{"id":37130,"date":"2022-07-16T08:03:09","date_gmt":"2022-07-16T08:03:09","guid":{"rendered":"https:\/\/quera.org\/blog\/?p=37130"},"modified":"2022-08-06T12:39:55","modified_gmt":"2022-08-06T08:09:55","slug":"rahnema-college-bootcamp-contest","status":"publish","type":"post","link":"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/","title":{"rendered":"\u0631\u0627\u0647\u0646\u0645\u0627\u06cc\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0622\u0632\u0645\u0648\u0646 \u0648\u0631\u0648\u062f\u06cc \u0628\u0648\u062a\u200c\u06a9\u0645\u067e \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0631\u0647\u0646\u0645\u0627\u06a9\u0627\u0644\u062c"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\" style=\"font-size:18px\"><strong>\u0633\u0644\u0627\u0645!<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0622\u0632\u0645\u0648\u0646 \u0648\u0631\u0648\u062f\u06cc \u0628\u0648\u062a\u200c\u06a9\u0645\u067e \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0631\u0647\u0646\u0645\u0627\u06a9\u0627\u0644\u062c \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0646\u062f. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0645\u062a\u0648\u062c\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u06cc \u0646\u0634\u062f\u06cc\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0646\u06cc\u062f \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a\u060c \u0633\u0624\u0627\u0644\u0627\u062a \u0648 \u0627\u0628\u0647\u0627\u0645\u200c\u0647\u0627\u06cc \u062e\u0648\u062f\u062a\u0648\u0646 \u0631\u0648 \u0645\u0637\u0631\u062d \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0646\u06a9\u062a\u0647: \u0627\u0645\u06a9\u0627\u0646 \u0627\u0646\u062a\u0634\u0627\u0631 \u067e\u0627\u0633\u062e\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u062a\u06a9\u0646\u0648\u0644\u0648\u0698\u06cc \u0628\u0647\u200c\u062f\u0644\u06cc\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647\u200c \u0627\u0632 \u0627\u0648\u0646\u200c\u0647\u0627 \u062f\u0631 \u0645\u0647\u0627\u0631\u062a\u200c\u0633\u0646\u062c\u06cc\u060c \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u0647.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \u0627\u06af\u0647 \u0631\u0627\u0647\u200c\u062d\u0644 \u062f\u06cc\u06af\u0647\u200c\u0627\u06cc \u0628\u0631\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u062f\u0627\u0631\u06cc\u062f\u060c \u062e\u0648\u0634\u062d\u0627\u0644 \u0645\u06cc\u200c\u0634\u06cc\u0645 \u06a9\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u062a\u0648\u0646 \u0631\u0648 \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a \u0628\u0627 \u0645\u0627 \u0648 \u062f\u0648\u0633\u062a\u0627\u0646\u062a\u0648\u0646 \u0628\u0647 \u0627\u0634\u062a\u0631\u0627\u06a9 \u0628\u0630\u0627\u0631\u06cc\u062f.<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"\u062a\u063a\u06cc\u06cc\u0631 \u0648\u0636\u0639\u06cc\u062a \u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/#%DA%A9%D9%88%D9%84%D8%B1_%DB%8C%D8%A7_%D8%A8%D8%AE%D8%A7%D8%B1%DB%8C\" >\u06a9\u0648\u0644\u0631 \u06cc\u0627 \u0628\u062e\u0627\u0631\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/#%DB%8C%DA%A9_%D9%85%DB%8C%D9%84%DB%8C%D9%88%D9%86_%D8%AF%D9%84%D8%A7%D8%B1\" >\u06cc\u06a9 \u0645\u06cc\u0644\u06cc\u0648\u0646 \u062f\u0644\u0627\u0631<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/#%D8%B1%D8%A7%D8%B2%E2%80%8C%D8%AF%D8%A7%D8%B1%DB%8C_%D8%AF%D8%B1_%D9%85%D8%AF%D8%B1%D8%B3%D9%87\" >\u0631\u0627\u0632\u200c\u062f\u0627\u0631\u06cc \u062f\u0631 \u0645\u062f\u0631\u0633\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/#%D9%82%D8%A7%D8%A6%D9%85%E2%80%8C%D8%B4%D9%85%D8%A7%D8%B1%DB%8C\" >\u0642\u0627\u0626\u0645\u200c\u0634\u0645\u0627\u0631\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/quera.org\/blog\/rahnema-college-bootcamp-contest\/#%D8%AA%D8%A3%D8%B3%DB%8C%D8%B3_%D8%A7%D8%B3%D8%AA%D8%A7%D8%B1%D8%AA%E2%80%8C%D8%A2%D9%BE\" >\u062a\u0623\u0633\u06cc\u0633 \u0627\u0633\u062a\u0627\u0631\u062a\u200c\u0622\u067e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"\u0628\u062e\u0627\u0631\u06cc-\u06cc\u0627-\u06a9\u0648\u0644\u0631\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%DA%A9%D9%88%D9%84%D8%B1_%DB%8C%D8%A7_%D8%A8%D8%AE%D8%A7%D8%B1%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/147635\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u06a9\u0648\u0644\u0631 \u06cc\u0627 \u0628\u062e\u0627\u0631\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u0639\u062f \u0627\u0632 \u0648\u0631\u0648\u062f\u06cc\u200c\u06af\u0631\u0641\u062a\u0646&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>&nbsp;\u0648 \u062f\u0646\u0628\u0627\u0644\u0647\u200c\u06cc&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">t_i<\/span><\/em>\u200b\u0647\u0627\u060c \u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u062d\u0644\u0642\u0647 (<code>for<\/code>) \u0628\u0631 \u0631\u0648\u06cc \u0647\u0645\u0647\u200c\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">t_i<\/span>\u200b\u0647\u0627 \u0648 \u06cc\u06a9 \u0634\u0631\u0637 (<code>if<\/code>) \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">t_i<\/span><\/em>\u200b&nbsp;\u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u06f1\u06f5 \u0627\u0633\u062a \u06cc\u0627 \u0646\u0647. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">t_i<\/span><\/em>\u200b&nbsp;\u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u06f1\u06f5 \u0628\u0648\u062f\u060c \u0631\u0634\u062a\u0647\u200c\u06cc&nbsp;<code>cooler<\/code>&nbsp;\u0648 \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0631\u0634\u062a\u0647\u200c\u06cc&nbsp;<code>heater<\/code>&nbsp;\u0631\u0627 \u0686\u0627\u067e \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u06cc\u06a9-\u0645\u06cc\u0644\u06cc\u0648\u0646-\u062f\u0644\u0627\u0631\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%DB%8C%DA%A9_%D9%85%DB%8C%D9%84%DB%8C%D9%88%D9%86_%D8%AF%D9%84%D8%A7%D8%B1\"><\/span><a href=\"https:\/\/quera.org\/problemset\/147637\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u06cc\u06a9 \u0645\u06cc\u0644\u06cc\u0648\u0646 \u062f\u0644\u0627\u0631<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06af\u0631 \u06cc\u06a9 \u062c\u062f\u0648\u0644&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n \\times m<\/span>&nbsp;\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u06a9\u0645\u062a\u0631\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u0628\u0644\u0648\u06a9&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a \\times b<\/span>&nbsp;\u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0622\u0646 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f \u0628\u0647\u200c\u0637\u0648\u0631\u06cc \u06a9\u0647 \u0647\u06cc\u0686 \u0628\u0644\u0648\u06a9 \u062f\u06cc\u06af\u0631\u06cc \u062f\u0631 \u0622\u0646 \u062c\u0627 \u0646\u0634\u0648\u062f \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\lfloor \\frac{n - a + 1}{2a - 1} \\rfloor . \\lfloor \\frac{m - b + 1}{2b - 1} \\rfloor<\/pre><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:16px\"><strong>\u0627\u062b\u0628\u0627\u062a:<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0631\u0648\u0634 \u0632\u06cc\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">\\lceil \\frac{n - a + 1}{2a - 1} \\rceil . \\lceil \\frac{m - b + 1}{2b - 1} \\rceil<\/span> \u0628\u0644\u0648\u06a9\u0650&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a \\times b<\/span>&nbsp;\u06a9\u0627\u0631\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0647\u06cc\u0686 \u0628\u0644\u0648\u06a9 \u062f\u06cc\u06af\u0631\u06cc \u0646\u062a\u0648\u0627\u0646 \u062f\u0631 \u0635\u0641\u062d\u0647 \u06af\u0630\u0627\u0634\u062a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a - 1<\/span>&nbsp;\u0633\u0637\u0631 \u0627\u0648\u0644 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;\u0633\u0637\u0631 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a - 1<\/span>&nbsp;\u0633\u0637\u0631 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f \u0648&#8230; \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0633\u0637\u0631\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f. \u0633\u067e\u0633&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b - 1<\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0627\u0648\u0644 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b - 1<\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f \u0648&#8230; \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0633\u062a\u0648\u0646\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f. \u062d\u0627\u0644 \u0627\u06af\u0631 \u0647\u0645 \u0633\u0637\u0631 \u0648 \u0647\u0645 \u0633\u062a\u0648\u0646 \u06cc\u06a9 \u062e\u0627\u0646\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647\u200c\u0627\u06cc\u062f\u060c \u0622\u0646 \u0631\u0627 \u0628\u062e\u0631\u06cc\u062f. (\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0647\u0645\u0648\u0627\u0631\u0647 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a \\times b<\/span>&nbsp;\u062e\u0631\u06cc\u062f\u0627\u0631\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062d\u0627\u0644 \u0628\u0627\u06cc\u062f \u062b\u0627\u0628\u062a \u06a9\u0646\u06cc\u0645 \u0647\u06cc\u0686 \u0631\u0648\u0634\u06cc \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u06a9\u0645\u062a\u0631\u06cc \u0628\u0644\u0648\u06a9\u060c \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u062c\u062f\u062f\u0627\u064b&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;\u0633\u0637\u0631 \u0627\u0648\u0644 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a - 1<\/span>&nbsp;\u0633\u0637\u0631 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;\u0633\u0637\u0631 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u0648&#8230; \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0633\u0637\u0631\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f. \u0633\u067e\u0633&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0627\u0648\u0644 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b - 1<\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u06af\u06cc\u0631\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b <\/span>&nbsp;\u0633\u062a\u0648\u0646 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u0648&#8230; \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0633\u062a\u0648\u0646\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f. \u062d\u0627\u0644 \u0627\u06af\u0631 \u0647\u0645 \u0633\u0637\u0631 \u0648 \u0647\u0645 \u0633\u062a\u0648\u0646 \u06cc\u06a9 \u062e\u0627\u0646\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647\u200c\u0627\u06cc\u062f\u060c \u0622\u0646 \u0631\u0627 \u0628\u062e\u0631\u06cc\u062f. (\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0647\u0645\u0648\u0627\u0631\u0647 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc&nbsp; <span class=\"katex-eq\" data-katex-display=\"false\">a \\times b<\/span>&nbsp;\u062e\u0631\u06cc\u062f\u0627\u0631\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0647\u0631 \u0631\u0648\u0634\u06cc \u06a9\u0647 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627 \u0631\u0627 \u0628\u06af\u0630\u0627\u0631\u06cc\u0645 \u062a\u0627 \u0647\u06cc\u0686 \u0628\u0644\u0648\u06a9 \u062f\u06cc\u06af\u0631\u06cc \u0646\u062a\u0648\u0627\u0646 \u06af\u0630\u0627\u0634\u062a\u060c \u0628\u0627\u06cc\u062f \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u0628\u0631\u0627\u06cc \u0646\u0648\u0627\u062d\u06cc \u0628\u0627\u0644\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u0648\u062f. (\u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631 \u0647\u06cc\u0686 \u062f\u0648\u062a\u0627\u06cc\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0646\u0627\u062d\u06cc\u0647\u200c\u0647\u0627 \u0631\u0627 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u067e\u0648\u0634\u0627\u0646\u062f.) \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0646\u0648\u0627\u062d\u06cc \u0628\u0627 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc \u06af\u0630\u0627\u0634\u062a\u0647\u200c\u0634\u062f\u0647 \u0627\u0634\u062a\u0631\u0627\u06a9 \u067e\u06cc\u062f\u0627 \u0646\u06a9\u0646\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0622\u0646\u200c\u062c\u0627 \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f. (\u06a9\u0647 \u0627\u06cc\u0646 \u06cc\u0639\u0646\u06cc \u062e\u0648\u0627\u0633\u062a\u0647 \u0633\u0624\u0627\u0644 \u0628\u0631\u0622\u0648\u0631\u062f\u0647 \u0646\u0634\u062f\u0647 \u0627\u0633\u062a.