{"id":15803,"date":"2024-01-17T08:37:11","date_gmt":"2024-01-17T05:07:11","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-17T08:37:11","modified_gmt":"2024-01-17T05:07:11","slug":"%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%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%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \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\/%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%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\/%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c_%e2%80%93_%d9%85%d8%ab%d8%a7%d9%84\" >\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc &#8211; \u0645\u062b\u0627\u0644<\/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\/%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%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_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c\" >\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c-%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c-%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\"> 5<\/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><em>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/em> \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a \u06a9\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647  \u0627\u063a\u0644\u0628 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u0648\u0644\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u0646\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f (<em>O(logn)<\/em>) \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0631\u0641\u062a\u0627\u0631 \u0634\u0647\u0648\u062f\u06cc \u0622\u0646 \u0648 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0633\u0627\u0633\u06cc \u062f\u0631 \u0639\u0644\u0648\u0645 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0627\u0633\u062a.<\/p>\n<blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0645\u0627 \u0628\u0647 \u0627\u06cc\u062f\u0647 \u067e\u0634\u062a \u0648 \u0627\u062c\u0631\u0627\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a <em>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/em>.<\/p>\n<\/blockquote>\n<h3 id=\"binarysearchexample\"><span class=\"ez-toc-section\" id=\"%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c_%e2%80%93_%d9%85%d8%ab%d8%a7%d9%84\"><\/span>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc &#8211; \u0645\u062b\u0627\u0644<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0622 <em>\u062a\u0641\u0631\u0642\u0647 \u0628\u06cc\u0646\u062f\u0627\u0632 \u0648 \u062d\u06a9\u0648\u0645\u062a \u06a9\u0646<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f \u0648 \u062a\u06a9\u06cc\u0647 \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u0627\u06cc\u0646 \u0648\u0627\u0642\u0639\u06cc\u062a \u06a9\u0647 <em>\u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a<\/em> \u0628\u0631\u0627\u06cc \u062d\u0630\u0641 \u0646\u06cc\u0645\u06cc \u0627\u0632 \u0646\u0627\u0645\u0632\u062f\u0647\u0627\u06cc \u0627\u062d\u062a\u0645\u0627\u0644\u06cc \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631.  \u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635\u060c \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0631\u0627 \u0628\u0627 \u0639\u0646\u0635\u0631\u06cc \u06a9\u0647 \u062f\u0631 \u062c\u0633\u062a\u062c\u0648\u06cc \u0622\u0646 \u0627\u0633\u062a \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u062a\u0635\u0645\u06cc\u0645 \u0628\u06af\u06cc\u0631\u062f \u06a9\u062c\u0627 \u0628\u0647 \u062c\u0633\u062a\u062c\u0648 \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u062f.<\/p>\n<p>\u0627\u06af\u0631 \u0639\u0646\u0635\u0631 \u0647\u062f\u0641 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0628\u0627\u0634\u062f &#8211; \u0646\u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0648\u0644 \u0645\u062c\u0645\u0648\u0639\u0647 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0648\u0631 \u0627\u0646\u062f\u0627\u062e\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0647\u0645\u06cc\u0646 \u0627\u0645\u0631 \u0628\u0631\u0639\u06a9\u0633 \u0627\u0633\u062a.