{"id":42613,"date":"2023-04-26T12:55:14","date_gmt":"2023-04-26T08:25:14","guid":{"rendered":"https:\/\/quera.org\/blog\/?p=42613"},"modified":"2023-04-26T12:55:18","modified_gmt":"2023-04-26T08:25:18","slug":"acm-icpc-challenge-solutions","status":"publish","type":"post","link":"https:\/\/quera.org\/blog\/acm-icpc-challenge-solutions\/","title":{"rendered":"\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc ACM-ICPC Challenge"},"content":{"rendered":"\n<p>\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc ACM-ICPC Challenge \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. \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_81 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=\"Toggle Table of Content\"><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\/acm-icpc-challenge-solutions\/#%DA%AF%D8%B1%D9%88%D9%87_%D8%AE%D9%88%D9%86%DB%8C\" >\u06af\u0631\u0648\u0647 \u062e\u0648\u0646\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\/acm-icpc-challenge-solutions\/#%D9%85%D8%A7%D9%85%D9%88%D8%B1_%D9%85%D8%AE%D9%81%DB%8C\" >\u0645\u0627\u0645\u0648\u0631 \u0645\u062e\u0641\u06cc<\/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\/acm-icpc-challenge-solutions\/#%D8%B4%DB%8C%D8%B1_%D8%AA%D9%88_%D8%B4%DB%8C%D8%B1\" >\u0634\u06cc\u0631 \u062a\u0648 \u0634\u06cc\u0631<\/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\/acm-icpc-challenge-solutions\/#%DA%A9%D8%A7%D8%BA%D8%B0_%D8%AF%DB%8C%D9%88%D8%A7%D8%B1%DB%8C\" >\u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\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\/acm-icpc-challenge-solutions\/#%D9%85%D9%88%D8%AC_%D9%85%DA%A9%D8%B2%DB%8C%DA%A9%DB%8C\" >\u0645\u0648\u062c \u0645\u06a9\u0632\u06cc\u06a9\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/quera.org\/blog\/acm-icpc-challenge-solutions\/#%D9%86%D9%88%D8%A7%D8%B1_%D9%85%D8%B4%E2%80%8C%D8%B1%D8%AC%D8%A8\" >\u0646\u0648\u0627\u0631 \u0645\u0634\u200c\u0631\u062c\u0628<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/quera.org\/blog\/acm-icpc-challenge-solutions\/#%D8%B9%D9%85%D9%84%DB%8C%D8%A7%D8%AA_%D8%B3%D8%B1%DB%8C_%DA%A9%D8%A7_%DA%AF_%D8%A8\" >\u0639\u0645\u0644\u06cc\u0627\u062a \u0633\u0631\u06cc \u06a9\u0627. \u06af. \u0628.<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u06af\u0631\u0648\u0647-\u062e\u0648\u0646\u06cc\"><span class=\"ez-toc-section\" id=\"%DA%AF%D8%B1%D9%88%D9%87_%D8%AE%D9%88%D9%86%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170173\/\"><strong>\u06af\u0631\u0648\u0647 \u062e\u0648\u0646\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u062c\u0648\u0627\u0628 \u0633\u0624\u0627\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">valid<\/span> \u0627\u0633\u062a \u0627\u06af\u0631 \u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0645\u0627\u062f\u0647 (<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u06cc\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u06cc\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">+<\/span>) \u062f\u0631 \u06af\u0631\u0648\u0647 \u062e\u0648\u0646\u06cc \u0641\u0631\u0632\u0646\u062f\u200c\u060c \u0622\u0646 \u062f\u0631 \u062d\u062f\u0627\u0642\u0644 \u06cc\u06a9\u06cc \u0627\u0632 \u0648\u0627\u0644\u062f\u06cc\u0646 \u0628\u0627\u0634\u062f. \u0646\u0648\u0639\u06cc \u0627\u0632 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u062a\u0645\u06cc\u0632 \u0648 \u0633\u0631\u06cc\u0639 \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0647\u0631 \u06af\u0631\u0648\u0647 \u062e\u0648\u0646\u06cc \u06cc\u06a9 \u0639\u062f\u062f \u06f3 \u0628\u06cc\u062a\u06cc \u0646\u0633\u0628\u062a \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u06cc\u062a\u200c\u0647\u0627\u06cc \u0622\u0646 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f \u06a9\u0647 \u0645\u0627\u062f\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">+<\/span> \u062f\u0631 \u06af\u0631\u0648\u0647 \u062e\u0648\u0646\u06cc \u0647\u0633\u062a \u06cc\u0627 \u0646\u0647. \u062d\u0627\u0644 \u0627\u06af\u0631 \u0639\u062f\u062f \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u06af\u0631\u0648\u0647 \u062e\u0648\u0646\u06cc \u067e\u062f\u0631, \u0645\u0627\u062f\u0631 \u0648 \u0641\u0631\u0632\u0646\u062f \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">dad<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">mom<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">son<\/span> \u0628\u0627\u0634\u062f\u060c \u062f\u0627\u0631\u06cc\u0645: <\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre> ((mom \\lor dad) \\land  son == son) \\Leftrightarrow valid<\/pre><\/div>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(t)<\/span><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0645\u0627\u0645\u0648\u0631-\u0645\u062e\u0641\u06cc\"><span class=\"ez-toc-section\" id=\"%D9%85%D8%A7%D9%85%D9%88%D8%B1_%D9%85%D8%AE%D9%81%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170171\/\"><strong>\u0645\u0627\u0645\u0648\u0631 \u0645\u062e\u0641\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u062d\u062f\u0627\u0642\u0644 \u062f\u0631\u0635\u062f \u0645\u0623\u0645\u0648\u0631 \u0645\u062e\u0641\u06cc\u200c\u0647\u0627:<br>\u0628\u0631\u0627\u06cc \u062d\u0627\u0644\u062a <span class=\"katex-eq\" data-katex-display=\"false\">n=1<\/span> \u06a9\u0647 \u0628\u062f\u06cc\u0647\u06cc \u0627\u0633\u062a. \u0627\u06af\u0631 \u062f\u0648 \u0637\u0631\u062d \u0628\u0627 \u062f\u0631\u0635\u062f\u0647\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u0622\u0646\u06af\u0627\u0647 \u067e\u0627\u0633\u062e \u0645\u0634\u062e\u0635\u0627 \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\max(0,x+y-100)<\/span> \u0627\u0633\u062a. \u062d\u0627\u0644 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0637\u0631\u062d \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645. \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062c\u0648\u0627\u0628 \u0631\u0627 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">n-1<\/span> \u0637\u0631\u062d \u0627\u0648\u0644 \u062d\u0633\u0627\u0628 \u06a9\u0646\u06cc\u0645(\u0622\u0646 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">ans_{pre}<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645.) \u0648 \u062c\u0648\u0627\u0628 \u0645\u0634\u0627\u0628\u0647\u0627\u064b \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">max(0,ans_{pre}+p_n-100)<\/span> \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u06cc\u0646 \u062c\u0648\u0627\u0628 \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(0,  \\sum_{i=1}^n{p_i} - (n-1) \\times 100)<\/pre><\/div>\n\n\n\n<p>\u062d\u062f\u0627\u06a9\u062b\u0631 \u062f\u0631\u0635\u062f \u0645\u0623\u0645\u0648\u0631 \u0645\u062e\u0641\u06cc\u200c\u0647\u0627:<br>\u062b\u0627\u0628\u062a \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u067e\u0627\u0633\u062e \u0627\u06cc\u0646 \u0628\u062e\u0634 \u0628\u0631\u0627\u0628\u0631 \u06a9\u0645\u06cc\u0646\u0647 \u0627\u0639\u062f\u0627\u062f \u0627\u0633\u062a.(\u0622\u0646 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f.) \u0645\u0634\u062e\u0635\u0627\u064b \u067e\u0627\u0633\u062e \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0628\u06cc\u0634\u062a\u0631 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0627\u0634\u062f \u0686\u0631\u0627 \u06a9\u0647 \u06cc\u06a9 \u0637\u0631\u062d <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0631\u0635\u062f \u0645\u0648\u0627\u0641\u0642 \u062f\u0627\u0634\u062a\u0647\u200c\u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0631\u0635\u062f \u0627\u0641\u0631\u0627\u062f \u0628\u0647 \u0647\u0645\u0647 \u0637\u0631\u062d\u200c\u0647\u0627 \u0631\u0627\u06cc \u0645\u062b\u0628\u062a \u062f\u0627\u062f\u0647 \u0628\u0627\u0634\u0646\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(n)<\/span><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0634\u06cc\u0631-\u062a\u0648-\u0634\u06cc\u0631\"><span class=\"ez-toc-section\" id=\"%D8%B4%DB%8C%D8%B1_%D8%AA%D9%88_%D8%B4%DB%8C%D8%B1\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170167\/\"><strong>\u0634\u06cc\u0631 \u062a\u0648 \u0634\u06cc\u0631<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u062c\u0648\u0627\u0628 \u0631\u0627 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645. \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u0634\u06cc\u0631 \u0638\u0631\u0648\u0641 <span class=\"katex-eq\" data-katex-display=\"false\">i+1, i+2, \\dots, n<\/span> \u0628\u0647 \u0637\u0648\u0631 \u06cc\u06a9\u0633\u0627\u0646 \u0628\u06cc\u0646 \u0638\u0631\u0648\u0641 <span class=\"katex-eq\" data-katex-display=\"false\">1,2,\\dots,i<\/span> \u062a\u0648\u0632\u06cc\u0639 \u0634\u062f\u0647\u200c\u0627\u0633\u062a. \u067e\u0633 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>ans_i = \\frac{\\sum_{k = i+1}^n{a_k}}{i} + a_i<\/pre><\/div>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">\\sum_{k = i+1}^n{a_k}<\/span> \u0646\u06cc\u0632 (\u0622\u0646 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">S_i<\/span> \u0628\u0646\u0627\u0645\u06cc\u062f.) \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>S_n = 0, \\space S_i = S_{i+1}+a_{i+1} (i &lt; n)<\/pre><\/div>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(n)<\/span><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u06a9\u0627\u063a\u0630-\u062f\u06cc\u0648\u0627\u0631\u06cc\"><span class=\"ez-toc-section\" id=\"%DA%A9%D8%A7%D8%BA%D8%B0_%D8%AF%DB%8C%D9%88%D8%A7%D8%B1%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170168\/\"><strong>\u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\u0627\u0631\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u06af\u0631 \u0633\u062a\u0648\u0646\u06cc \u0634\u0627\u0645\u0644 \u062f\u0648 \u067e\u0631\u06cc\u0632 \u0628\u0627\u0634\u062f \u0622\u0646\u06af\u0627\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0633\u0645\u062a \u0686\u067e \u0648 \u0631\u0627\u0633\u062a \u0622\u0646 \u0631\u0627 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u062d\u0644 \u06a9\u0646\u06cc\u0645. \u067e\u0633 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0631\u0627\u0647 \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0633\u062a\u0648\u0646\u06cc \u062f\u0648 \u067e\u0631\u06cc\u0632 \u0646\u062f\u0627\u0631\u062f \u0648 \u0646\u06cc\u0632 \u0627\u06af\u0631 \u062f\u06cc\u0648\u0627\u0631 \u0628\u062f\u0648\u0646 \u067e\u0631\u06cc\u0632 \u0628\u0627\u0634\u062f \u062c\u0648\u0627\u0628 \u0645\u0633\u0644\u0645\u0627\u064b \u06f1 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u062f\u0639\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0628\u0647 \u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\u0627\u0631\u06cc \u0628\u0627 \u0639\u0631\u0636 \u06f2 \u0646\u06cc\u0627\u0632 \u0646\u062f\u0627\u0631\u06cc\u0645, \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\u0627\u0631\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">2 \\times k<\/span> \u0645\u0641\u06cc\u062f \u0628\u0627\u0634\u062f. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06cc\u06a9 \u0637\u0631\u0641 \u0622\u0646 \u062d\u062f\u0627\u0642\u0644 \u067e\u0631\u06cc\u0632 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f. (\u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u06cc\u0627 \u06a9\u0644\u0627 \u067e\u0631\u06cc\u0632 \u0646\u062f\u0627\u0631\u06cc\u0645 \u0648 \u06cc\u0627 \u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\u0627\u0631\u06cc \u0645\u062f \u0646\u0638\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0633\u062a <span class=\"katex-eq\" data-katex-display=\"false\">2 \\times (k+1)<\/span> \u0628\u0627\u0634\u062f.) \u0648 \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u062f\u0631 \u0633\u062a\u0648\u0646\u06cc \u06a9\u0647 \u067e\u0631\u06cc\u0632 \u0647\u0633\u062a \u06cc\u06a9 \u062e\u0627\u0646\u0647 \u062e\u0627\u0644\u06cc \u0647\u0645 \u0647\u0633\u062a \u06a9\u0647 \u062a\u0648\u0633\u0637 \u06a9\u0627\u063a\u0630 \u062f\u06cc\u0648\u0627\u0631\u06cc \u0628\u0647 \u0627\u0628\u0639\u0627\u062f <span class=\"katex-eq\" data-katex-display=\"false\">1 \\times l<\/span> \u067e\u0648\u0634\u0627\u0646\u062f\u0647 \u0634\u062f\u0647. \u067e\u0633 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0633\u062a\u06cc\u0645 \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u06a9\u0644\u06cc\u062a \u06a9\u0627\u0631 \u0628\u062c\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">2 \\times k<\/span> \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">1 \\times k<\/span> \u0648 \u0628\u062c\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">1 \\times l<\/span> \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">1 \\times (l+k)<\/span> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u0628\u0646\u0627\u0628\u0631\u06cc\u0646 \u062a\u0646\u0647\u0627 \u0627\u0632 \u067e\u0631\u06cc\u0632\u0647\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">1 \\times u<\/span> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0627 \u0627\u06cc\u0646 \u0641\u0631\u0636 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u062a\u0639\u062f\u0627\u062f \u0642\u0633\u0645\u062a\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u067e\u0631\u06cc\u0632\u0647\u0627 \u0631\u0648\u06cc \u0647\u0631 \u0633\u0637\u0631 \u062f\u0631\u0633\u062a \u06a9\u0631\u062f\u0647\u200c\u0627\u0646\u062f \u0631\u0627 \u0628\u0627 \u0647\u0645 \u062c\u0645\u0639 \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: (<span class=\"katex-eq\" data-katex-display=\"false\">K = \\sum k_i<\/span>) <\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(K \\log K)<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0645\u0648\u062c-\u0645\u06a9\u0632\u06cc\u06a9\u06cc\"><span class=\"ez-toc-section\" id=\"%D9%85%D9%88%D8%AC_%D9%85%DA%A9%D8%B2%DB%8C%DA%A9%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170169\/\"><strong>\u0645\u0648\u062c \u0645\u06a9\u0632\u06cc\u06a9\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0647 \u0645\u0648\u062c\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>-\u0645\u06a9\u0632\u06cc\u06a9\u06cc \u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u0627\u0641\u0631\u0627\u062f \u062f\u0631 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u062a\u0627\u06cc\u06cc \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 \u06cc\u0627 \u0646\u0634\u0633\u062a\u0647 \u0628\u0627\u0634\u0646\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u0628\u0631\u0627\u0628\u0631 \u0637\u0648\u0644 \u0628\u0644\u0646\u062f\u062a\u0631\u06cc\u0646 \u0632\u06cc\u0631\u062f\u0646\u0628\u0627\u0644\u0647 \u0645\u0648\u062c <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>-\u0645\u06a9\u0632\u06cc\u06a9\u06cc \u0627\u0633\u062a. \u0637\u0628\u0642 \u0635\u0648\u0631\u062a \u0645\u0633\u0626\u0644\u0647 \u062c\u0648\u0627\u0628 \u0628\u0631\u0627\u0628\u0631<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\max(ans_1, ans_2, \\dots, ans_n)<\/pre><\/div>\n\n\n\n<p>\u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u06a9\u0627\u0645\u0644\u0627\u064b \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">1 \\le i \\le n<\/span> \u0645\u0648\u0642\u0639\u06cc\u062a \u0627\u0648\u0644\u06cc\u0646 \u0645\u06a9\u0627\u0646\u06cc \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0627\u0646\u0646\u062f <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span> \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">i+2\\times k \\le a_i \\le n+1<\/span> \u0631\u0627 \u0628\u062f\u0627\u0646\u06cc\u0645 \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0632\u06cc\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">2k<\/span> \u062a\u0627\u06cc\u06cc \u0634\u0627\u0645\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0646\u0641\u0631 \u0646\u0634\u0633\u062a\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0648 \u0633\u067e\u0633 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0646\u0641\u0631 \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 \u062f\u0631 \u0628\u0627\u0632\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">[i,a_i)<\/span> \u0645\u0648\u062c\u0648\u062f \u0628\u0627\u0634\u062f. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span> \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u0628\u0631\u062e\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>\u0647\u0627 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">a_1<\/span> \u062a\u0639\u0631\u06cc\u0641 \u0634\u0648\u062f <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u062d\u062f\u0627\u0642\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">2k<\/span> \u0627\u0633\u062a \u0648 \u0646\u06cc\u0632 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">a_{a_1}<\/span> \u062a\u0639\u0631\u06cc\u0641 \u0634\u0648\u062f \u0622\u0646\u06af\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u062d\u062f\u0627\u0642\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">4k<\/span> \u0627\u0633\u062a \u0648 \u0627\u0644\u06cc \u0622\u062e\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\dots<\/span> (\u062d\u0627\u0644\u062a\u06cc \u06a9\u0647 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0646\u0641\u0631 \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 \u0634\u0631\u0648\u0639 \u0634\u0648\u062f \u0645\u0634\u0627\u0628\u0647 \u0627\u0633\u062a.)<\/p>\n\n\n\n<p>\u0627\u06af\u0631 \u0628\u062f\u0627\u0646\u06cc\u0645 \u0647\u0631 \u06a9\u0633 \u0686\u0646\u062f\u0645\u06cc\u0646 \u0641\u0631\u062f \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 (\u0627\u0632 \u0633\u0645\u062a \u0686\u067e) \u0627\u0633\u062a \u0648 \u0646\u06cc\u0632 \u0645\u06a9\u0627\u0646 \u0627\u0641\u0631\u0627\u062f \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0644\u06cc\u0633\u062a\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u0622\u0646\u06af\u0627\u0647 \u062f\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(1)<\/span> \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0648\u0644\u06cc\u0646 \u0645\u06a9\u0627\u0646 \u0628\u0639\u062f \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u0645\u0627\u0646\u0646\u062f <span class=\"katex-eq\" data-katex-display=\"false\">j<\/span> \u06a9\u0647 \u0632\u06cc\u0631\u062f\u0646\u0628\u0627\u0644\u0647 \u0628\u0647 \u0637\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0627\u0632 \u0627\u0641\u0631\u0627\u062f \u0627\u06cc\u0633\u062a\u0627\u062f\u0647 \u062f\u0631 \u0628\u0627\u0632\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">[i,j)<\/span> \u0645\u0648\u062c\u0648\u062f \u0627\u0633\u062a \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645. \u067e\u0633 \u0628\u0627 \u06a9\u0645\u06cc \u062c\u0632\u0626\u06cc\u0627\u062a \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span> \u062f\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(1)<\/span> \u0642\u0627\u0628\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u0633\u062a \u0628\u0646\u0627\u0628\u0631\u06cc\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u062f\u0631 \u0632\u0645\u0627\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(\\frac{n}{k})<\/span> \u0642\u0627\u0628\u0644 \u06cc\u0627\u0641\u062a\u0646 \u0627\u0633\u062a \u0686\u0631\u0627 \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">ans_k<\/span> \u062d\u062f\u0627\u06a9\u062b\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{n}{2\\times k}<\/span> \u0628\u0644\u0648\u06a9 \u062f\u0627\u0631\u062f.