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u067e\u0633 \u062d\u062f\u0627\u0642\u0644 \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u062a\u0639\u062f\u0627\u062f \u0646\u0648\u0627\u062d\u06cc \u0628\u0627\u0644\u0627\u060c \u0628\u0627\u06cc\u062f \u0628\u0644\u0648\u06a9 \u062f\u0631 \u0635\u0641\u062d\u0647 \u0628\u06af\u0630\u0627\u0631\u06cc\u0645. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\lfloor \\frac{n + a + 1}{2a - 1} \\rfloor . \\lfloor \\frac{m + b + 1}{2b - 1} \\rfloor<\/pre><\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u0631\u0627\u0632-\u062f\u0627\u0631\u06cc\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%B1%D8%A7%D8%B2%E2%80%8C%D8%AF%D8%A7%D8%B1%DB%8C_%D8%AF%D8%B1_%D9%85%D8%AF%D8%B1%D8%B3%D9%87\"><\/span><a href=\"https:\/\/quera.org\/problemset\/147634\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u0631\u0627\u0632\u200c\u062f\u0627\u0631\u06cc \u062f\u0631 \u0645\u062f\u0631\u0633\u0647<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u0633\u0626\u0644\u0647 \u0631\u0627 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u06cc\u06a9 \u06af\u0631\u0627\u0641 \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0645\u062f\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u061b \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0634\u062e\u0635&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>&nbsp;\u0631\u0627\u0628\u0637\u0647\u200c\u06cc \u062f\u0647\u0646\u200c\u0644\u0642\u06cc \u0628\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">v<\/span>&nbsp;\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u06cc\u06a9 \u06cc\u0627\u0644 \u062c\u0647\u062a\u200c\u062f\u0627\u0631 \u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>&nbsp;\u0628\u0647&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">v<\/span>&nbsp;\u0631\u0633\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062d\u0627\u0644 \u0645\u0633\u0626\u0644\u0647 \u0628\u0647 \u067e\u06cc\u062f\u0627\u200c\u06a9\u0631\u062f\u0646 \u06a9\u0648\u062a\u0627\u0647\u200c\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u0631\u0623\u0633&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">t<\/span>&nbsp;\u0628\u0647 \u0631\u0623\u0633&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">s<\/span>&nbsp;\u06a9\u0627\u0647\u0634 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645&nbsp;<code>BFS<\/code>&nbsp;\u0627\u0632 \u0645\u0631\u062a\u0628\u0647\u200c\u06cc \u0632\u0645\u0627\u0646\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">O(n + m)<\/span>&nbsp;\u062d\u0644 \u06a9\u0631\u062f \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0641\u0635\u0644 \u06f1\u06f4 \u06a9\u0627\u0644\u062c <a href=\"https:\/\/quera.org\/college\/land\/register\/3016\/%D8%A2%D9%85%D9%88%D8%B2%D8%B4-%D9%85%D8%B3%D8%A6%D9%84%D9%87-%D9%85%D8%AD%D9%88%D8%B1-%D8%AA%D9%81%DA%A9%D8%B1-%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85%DB%8C-%D9%BE%DB%8C%D8%B4%D8%B1%D9%81%D8%AA%D9%87-%D9%88-%D8%B3%D8%A7%D8%AE%D8%AA%D9%85%D8%A7%D9%86%E2%80%8C%D8%AF%D8%A7%D8%AF%D9%87%E2%80%8C%D9%87%D8%A7\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u062a\u0641\u06a9\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u067e\u06cc\u0634\u0631\u0641\u062a\u0647 \u0648 \u0633\u0627\u062e\u062a\u0645\u0627\u0646\u200c\u062f\u0627\u062f\u0647\u200c\u0647\u0627<\/a> \u0622\u0645\u0648\u0632\u0634 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc\u0645.