<\/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>: \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0627\u0631\u0627\u06cc \u062a\u0639\u062f\u0627\u062f\u06cc \u0639\u0646\u0635\u0631 \u0632\u0648\u062c \u0628\u0627\u0634\u062f\u060c \u0628\u0631\u0627\u06cc \u0634\u0631\u0648\u0639 \u0627\u0632 \u06a9\u062f\u0627\u0645 \u06cc\u06a9 \u0627\u0632 \u062f\u0648 \u0639\u0646\u0635\u0631 &#8220;\u0648\u0633\u0637&#8221; \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0628\u0647 \u062a\u0648\u0636\u06cc\u062d \u0686\u06af\u0648\u0646\u06af\u06cc \u06a9\u0627\u0631\u06a9\u0631\u062f \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u06cc\u0645\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0631\u06cc\u0639 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/binary-search-in-python-1.png\" alt=\"\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u062f\u0631 python \u062a\u062c\u0633\u0645\" title=\"\"><\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645\u060c \u0645\u0627 \u0628\u0627 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0645\u0627 (<code>18<\/code>) \u062f\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0648\u0644 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0635\u0644\u06cc \u0646\u06cc\u0633\u062a.<\/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> \u0627\u0632 \u062d\u0627\u0644\u0627 \u0631\u0648\u06cc\u060c \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0639\u0644\u0627\u0645\u062a \u06af\u0630\u0627\u0631\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>x<\/code>.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0648\u0642\u062a\u06cc \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u06a9\u062f\u0627\u0645 \u0646\u06cc\u0645\u06cc \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0635\u0644\u06cc \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f <code>x<\/code> \u0627\u0633\u062a\u060c \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0631\u0627 \u062f\u0642\u06cc\u0642\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645 process \u0628\u0627 \u0622\u0646 \u0646\u06cc\u0645\u0647 \u0648 \u062f\u0648\u0628\u0627\u0631\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0646\u06cc\u0645 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u062f\u060c \u0646\u06cc\u0645\u0647 \u0627\u06cc \u06a9\u0647 \u0645\u0637\u0645\u0626\u0646\u0627\u064b \u062d\u0627\u0648\u06cc \u0622\u0646 \u0646\u06cc\u0633\u062a \u0631\u0627 \u062f\u0648\u0631 \u0628\u0631\u06cc\u0632\u06cc\u062f <code>x<\/code>:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/binary-search-in-python-2.png\" alt=\"\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u062f\u0631 python \u062a\u062c\u0633\u0645\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645 process \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u06cc\u06a9 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u06a9\u0647 \u0641\u0642\u0637 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0634\u0627\u0645\u0644 \u0645\u06cc \u0634\u0648\u062f\u060c \u0645\u06cc \u0631\u0633\u06cc\u0645.  \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0622\u0646 \u0639\u0646\u0635\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631 <code>x<\/code>.  \u0627\u06af\u0631 \u0686\u0646\u06cc\u0646 \u0627\u0633\u062a &#8211; \u0645\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u06cc\u0645 <code>x<\/code>\u060c \u0627\u06af\u0631 \u0627\u06cc\u0646\u0637\u0648\u0631 \u0646\u06cc\u0633\u062a &#8211; <code>x<\/code> \u0627\u0635\u0644\u0627 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.<\/p>\n<p>\u0627\u06af\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u062f\u0642\u062a \u06a9\u0646\u06cc\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u062a\u0648\u062c\u0647 \u0634\u0648\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a (<code>x<\/code> \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f)\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u062a\u0639\u062f\u0627\u062f \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0645\u062a\u0631\u06cc \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u0646\u0633\u0628\u062a \u0628\u0647 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 &#8211; \u06a9\u0647 \u0628\u0647 \u0686\u06cc\u0632\u06cc \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0637\u0648\u0644 \u062e\u0637\u0648\u0637 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f. <em>\u062c\u0633\u062a\u062c\u0648\u06cc \u062e\u0637\u06cc<\/em>\u060c \u06a9\u0647 \u0628\u0647 \u0637\u0631\u0632 \u062f\u06cc\u0648\u0627\u0646\u0647 \u06a9\u0646\u0646\u062f\u0647 \u0627\u06cc \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0642\u06cc\u0642 \u062a\u0631\u060c \u062a\u0639\u062f\u0627\u062f \u0639\u0646\u0627\u0635\u0631\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0627\u0633\u062a <em>O(log<sub>2<\/sub>\u0646)<\/em> \u062c\u0627\u06cc\u06cc \u06a9\u0647 <em>\u0646<\/em> \u062a\u0639\u062f\u0627\u062f \u0639\u0646\u0627\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u0647\u0631 \u0686\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u062a\u0623\u062b\u06cc\u0631 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0645\u06cc \u06af\u0630\u0627\u0631\u062f:<\/p>\n<blockquote>\n<p>\u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0627 10 \u0639\u0646\u0635\u0631 \u062f\u0627\u0634\u062a\u060c \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0628\u0627\u06cc\u062f \u0641\u0642\u0637 3 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 <code>x<\/code> \u06cc\u0627 \u0646\u062a\u06cc\u062c\u0647 \u0628\u06af\u06cc\u0631\u06cc\u062f \u06a9\u0647 \u0622\u0646\u062c\u0627 \u0646\u06cc\u0633\u062a.  \u06cc\u0639\u0646\u06cc 33.3 \u062f\u0631\u0635\u062f.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0627 10\u060c000\u060c000 \u0639\u0646\u0635\u0631 \u062f\u0627\u0634\u062a\u060c \u0641\u0642\u0637 \u0628\u0627\u06cc\u062f 24 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u06cc\u0646 0.0002\u066a \u0627\u0633\u062a.<\/p>\n<\/blockquote>\n<h3 id=\"binarysearchimplementation\"><span class=\"ez-toc-section\" id=\"%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d8%ac%d8%b3%d8%aa%d8%ac%d9%88%db%8c_%d8%a8%d8%a7%db%8c%d9%86%d8%b1%db%8c\"><\/span>\u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u06cc\u06a9 \u0627\u0633\u062a <em>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0637\u0628\u06cc\u0639\u06cc<\/em> \u0627\u0632 \u0647\u0645\u0627\u0646 \u0632\u0645\u0627\u0646 process \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0648 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 1 \u067e\u06cc\u062f\u0627 \u0634\u0648\u062f.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u0644\u0628\u062a\u0647 \u06cc\u06a9 \u0627\u062c\u0631\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631\u06cc \u0646\u06cc\u0632 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0648 \u0645\u0627 \u0647\u0631 \u062f\u0648 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0631\u0627 \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f.<\/p>\n<h4 id=\"recursive\">\u0628\u0627\u0632\u06af\u0634\u062a\u06cc<\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645 \u0632\u06cc\u0631\u0627 \u0637\u0628\u06cc\u0639\u06cc \u062a\u0631 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">binary_search_recursive<\/span>(<span class=\"hljs-params\">array, element, start, end<\/span>):<\/span>\n    <span class=\"hljs-keyword\">if<\/span> start &gt; end:\n        <span class=\"hljs-keyword\">return<\/span> -<span class=\"hljs-number\">1<\/span>\n\n    mid = (start + end) \/\/ <span class=\"hljs-number\">2<\/span>\n    <span class=\"hljs-keyword\">if<\/span> element == array(mid):\n        <span class=\"hljs-keyword\">return<\/span> mid\n\n    <span class=\"hljs-keyword\">if<\/span> element &lt; array(mid):\n        <span class=\"hljs-keyword\">return<\/span> binary_search_recursive(array, element, start, mid-<span class=\"hljs-number\">1<\/span>)\n    <span class=\"hljs-keyword\">else<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> binary_search_recursive(array, element, mid+<span class=\"hljs-number\">1<\/span>, end)\n<\/code><\/pre>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0627\u06cc\u0646 \u06a9\u062f \u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 serach \u0628\u0627\u06cc\u0646\u0631\u06cc \u0633\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0627\u06cc\u0646 \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u0622\u0645\u0627\u062f\u0647 \u062a\u0648\u0644\u06cc\u062f \u0646\u06cc\u0633\u062a\u060c \u0632\u06cc\u0631\u0627 \u0641\u0627\u0642\u062f \u0645\u062f\u06cc\u0631\u06cc\u062a \u0635\u062d\u06cc\u062d \u062e\u0637\u0627 \u0627\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u0648\u062c\u0648\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u0622\u0646 \u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f\u060c \u0641\u0642\u0637 \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u067e\u06cc\u0627\u0645\u200c\u0647\u0627\u06cc \u062e\u0637\u0627\u06cc \u0645\u0646\u0627\u0633\u0628\u06cc \u0631\u0627 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0646\u06cc\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u062f\u0642\u06cc\u0642 \u062a\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u06a9\u062f \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.  \u0627\u06af\u0631 \u0627\u0632 \u0628\u0627\u0632\u06af\u0634\u062a \u062e\u0627\u0631\u062c \u0645\u06cc \u0634\u0648\u06cc\u0645 <code>start<\/code> \u0639\u0646\u0635\u0631 \u0628\u0627\u0644\u0627\u062a\u0631 \u0627\u0632 <code>end<\/code> \u0639\u0646\u0635\u0631:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">if<\/span> start &gt; end:\n        <span class=\"hljs-keyword\">return<\/span> -<span class=\"hljs-number\">1<\/span>\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u0648\u0636\u0639\u06cc\u062a \u062a\u0646\u0647\u0627 \u0632\u0645\u0627\u0646\u06cc \u0631\u062e \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.  \u0627\u062a\u0641\u0627\u0642\u06cc \u06a9\u0647 \u0645\u06cc \u0627\u0641\u062a\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0641\u0639\u0644\u06cc \u0641\u0642\u0637 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062f\u0627\u0631\u06cc\u0645 \u0648 \u0622\u0646 \u0639\u0646\u0635\u0631 \u0628\u0627 \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0645\u0627 \u0645\u0637\u0627\u0628\u0642\u062a \u0646\u062f\u0627\u0631\u062f.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647\u060c <code>start<\/code> \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 <code>end<\/code>.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 <code>element<\/code> \u0628\u0631\u0627\u0628\u0631 \u0646\u06cc\u0633\u062a <code>array(mid)<\/code>\u060c \u062f\u0648\u0628\u0627\u0631\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0647 \u06af\u0648\u0646\u0647 \u0627\u06cc &#8220;\u062a\u0642\u0633\u06cc\u0645&#8221; \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u06cc\u0627 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645 <code>end<\/code> 1 \u06cc\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u06cc\u062f <code>start<\/code> \u062a\u0648\u0633\u0637 \u06cc\u06a9\u060c \u0648 \u0628\u0627\u0632\u06af\u0634\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u0622\u0646 \u0634\u0631\u0637<\/p>\n<p>\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u0633\u062a\u06cc\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">if<\/span> <span class=\"hljs-built_in\">len<\/span>(array) == <span class=\"hljs-number\">1<\/span>:\n    <span class=\"hljs-keyword\">if<\/span> element == array(mid):\n        <span class=\"hljs-keyword\">return<\/span> mid\n    <span class=\"hljs-keyword\">else<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> -<span class=\"hljs-number\">1<\/span>\n<\/code><\/pre>\n<p>\u0628\u0642\u06cc\u0647 \u06a9\u062f \u0645\u0646\u0637\u0642 &#8220;\u0628\u0631\u0631\u0633\u06cc \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc\u060c \u0627\u062f\u0627\u0645\u0647 \u062c\u0633\u062a\u062c\u0648 \u062f\u0631 \u0646\u06cc\u0645\u0647 \u0645\u0646\u0627\u0633\u0628 \u0622\u0631\u0627\u06cc\u0647&#8221; \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f.  \u0634\u0627\u062e\u0635 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u062c\u0633\u062a\u062c\u0648 \u0628\u0627 \u0622\u0646 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631:<\/p>\n<pre><code class=\"hljs\">mid = (start + end) \/\/ <span class=\"hljs-number\">2<\/span>\n<span class=\"hljs-keyword\">if<\/span> elem == array(mid):\n    <span class=\"hljs-keyword\">return<\/span> mid\n<\/code><\/pre>\n<p>\u0627\u06af\u0631 \u0627\u06cc\u0646\u0637\u0648\u0631 \u0646\u06cc\u0633\u062a\u060c \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0639\u0646\u0635\u0631 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u06cc\u0627 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">if<\/span> element &lt; array(mid):\n    \n    <span class=\"hljs-keyword\">return<\/span> binary_search_recursive(array, element, start, mid-<span class=\"hljs-number\">1<\/span>)\n<span class=\"hljs-keyword\">else<\/span>:\n    \n    <span class=\"hljs-keyword\">return<\/span> binary_search_recursive(array, element, mid+<span class=\"hljs-number\">1<\/span>, end)\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u06cc\u0645 \u0648 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0627 \u06a9\u0645\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u062f \u06a9\u062f\u0627\u0645 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631:<\/p>\n<pre><code class=\"hljs\">element = <span class=\"hljs-number\">18<\/span>\narray = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">13<\/span>, <span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">16<\/span>, <span