<\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0634\u0627\u0628\u0647 \u062a\u062d\u0644\u06cc\u0644 \u0645\u0631\u062a\u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u063a\u0631\u0628\u0627\u0644 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\sum_{i=1}^n{\\mathcal{O}(\\frac{n}{i})} = \\mathcal{O}(n\\log(n))<\/pre><\/div>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: ( <span class=\"katex-eq\" data-katex-display=\"false\">N = \\sum n_i<\/span>)<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(N \\log N)<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0646\u0648\u0627\u0631-\u0645\u0634-\u0631\u062c\u0628\"><span class=\"ez-toc-section\" id=\"%D9%86%D9%88%D8%A7%D8%B1_%D9%85%D8%B4%E2%80%8C%D8%B1%D8%AC%D8%A8\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170170\/\"><strong>\u0646\u0648\u0627\u0631 \u0645\u0634\u200c\u0631\u062c\u0628<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0642\u0635\u062f \u062f\u0627\u0631\u06cc\u0645 \u0633\u0624\u0627\u0644\u06cc \u06a9\u0644\u06cc\u200c\u062a\u0631 \u0631\u0627 \u062d\u0644 \u06a9\u0646\u06cc\u0645. \u0622\u0631\u0627\u06cc\u0647\u200c\u0627\u06cc \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u062f\u0627\u0631\u06cc\u0645 \u0648 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0639\u0648\u0636 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062d\u0627\u0644 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062c\u0645\u0639 \u0632\u06cc\u0631\u0628\u0627\u0632\u0647\u200c\u0627\u06cc \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0686\u0642\u062f\u0631 \u0627\u0633\u062a\u061f \u0628\u0631\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0633\u0624\u0627\u0644\u0627\u062a \u0647\u0645 \u0628\u0647 \u0647\u0645 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u062f\u0631 \u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u0622\u0628\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">-a_i<\/span> \u0648 \u062f\u0631 \u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u0642\u0631\u0645\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span> \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u0624\u0627\u0644 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 <a href=\"https:\/\/opedia.ir\/%D8%A2%D9%85%D9%88%D8%B2%D8%B4\/%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85_%D9%87%D8%A7%DB%8C_%D8%AA%DA%A9%D9%85%DB%8C%D9%84%DB%8C\/%D8%AF%D8%B1%D8%AE%D8%AA_%D8%A8%D8%A7%D8%B2%D9%87_%D8%A7%DB%8C\">\u062f\u0631\u062e\u062a-\u0628\u0627\u0632\u0647\u200c\u0627\u06cc<\/a> (segment-tree) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0631\u0627\u06cc \u0647\u0631 \u06af\u0631\u0647 \u062f\u0631 \u062f\u0631\u062e\u062a \u06f4 \u0686\u06cc\u0632 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u06cc\u0645: \u062c\u0645\u0639 \u06a9\u0644, \u062c\u0645\u0639 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0632\u06cc\u0631 \u0628\u0627\u0632\u0647, \u062c\u0645\u0639 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u067e\u06cc\u0634\u0648\u0646\u062f \u0648 \u062c\u0645\u0639 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u067e\u0633\u0648\u0646\u062f. (\u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">sum<\/span> \u060c <span class=\"katex-eq\" data-katex-display=\"false\">max_{all}<\/span> \u060c <span class=\"katex-eq\" data-katex-display=\"false\">max_{pre}<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">max_{suf}<\/span> \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.) \u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u0627\u062f\u063a\u0627\u0645 \u062f\u0648 \u06af\u0631\u0647 \u0645\u062a\u0648\u0627\u0644\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span> \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>sum = L_{sum}+R_{sum}\n\\\\\nmax_{all} = \\max(L_{max_{all}}, R_{max_{all}}, L_{max_{suf}}+R_{max_{pre}})\n\\\\\nmax_{pre} = \\max(L_{max_{pre}}, L_{sum}+R_{max_{pre}})\n\\\\\nmax_{suf} = \\max(R_{max_{suf}}, R_{sum}+L_{max_{suf}})<\/pre><\/div>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0639\u0648\u0636 \u06a9\u0631\u062f\u0646 \u06cc\u06a9 \u062e\u0627\u0646\u0647 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0647\u0645\u0647 \u0628\u0627\u0632\u0647\u200c\u0647\u0627\u06cc \u0634\u0627\u0645\u0644 \u0622\u0646 \u062e\u0627\u0646\u0647 \u0631\u0627 \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">max_{all}<\/span> \u0631\u06cc\u0634\u0647 \u062f\u0631\u062e\u062a \u0647\u0645 \u0647\u0631 \u0628\u0627\u0631 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(n \\times \\log n)<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u0631\u0627\u0647 \u062f\u06cc\u06af\u0631 \u0633\u0624\u0627\u0644 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0628\u0647 \u0628\u0627\u0632\u0647\u200c\u0647\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u062a\u0627\u06cc\u06cc \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0632\u0647 \u06f4 \u0645\u0648\u0631\u062f \u06af\u0641\u062a\u0647 \u0634\u062f\u0647 \u0631\u0627 \u0646\u06af\u0647 \u062f\u0627\u0631\u06cc\u0645. \u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u06cc\u06a9 \u062e\u0627\u0646\u0647 \u0647\u0632\u06cc\u0646\u0647 \u0632\u0645\u0627\u0646\u06cc \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u062f\u0627\u0631\u062f \u0648 \u0628\u0631\u0627\u06cc \u067e\u0627\u0633\u062e \u0628\u0647 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062c\u0645\u0639 \u0632\u06cc\u0631 \u0628\u0627\u0632\u0647 \u0686\u0646\u06cc\u0646 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645: \u06cc\u0627 \u062e\u0627\u0646\u0647 \u0627\u06cc \u06a9\u0647 \u0627\u062e\u06cc\u0631\u0627\u064b \u0642\u0631\u0645\u0632 \u0634\u062f\u0647 \u062c\u0632 \u062c\u0648\u0627\u0628 \u0627\u0633\u062a \u06cc\u0627 \u062c\u0648\u0627\u0628 \u062c\u0648\u0627\u0628 \u0642\u0628\u0644\u06cc \u0647\u0633\u062a. \u0627\u06af\u0631 \u062e\u0627\u0646\u0647 \u0642\u0631\u0645\u0632 \u062c\u0632 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0628\u0627\u0632\u0647 \u0628\u0627\u0634\u062f. \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u067e\u06cc\u0634\u0648\u0646\u062f \u06a9\u0647 \u0639\u0636\u0648 \u0627\u0648\u0644 \u0622\u0646 \u062e\u0627\u0646\u0647 \u062c\u062f\u06cc\u062f \u0628\u0627\u0634\u062f \u0648 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u067e\u0633\u0648\u0646\u062f \u0645\u0646\u062a\u0647\u06cc \u0628\u0647 \u062e\u0627\u0646\u0647 \u062c\u062f\u06cc\u062f \u0631\u0627 \u0628\u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">T + \\frac{n}{T}<\/span> \u0647\u0631 \u062f\u0648 \u0642\u0627\u0628\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0633\u062a\u0646\u062f \u0648 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u06a9\u0644\u06cc \u0628\u0631\u0627\u0628\u0631<br><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(n \\times (T + \\frac{n}{T}))<\/span><br>\u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">T = \\sqrt n<\/span> \u0633\u0624\u0627\u0644 \u062d\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0639\u0645\u0644\u06cc\u0627\u062a-\u0633\u0631\u06cc-\u06a9\u0627-\u06af-\u0628\"><span class=\"ez-toc-section\" id=\"%D8%B9%D9%85%D9%84%DB%8C%D8%A7%D8%AA_%D8%B3%D8%B1%DB%8C_%DA%A9%D8%A7_%DA%AF_%D8%A8\"><\/span><a href=\"https:\/\/quera.org\/problemset\/170172\/\"><strong>\u0639\u0645\u0644\u06cc\u0627\u062a \u0633\u0631\u06cc \u06a9\u0627. \u06af. \u0628.