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u0642\u0627\u0626\u0645-\u0634\u0645\u0627\u0631\u06cc\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D9%82%D8%A7%D8%A6%D9%85%E2%80%8C%D8%B4%D9%85%D8%A7%D8%B1%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/147639\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u0642\u0627\u0626\u0645\u200c\u0634\u0645\u0627\u0631\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u0633\u0626\u0644\u0647\u060c \u0634\u0645\u0627\u0631\u0634\u0650 \u062a\u0639\u062f\u0627\u062f \u0645\u062b\u0644\u062b\u200c\u0647\u0627\u06cc \u0642\u0627\u0626\u0645\u200c\u0627\u0644\u0632\u0627\u0648\u06cc\u0647\u200c \u0628\u0627 \u0627\u0636\u0644\u0627\u0639 \u0637\u0628\u06cc\u0639\u06cc \u0648 \u0637\u0648\u0644 \u0648\u062a\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>&nbsp;\u0627\u0633\u062a. \u067e\u0627\u0633\u062e \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0645\u0639\u0627\u062f\u0644 \u062a\u0639\u062f\u0627\u062f \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u0637\u0628\u06cc\u0639\u06cc \u0627\u0633\u062a. (\u06cc\u0639\u0646\u06cc \u0647\u0631 \u062c\u0648\u0627\u0628 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0627 \u06cc\u06a9 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645\u200c\u0627\u0644\u0632\u0627\u0648\u06cc\u0647 \u062f\u0631 \u062a\u0646\u0627\u0638\u0631 \u06cc\u06a9\u200c\u0628\u0647\u200c\u06cc\u06a9 \u0627\u0633\u062a.)<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{matrix}\na^{2} +  b^{2} =  n^{2} &amp; &amp; \\big(a \\leq b\\big) \n\\end{matrix}<\/pre><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"\u0632\u06cc\u0631-\u0645\u0633\u0626\u0644\u0647-\u0627\u0648\u0644\" style=\"font-size:16px\"><strong>\u0632\u06cc\u0631\u200c\u0645\u0633\u0626\u0644\u0647 \u0627\u0648\u0644<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u062f\u0648 \u062d\u0644\u0642\u0647\u200c\u06cc \u062a\u0648\u200c\u062f\u0631\u200c\u062a\u0648 \u0648 \u062d\u0627\u0644\u062a\u200c\u0628\u0646\u062f\u06cc \u0631\u0648\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;(\u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">1<\/span>&nbsp;\u062a\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>) \u0648&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>&nbsp;(\u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;\u062a\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0627\u06cc\u0646 \u062f\u0648 \u0645\u0642\u062f\u0627\u0631 \u06cc\u06a9 \u062c\u0648\u0627\u0628 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0633\u062a\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong>&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">O(n^2)<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"\u0632\u06cc\u0631-\u0645\u0633\u0626\u0644\u0647-\u062f\u0648\u0645\" style=\"font-size:16px\"><strong>\u0632\u06cc\u0631\u200c\u0645\u0633\u0626\u0644\u0647 \u062f\u0648\u0645<\/strong><a href=\"https:\/\/quera.org\/course\/9940\/lectures\/1715\/#%D8%B2%DB%8C%D8%B1-%D9%85%D8%B3%D8%A6%D9%84%D9%87-%D8%AF%D9%88%D9%85\"><\/a><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u062d\u0627\u0644\u062a\u200c\u0628\u0646\u062f\u06cc \u0631\u0648\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;(\u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">1<\/span>&nbsp;\u062a\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>) \u0645\u0642\u062f\u0627\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>&nbsp;\u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a^2 + b^2 = n^2 \\quad \\Rightarrow \\quad b^2 = n^2 - a^2 \\quad\\Rightarrow \\quad b = \\sqrt{n^2 - a^2}<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u062a\u0646\u0647\u0627 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0634\u0631\u0637 <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{ n^{2} - a^{2} } \\geq a<\/span> \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0631\u0627 \u0628\u0647\u200c\u062f\u0631\u0633\u062a\u06cc \u0628\u0634\u0645\u0627\u0631\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong>&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">O(n^2)<\/span><\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"\u0632\u06cc\u0631-\u0645\u0633\u0626\u0644\u0647-\u0633\u0648\u0645\" style=\"font-size:16px\"><strong>\u0632\u06cc\u0631\u200c\u0645\u0633\u0626\u0644\u0647 \u0633\u0648\u0645<\/strong><a href=\"https:\/\/quera.org\/course\/9940\/lectures\/1715\/#%D8%B2%DB%8C%D8%B1-%D9%85%D8%B3%D8%A6%D9%84%D9%87-%D8%B3%D9%88%D9%85\"><\/a><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u062a\u0639\u062f\u0627\u062f \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0647\u200c\u0634\u0631\u0637\u06cc \u06a9\u0647&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a, b, n<\/span>&nbsp;\u0646\u0633\u0628\u062a \u0628\u0647 \u0647\u0645 \u0627\u0648\u0644 \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0631\u0627\u0628\u0631 \u0628\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">f(n)<\/span>&nbsp;\u0628\u0627\u0634\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062f\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u06a9\u0647 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\sum_{d | n} f(d) <\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0686\u0648\u0646 \u0627\u06af\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">g<\/span>&nbsp;\u0645\u0642\u0633\u0648\u0645\u200c\u0639\u0644\u06cc\u0647 \u0645\u0634\u062a\u0631\u06a9&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a, b, n<\/span>&nbsp;\u0628\u0627\u0634\u062f\u060c \u0628\u0627 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f\u0646&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">g^2<\/span>&nbsp;\u0628\u0647 \u062f\u0648 \u0637\u0631\u0641 \u062a\u0633\u0627\u0648\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u06cc\u06a9 \u062c\u0648\u0627\u0628&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">f(\\frac{n}{g})<\/span>&nbsp;\u0645\u062a\u0646\u0627\u0638\u0631 \u06a9\u0631\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062d\u0627\u0644 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0642\u062f\u0627\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">f(n)<\/span>&nbsp;\u0631\u0627 \u062d\u0633\u0627\u0628 \u06a9\u0646\u06cc\u0645. \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f \u06a9\u0647 \u0627\u06af\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a, b, n<\/span>&nbsp;\u0646\u0633\u0628\u062a \u0628\u0647 \u0647\u0645 \u0627\u0648\u0644 \u0628\u0627\u0634\u0646\u062f\u060c \u062f\u0648 \u0639\u062f\u062f \u0635\u062d\u06cc\u062d \u0648 \u0645\u062b\u0628\u062a&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>&nbsp;\u0648&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">v<\/span>&nbsp;\u0686\u0646\u0627\u0646 \u0645\u0648\u062c\u0648\u062f \u0627\u0633\u062a \u06a9\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a = u^2 - v^2, \\quad b = 2uv, \\quad n = u^2 + v^2, \\quad \\quad (v \\leq u) <\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06a9\u0646\u0648\u0646 \u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u062d\u0644\u0642\u0647 \u0631\u0648\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>&nbsp;(\u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">1<\/span>&nbsp;\u062a\u0627&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{n}<\/span><\/em>) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0642\u062f\u0627\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">v<\/span>&nbsp;\u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f \u0648 \u0633\u067e\u0633 \u0627\u0632 \u0631\u0648\u06cc \u0622\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>&nbsp;\u0648&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>&nbsp;\u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f \u0648 \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0645\u0647\u200c\u06cc \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">O(div(n). \\sqrt{n})<\/span> (\u0645\u0646\u0638\u0648\u0631 \u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">div(n)<\/span>&nbsp;\u062a\u0639\u062f\u0627\u062f \u0645\u0642\u0633\u0648\u0645\u200c\u0639\u0644\u06cc\u0647\u200c\u0647\u0627\u06cc \u0639\u062f\u062f&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>&nbsp;\u0627\u0633\u062a.)