\u0646\u0627\u0635\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0646\u0634\u0648\u062f.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u0628\u0627 \u0627\u0634\u06cc\u0627\u0621 \u067e\u06cc\u0686\u06cc\u062f\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u062f \u06cc\u0627 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062e\u0627\u0635\u06cc \u062f\u0627\u0631\u06cc\u062f\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc \u0636\u0631\u0648\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0647\u062f\u0641\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u06a9\u0644\u0627\u0633 \u06a9\u0645\u06a9\u06cc \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u062f \u06a9\u0647 \u0639\u0645\u0644\u06af\u0631\u0647\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0631\u0627 \u0644\u063a\u0648 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> heapq\n\n<span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">CustomElement<\/span>:<\/span>\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__init__<\/span>(<span class=\"hljs-params\">self, obj, comparator<\/span>):<\/span>\n        self.obj = obj\n        self.comparator = comparator\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__lt__<\/span>(<span class=\"hljs-params\">self, other<\/span>):<\/span>\n        <span class=\"hljs-keyword\">return<\/span> self.comparator(self.obj, other.obj)\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">custom_heappush<\/span>(<span class=\"hljs-params\">heap, obj, comparator=<span class=\"hljs-keyword\">lambda<\/span> x, y: x &lt; y<\/span>):<\/span>\n    heapq.heappush(heap, CustomElement(obj, comparator))\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">custom_heappop<\/span>(<span class=\"hljs-params\">heap<\/span>):<\/span>\n    <span class=\"hljs-keyword\">return<\/span> heapq.heappop(heap).obj\n<\/code><\/pre>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062a\u0646\u0638\u06cc\u0645\u0627\u062a\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0647\u0631 \u062a\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0646\u0646\u062f\u0647 \u0633\u0641\u0627\u0631\u0634\u06cc \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u062f \u0648 \u0627\u0632 \u0622\u0646 \u0628\u0627 heap \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<h3 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Heaps \u0639\u0645\u0644\u06a9\u0631\u062f \u0642\u0627\u0628\u0644 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0627\u0646\u062a\u062e\u0627\u0628\u06cc \u0645\u0637\u0645\u0626\u0646 \u0628\u0631\u0627\u06cc \u0648\u0638\u0627\u06cc\u0641 \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0627\u0648\u0644\u0648\u06cc\u062a \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0627\u0644\u0632\u0627\u0645\u0627\u062a \u0648 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062e\u0627\u0635 \u0628\u0631\u0646\u0627\u0645\u0647 \u062f\u0631 \u062f\u0633\u062a \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a.  \u062f\u0631 \u0628\u0631\u062e\u06cc \u0645\u0648\u0627\u0631\u062f\u060c \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u0627\u062c\u0631\u0627\u06cc heap \u06cc\u0627 \u062d\u062a\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647\u062a\u0631\u06cc \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>Heaps\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u0627 \u0627\u0632 \u067e\u0633\u062a\u06cc \u0648 \u0628\u0644\u0646\u062f\u06cc \u0622\u0646 \u0633\u0641\u0631 \u06a9\u0631\u062f\u06cc\u0645\u060c \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u062f\u06cc\u06af\u0631 \u0647\u0633\u062a\u0646\u062f.  \u0622\u0646\u0647\u0627 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u06a9\u0627\u0631\u0627\u06cc\u06cc\u060c \u0633\u0627\u062e\u062a\u0627\u0631 \u0648 \u0633\u0627\u0632\u06af\u0627\u0631\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u0646\u062f.  \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0627\u0633\u0627\u0633\u06cc \u0622\u0646\u0647\u0627 \u062a\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0622\u0646\u0647\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 <code>heapq<\/code> \u0645\u0627\u0698\u0648\u0644\u060c heaps \u06cc\u06a9 \u0631\u0627\u0647 \u062d\u0644 \u0642\u0648\u06cc \u0628\u0631\u0627\u06cc \u062a\u0639\u062f\u0627\u062f \u0628\u06cc \u0634\u0645\u0627\u0631\u06cc \u0627\u0632 \u0686\u0627\u0644\u0634 \u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc\u060c \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0622\u0646\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 \u0627\u0648\u0644\u0648\u06cc\u062a \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<\/div>\n<p><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1402-12-26 02:39:58<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;9027&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;\u0631\u0627\u0647\u0646\u0645\u0627\u06cc Heaps \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\"> 10<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0641\u0631\u0648\u062f\u06af\u0627\u0647\u06cc \u0634\u0644\u0648\u063a \u0631\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0647\u0631 \u062f\u0642\u06cc\u0642\u0647 \u067e\u0631\u0648\u0627\u0632\u0647\u0627\u06cc\u06cc \u0627\u0632 \u0622\u0646 \u0628\u0644\u0646\u062f \u0648 \u0641\u0631\u0648\u062f \u0645\u06cc\u200c\u0622\u06cc\u0646\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u06a9\u0646\u062a\u0631\u0644\u200c\u06a9\u0646\u0646\u062f\u0647\u200c\u0647\u0627\u06cc \u062a\u0631\u0627\u0641\u06cc\u06a9 \u0647\u0648\u0627\u06cc\u06cc \u067e\u0631\u0648\u0627\u0632\u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0648\u0631\u06cc\u062a \u0627\u0648\u0644\u0648\u06cc\u062a\u200c\u0628\u0646\u062f\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c heaps \u0628\u0647 \u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u062e\u0627\u0635 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0648 \u067e\u0631\u062f\u0627\u0632\u0634 \u06a9\u0646\u06cc\u0645 \u0648 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u062d\u0627\u0635\u0644 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u00ab\u0641\u0648\u0631\u06cc\u200c\u062a\u0631\u06cc\u0646\u00bb \u06cc\u0627 \u00ab\u0645\u0647\u0645\u200c\u062a\u0631\u06cc\u0646\u00bb \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0647\u0645\u06cc\u0634\u0647 \u062f\u0631 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":9029,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[1749,1750,1760,1747,1746,1753,1744,1759,1752],"class_list":["post-9027","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming","tag-python","tag-1750","tag-heaps","tag-python-vps","tag-vps-","tag-1753","tag-1744","tag-1759","tag-1752"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/9027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=9027"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/9027\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/9029"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=9027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=9027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=9027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}