<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u0627\u0633 \u062f\u0631 \u062f\u0631\u062e\u062a \u0645\u0627\u0646\u0646\u062f <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>\u060c \u0648 \u0627\u0631\u062a\u0641\u0627\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span>\u060c <span class=\"katex-eq\" data-katex-display=\"false\">L_{u,h}<\/span> \u0631\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u06a9\u0645\u06cc\u0646\u0647 \u0639\u062f\u062f \u062f\u0631\u062e\u062a \u062c\u0633\u062a\u200c\u0648\u062c\u0648 \u062f\u0648\u062f\u0648\u06cc\u06cc \u06a9\u0627\u0645\u0644 \u0628\u0647 \u0627\u0631\u062a\u0641\u0627\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> \u0648 \u0628\u0627 \u0631\u06cc\u0634\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. \u0627\u06af\u0631 \u0686\u0646\u06cc\u0646 \u062f\u0631\u062e\u062a\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a <span class=\"katex-eq\" data-katex-display=\"false\">L_{u,h}<\/span> \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. <span class=\"katex-eq\" data-katex-display=\"false\">R_{u,h}<\/span> \u0645\u0634\u0627\u0628\u0647\u0627\u064b \u0628\u0631\u0627\u0628\u0631 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u0628\u06cc\u0634\u06cc\u0646\u0647 \u0639\u062f\u062f \u062f\u0631\u062e\u062a \u0628\u0627 \u0645\u0634\u062e\u0635\u0627\u062a \u06af\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">n+1<\/span> \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p>\u0646\u062d\u0648\u0647 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0646 \u0627\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0686\u0646\u06cc\u0646 \u0627\u0633\u062a:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>L_{v,0} = R_{v,0} = v\n\\\\\nL_{v,h} = max_{element}(\\{ L_{u,h-1} | u \\in N(v), R_{u,h-1} &lt; v \\})\n\\\\\nR_{v,h} = min_{element}(\\{ R_{u,h-1} | u \\in N(v), L_{u,h-1} &gt; v \\})<\/pre><\/div>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">h &gt; \\log n<\/span> \u0622\u0646\u06af\u0627\u0647 \u062f\u0631\u062e\u062a \u06a9\u0627\u0645\u0644 \u062f\u0648\u062f\u0648\u06cc\u06cc \u0627\u0632 \u0647\u06cc\u0686 \u0631\u0627\u0633\u06cc \u0628\u0647 \u0627\u0631\u062a\u0641\u0627\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.<\/p>\n\n\n\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0645\u0634\u062e\u0635\u0627\u064b<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>max_{element}(\\{ 2^{h+1}-1 | 1 \\le v \\le n, L_{v,h} &gt; 0\\}<\/pre><\/div>\n\n\n\n<p>\u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. (\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u062f\u0631\u062e\u062a \u062f\u0648\u062f\u0648\u06cc\u06cc \u06a9\u0627\u0645\u0644 \u0628\u0647 \u0627\u0631\u062a\u0641\u0627\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span>\u060c <span class=\"katex-eq\" data-katex-display=\"false\">2^{h+1}-1<\/span> \u0631\u0627\u0633 \u062f\u0627\u0631\u062f.)<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{O}(n \\times \\log n)<\/span><\/p>\n\n\n\n<p>\u0627\u0645\u06cc\u062f\u0648\u0631\u0627\u0645 \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627 \u0645\u0641\u06cc\u062f \u0628\u0648\u062f\u0647 \u0628\u0627\u0634\u0647. \u0627\u06af\u0631 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u06cc\u0627 \u0633\u0624\u0627\u0644\u06cc \u062f\u0627\u0634\u062a\u06cc\u0646\u060c \u062d\u062a\u0645\u0627 \u062f\u0631 \u0646\u0638\u0631\u0627\u062a \u0645\u0637\u0631\u062d \u0628\u0641\u0631\u0645\u0627\u06cc\u06cc\u062f.<\/p>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc ACM-ICPC Challenge \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&#8230;<\/p>\n","protected":false},"author":40,"featured_media":42674,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,50,141],"tags":[],"class_list":["post-42613","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-developer","category-quera-developer","category-contests-and-events"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc ACM-ICPC Challenge - \u06a9\u0648\u0626\u0631\u0627\u200c\u0628\u0644\u0627\u06af<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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