class=\"hljs-number\">18<\/span>, <span class=\"hljs-number\">24<\/span>, <span class=\"hljs-number\">28<\/span>, <span class=\"hljs-number\">29<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Searching for {}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(element))\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Index of {}: {}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(element, binary_search_recursive(array, element, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-built_in\">len<\/span>(array))))\n<\/code><\/pre>\n<p>\u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u062f \u0645\u0646\u062c\u0631 \u0628\u0647 \u0645\u0648\u0627\u0631\u062f \u0632\u06cc\u0631 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">Searching for 18\nSubarray in step 0:(1, 2, 5, 7, 13, 15, 16, 18, 24, 28, 29)\nSubarray in step 1:(16, 18, 24, 28, 29)\nSubarray in step 2:(16, 18)\nSubarray in step 3:(18)\nIndex of 18: 7\n<\/code><\/pre>\n<p>\u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0641\u0636\u0627\u06cc \u062c\u0633\u062a\u062c\u0648 \u0631\u0627 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0628\u0647 \u0646\u0635\u0641 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0628\u0647 \u0639\u0646\u0635\u0631 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0645\u0627 \u0646\u0632\u062f\u06cc\u06a9 \u0648 \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0639\u0646\u0635\u0631\u06cc \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c \u062e\u0631\u0648\u062c\u06cc \u0627\u06cc\u0646 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">Searching for 20\nSubarray in step 0: (4, 14, 16, 17, 19, 21, 24, 28, 30, 35, 36, 38, 39, 40, 41, 43)\nSubarray in step 1: (4, 14, 16, 17, 19, 21, 24, 28)\nSubarray in step 2: (19, 21, 24, 28)\nSubarray in step 3: (19)\nIndex of 20: -1\n<\/code><\/pre>\n<p>\u0648 \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0633\u0631\u06af\u0631\u0645\u06cc\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0686\u0646\u062f \u0622\u0631\u0627\u06cc\u0647 \u0628\u0632\u0631\u06af \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0686\u0646\u062f \u0645\u0631\u062d\u0644\u0647 \u0637\u0648\u0644 \u0645\u06cc\u200c\u06a9\u0634\u062f \u062a\u0627 \u0628\u0641\u0647\u0645\u06cc\u0645 \u0622\u06cc\u0627 \u06cc\u06a9 \u0639\u062f\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631:<\/p>\n<pre><code class=\"hljs\">Searching for 421, in an array with 200 elements\nSearch finished in 6 steps. Index of 421: 169\n\nSearching for 1800, in an array with 1500 elements\nSearch finished in 11 steps. Index of 1800: -1\n\nSearching for 3101, in an array with 3000 elements\nSearch finished in 8 steps. Index of 3101: 1551\n<\/code><\/pre>\n<h4 id=\"iterative\">\u062a\u06a9\u0631\u0627\u0631\u06cc<\/h4>\n<p>\u0631\u0648\u06cc\u06a9\u0631\u062f \u062a\u06a9\u0631\u0627\u0631\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0648 \u0634\u0628\u06cc\u0647 \u0628\u0647 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0627\u0633\u062a.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627\u060c \u0645\u0627 \u0641\u0642\u0637 \u0628\u0631\u0631\u0633\u06cc \u0647\u0627 \u0631\u0627 \u062f\u0631 a \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645 <code>while<\/code> \u062d\u0644\u0642\u0647:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">binary_search_iterative<\/span>(<span class=\"hljs-params\">array, element<\/span>):<\/span>\n    mid = <span class=\"hljs-number\">0<\/span>\n    start = <span class=\"hljs-number\">0<\/span>\n    end = <span class=\"hljs-built_in\">len<\/span>(array)\n    step = <span class=\"hljs-number\">0<\/span>\n\n    <span class=\"hljs-keyword\">while<\/span> (start &lt;= end):\n        <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Subarray in step {}: {}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(step, <span class=\"hljs-built_in\">str<\/span>(array(start:end+<span class=\"hljs-number\">1<\/span>))))\n        step = step+<span class=\"hljs-number\">1<\/span>\n        mid = (start + end) \/\/ <span class=\"hljs-number\">2<\/span>\n\n        <span class=\"hljs-keyword\">if<\/span> element == array(mid):\n            <span class=\"hljs-keyword\">return<\/span> mid\n\n        <span class=\"hljs-keyword\">if<\/span> element &lt; array(mid):\n            end = mid - <span class=\"hljs-number\">1<\/span>\n        <span class=\"hljs-keyword\">else<\/span>:\n            