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u062a\u0627\u0633\u06cc\u0633-\u0627\u0633\u062a\u0627\u0631\u062a\u200c\u0622\u067e\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%AA%D8%A3%D8%B3%DB%8C%D8%B3_%D8%A7%D8%B3%D8%AA%D8%A7%D8%B1%D8%AA%E2%80%8C%D8%A2%D9%BE\"><\/span><a href=\"https:\/\/quera.org\/problemset\/147636\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>\u062a\u0623\u0633\u06cc\u0633 \u0627\u0633\u062a\u0627\u0631\u062a\u200c\u0622\u067e<\/strong><\/a><a href=\"https:\/\/quera.org\/course\/9940\/lectures\/1715\/#%D8%AA%D8%A7%D8%B3%DB%8C%D8%B3-%D8%A7%D8%B3%D8%AA%D8%A7%D8%B1%D8%AA%E2%80%8C%D8%A2%D9%BE\"><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u06cc\u0627\u06cc\u062f \u0627\u06cc\u0646&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>&nbsp;\u062f\u0648\u0633\u062a \u0631\u0627 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u06a9\u0633\u06cc \u06a9\u0647 \u0645\u0647\u0627\u0631\u062a \u0641\u0631\u0627\u0646\u062a\u200c\u0627\u0646\u062f (<span class=\"katex-eq\" data-katex-display=\"false\">f_i<\/span>\u200b) \u06a9\u0645\u062a\u0631\u06cc \u062f\u0627\u0631\u062f\u060c \u0627\u0646\u062f\u06cc\u0633 \u06a9\u0645\u062a\u0631\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/li><li>\u0627\u06af\u0631 \u062f\u0648 \u0646\u0641\u0631 \u0645\u0647\u0627\u0631\u062a \u0641\u0631\u0627\u0646\u062a\u200c\u0627\u0646\u062f (<span class=\"katex-eq\" data-katex-display=\"false\">f_i<\/span>\u200b) \u06cc\u06a9\u0633\u0627\u0646\u06cc \u062f\u0627\u0631\u0646\u062f\u060c \u06a9\u0633\u06cc \u06a9\u0647 \u0645\u0647\u0627\u0631\u062a \u0628\u06a9\u200c\u0627\u0646\u062f (<span class=\"katex-eq\" data-katex-display=\"false\">b_i<\/span>\u200b) \u0628\u06cc\u0634\u062a\u0631\u06cc \u062f\u0627\u0631\u062f\u060c \u0627\u0646\u062f\u06cc\u0633 \u06a9\u0645\u062a\u0631\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/li><li>\u0627\u06af\u0631 \u062f\u0648 \u0646\u0641\u0631 \u0645\u0647\u0627\u0631\u062a \u0641\u0631\u0627\u0646\u062a\u200c\u0627\u0646\u062f \u0648 \u0628\u06a9\u200c\u0627\u0646\u062f \u06cc\u06a9\u0633\u0627\u0646\u06cc \u062f\u0627\u0631\u0646\u062f\u060c \u0628\u0647 \u0647\u0631 \u062a\u0631\u062a\u06cc\u0628\u06cc \u06a9\u0647 \u062f\u0648\u0633\u062a \u062f\u0627\u0631\u0646\u062f \u0642\u0631\u0627\u0631 \u0628\u06af\u06cc\u0631\u0646\u062f.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f \u062a\u0646\u0647\u0627 \u0632\u0645\u0627\u0646\u06cc \u0647\u06cc\u0686\u200c\u06a9\u0633 \u062f\u0631 \u06cc\u06a9 \u0632\u06cc\u0631\u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0648\u0633\u062a\u0627\u0646 \u0627\u062d\u0633\u0627\u0633 \u062d\u0642\u0627\u0631\u062a \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u062f\u0646\u0628\u0627\u0644\u0647\u200c\u06cc \u0622\u0646\u200c\u0647\u0627 \u062f\u0631 \u062a\u0631\u062a\u06cc\u0628 \u0628\u0627\u0644\u0627\u060c \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0647\u0627\u0631\u062a \u0628\u06a9\u200c\u0627\u0646\u062f (<span class=\"katex-eq\" data-katex-display=\"false\">b_i<\/span>\u200b) \u0646\u0632\u0648\u0644\u06cc \u0628\u0627\u0634\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062d\u0627\u0644 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0648 \u062a\u0631\u062a\u06cc\u0628 \u062c\u062f\u06cc\u062f\u060c&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">dp[i]<\/span>\u200b&nbsp;\u0631\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645: \u00ab\u0628\u06cc\u0634\u062a\u0631\u06cc\u0646 \u0645\u062c\u0645\u0648\u0639 \u067e\u0648\u0644 \u0646\u0642\u062f\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u06cc\u06a9 \u0632\u06cc\u0631\u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0627\u0641\u0631\u0627\u062f&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">1<\/span>&nbsp;\u062a\u0627&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>&nbsp;\u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f \u0628\u0647\u200c\u0637\u0648\u0631\u06cc \u06a9\u0647 \u062d\u062a\u0645\u0627\u064b&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>&nbsp;\u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u0648\u062f \u0648 \u0647\u06cc\u0686\u200c\u06a9\u0633 \u0627\u062d\u0633\u0627\u0633 \u062d\u0642\u0627\u0631\u062a \u0646\u06a9\u0646\u062f.