start = mid + <span class=\"hljs-number\">1<\/span>\n    <span class=\"hljs-keyword\">return<\/span> -<span class=\"hljs-number\">1<\/span>\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u067e\u0631 \u06a9\u0646\u06cc\u0645 \u0648 \u0639\u0646\u0635\u0631\u06cc \u0631\u0627 \u062f\u0631 \u0622\u0646 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">element = <span class=\"hljs-number\">18<\/span>\narray = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">13<\/span>, <span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">16<\/span>, <span class=\"hljs-number\">18<\/span>, <span class=\"hljs-number\">24<\/span>, <span class=\"hljs-number\">28<\/span>, <span class=\"hljs-number\">29<\/span>)       \n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Searching for {} in {}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(element, array))\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Index of {}: {}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(element, binary_search_iterative(array, element)))\n<\/code><\/pre>\n<p>\u0627\u062c\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u062f \u062e\u0631\u0648\u062c\u06cc \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u0645\u0627 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\">Searching for 18 in (1, 2, 5, 7, 13, 15, 16, 18, 24, 28, 29)\nSubarray in step 0: (1, 2, 5, 7, 13, 15, 16, 18, 24, 28, 29)\nSubarray in step 1: (16, 18, 24, 28, 29)\nSubarray in step 2: (16, 18)\nSubarray in step 3: (18)\nIndex of 18: 7\n<\/code><\/pre>\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>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u0648\u0631\u0646\u06a9\u0631\u062f\u0646\u06cc \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0648 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u06cc\u0627 \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u0642\u0635\u062f \u062f\u0627\u0631\u06cc\u0645 \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u06a9\u0631\u0631 \u062f\u0631 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0647\u0632\u06cc\u0646\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0622\u0631\u0627\u06cc\u0647 \u06cc\u06a9 \u0628\u0627\u0631 \u0648 \u0633\u067e\u0633 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0686\u0646\u062f\u06cc\u0646 \u0628\u0627\u0631 \u0639\u0646\u0627\u0635\u0631 \u062f\u0631 \u0622\u0646 \u0628\u0647 \u0645\u0631\u0627\u062a\u0628 \u0628\u0647\u062a\u0631 \u0627\u0632 \u062c\u0633\u062a\u062c\u0648\u06cc \u062e\u0637\u06cc \u0627\u0633\u062a. \u0631\u0648\u06cc \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647 \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0647\u0632\u06cc\u0646\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0622\u0646 \u062c\u0644\u0648\u06af\u06cc\u0631\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0641\u0642\u0637 \u06cc\u06a9 \u0628\u0627\u0631 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u062c\u0633\u062a\u062c\u0648\u06cc \u062e\u0637\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631 \u0627\u0633\u062a. \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0646\u0634\u062f\u0647<\/p>\n<p>\u0627\u06af\u0631 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0645\u0637\u0627\u0644\u0639\u0647 \u06a9\u0646\u06cc\u062f\u060c \u0645\u0627 \u0634\u0645\u0627 \u0631\u0627 \u062a\u062d\u062a \u067e\u0648\u0634\u0634 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0647 \u0627\u06cc\u0645!<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-17 08:37:04<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    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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\"> 5<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a \u06a9\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u063a\u0644\u0628 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u0648\u0644\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0644\u06af\u0627\u0631\u06cc\u062a\u0645\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u0646\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f (O(logn)) \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0631\u0641\u062a\u0627\u0631 \u0634\u0647\u0648\u062f\u06cc \u0622\u0646 \u0648 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0633\u0627\u0633\u06cc \u062f\u0631 \u0639\u0644\u0648\u0645 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0645\u0627 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