\u00bb<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0628\u0627\u0644\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0631\u0627\u0628\u0637\u0647\u200c\u06cc \u0632\u06cc\u0631 \u0631\u0627 \u0646\u0648\u0634\u062a:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>dp[i] = \\max_{b_j &gt; b_i,\\, j &lt; i} \\{dp[j]\\} + m_i <\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647\u200c\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u0628\u0639\u062f \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u06cc \u0647\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">dp[i]<\/span>&nbsp;\u0622\u0646 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633&nbsp;<em><span class=\"katex-eq\" data-katex-display=\"false\">b_i<\/span><\/em>\u200b&nbsp;\u062f\u0631 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0645\u0627\u0646 \u062f\u0627\u062f\u0647 \u0645\u062b\u0644 \u062f\u0631\u062e\u062a \u0641\u0646\u0648\u06cc\u06a9 (fenwick tree) \u06cc\u0627 \u062f\u0631\u062e\u062a \u0628\u0627\u0632\u0647\u200c\u0627\u06cc (segment tree) \u0630\u062e\u06cc\u0631\u0647 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0631\u062c \u0648 \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u06cc \u0627\u06cc\u0646 \u0645\u0627\u06a9\u0633\u06cc\u0645\u0645 \u0631\u0627 \u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">O(\\log{n})<\/span>&nbsp;\u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0639\u062f \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u06cc \u06a9\u0644 \u0622\u0631\u0627\u06cc\u0647\u200c\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">dp<\/span>\u060c \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\max_{1\\leq i \\leq n} \\{dp[i]\\} <\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/strong>&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">O(n.\\log{n})<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u0644\u0627\u0645! \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0622\u0632\u0645\u0648\u0646 \u0648\u0631\u0648\u062f\u06cc \u0628\u0648\u062a\u200c\u06a9\u0645\u067e \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0631\u0647\u0646\u0645\u0627\u06a9\u0627\u0644\u062c \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0646\u062f. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0645\u062a\u0648\u062c\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u06cc \u0646\u0634\u062f\u06cc\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0646\u06cc\u062f&#8230;<\/p>\n","protected":false},"author":22,"featured_media":37173,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[141,46,50],"tags":[],"class_list":["post-37130","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contests-and-events","category-developer","category-quera-developer"],"_links":{"self":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/37130","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/comments?post=37130"}],"version-history":[{"count":74,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/37130\/revisions"}],"predecessor-version":[{"id":37223,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/37130\/revisions\/37223"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/media\/37173"}],"wp:attachment":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/media?parent=37130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/categories?post=37130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/tags?post=37130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}