{"id":42649,"date":"2023-04-26T02:13:31","date_gmt":"2023-04-25T21:43:31","guid":{"rendered":"https:\/\/quera.org\/blog\/?p=42649"},"modified":"2023-04-26T02:13:34","modified_gmt":"2023-04-25T21:43:34","slug":"bye-1401-solutions","status":"publish","type":"post","link":"https:\/\/quera.org\/blog\/bye-1401-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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1"},"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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1 \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. \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u062a\u0634\u06a9\u0631 \u0645\u06cc\u200c\u06a9\u0646\u0645 \u0627\u0632 \u00ab<strong>\u0634\u0627\u06cc\u0627\u0646 \u0686\u0634\u0645\u200c\u062c\u0647\u0627\u0646<\/strong>\u00bb \u0639\u0632\u06cc\u0632\u060c \u0628\u0627\u0628\u062a \u0647\u0645\u06a9\u0627\u0631\u06cc \u062f\u0631 \u0646\u0648\u0634\u062a\u0646 \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0648\u0627\u0644\u0627\u062a \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647.<\/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\/bye-1401-solutions\/#%D8%AC%DB%8C%D8%BA%E2%80%8C%D8%B2%D8%AF%D9%86\" >\u062c\u06cc\u063a\u200c\u0632\u062f\u0646<\/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\/bye-1401-solutions\/#%D8%AA%D8%B1%D8%AF%D8%B3%D8%AA%DB%8C\" >\u062a\u0631\u062f\u0633\u062a\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\/bye-1401-solutions\/#%D8%AC%D8%B2%D9%88%D9%87_%D8%AF%D8%B1%D8%B3%DB%8C\" >\u062c\u0632\u0648\u0647 \u062f\u0631\u0633\u06cc<\/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\/bye-1401-solutions\/#%DA%86%D8%B4%D9%85%E2%80%8C%D9%86%D9%88%D8%A7%D8%B2\" >\u0686\u0634\u0645\u200c\u0646\u0648\u0627\u0632<\/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\/bye-1401-solutions\/#%D9%85%D9%87%D8%B1%D9%87_%D8%AF%D8%B1_%DA%AF%D9%88%D9%86%DB%8C\" >\u0645\u0647\u0631\u0647 \u062f\u0631 \u06af\u0648\u0646\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\/bye-1401-solutions\/#%D9%81%DB%8C%D9%84%E2%80%8C%D9%87%D8%A7%DB%8C_%D8%AF%D8%B9%D9%88%D8%A7%DB%8C%DB%8C\" >\u0641\u06cc\u0644\u200c\u0647\u0627\u06cc \u062f\u0639\u0648\u0627\u06cc\u06cc<\/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\/bye-1401-solutions\/#%D8%B1%D9%86%DA%AF%E2%80%8C%D8%A2%D9%85%DB%8C%D8%B2%DB%8C\" >\u0631\u0646\u06af\u200c\u0622\u0645\u06cc\u0632\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/quera.org\/blog\/bye-1401-solutions\/#%D8%AA%D9%82%D8%B3%DB%8C%D9%85_%D9%85%D9%86%D8%B5%D9%81%D8%A7%D9%86%D9%87\" >\u062a\u0642\u0633\u06cc\u0645 \u0645\u0646\u0635\u0641\u0627\u0646\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u062c\u06cc\u063a-\u0632\u062f\u0646\"><span class=\"ez-toc-section\" id=\"%D8%AC%DB%8C%D8%BA%E2%80%8C%D8%B2%D8%AF%D9%86\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175187\/\"><strong>\u062c\u06cc\u063a\u200c\u0632\u062f\u0646<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u0628\u062a\u062f\u0627 \u0627\u062f\u0639\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n=1<\/span> \u0628\u0627\u0634\u062f\u060c \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u0628\u0631 \u06f2 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0648\u0627\u0636\u062d \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u062f\u0631 \u0632\u0645\u0627\u0646 \u062f\u06cc\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9 \u0627\u0648\u0644 \u0647\u0631 \u062f\u0648\u06cc \u062f\u0627\u0631\u0627 \u0648 \u0633\u0627\u0631\u0627 \u062c\u06cc\u063a \u062e\u0648\u0627\u0647\u0646\u062f \u06a9\u0634\u06cc\u062f\u060c \u067e\u0633 \u062a\u0639\u062f\u0627\u062f \u062c\u06cc\u063a\u200c\u0647\u0627 \u0642\u0637\u0639\u0627 \u06f2 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">n \\ge 2<\/span> \u0628\u0627\u0634\u062f\u060c \u0627\u062f\u0639\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0647\u0645\u06cc\u0634\u0647 \u06f3 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0627\u0628\u062a\u062f\u0627 \u062b\u0627\u0628\u062a \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062d\u062f\u0627\u0642\u0644 \u06f3 \u062c\u06cc\u063a \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a. \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0639\u062f \u0627\u0632 \u062f\u06cc\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9 \u0627\u0648\u0644 \u0647\u0645 \u062f\u0627\u0631\u0627 \u0648 \u0647\u0645 \u0633\u0627\u0631\u0627 \u062c\u06cc\u063a \u062e\u0648\u0627\u0647\u0646\u062f \u06a9\u0634\u06cc\u062f. \u062d\u0627\u0644 \u062f\u0648 \u062d\u0627\u0644\u062a \u062f\u0627\u0631\u06cc\u0645\u060c \u0627\u06af\u0631 \u0639\u0631\u0648\u0633\u06a9 \u062f\u0648\u0645 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u0639\u0631\u0648\u0633\u06a9 \u0627\u0648\u0644 \u0628\u0627\u0634\u062f\u060c \u0633\u0627\u0631\u0627 \u062c\u06cc\u063a \u0645\u06cc\u200c\u06a9\u0634\u062f. \u0627\u06af\u0631 \u0639\u0631\u0648\u0633\u06a9 \u062f\u0648\u0645 \u0628\u0632\u0631\u06af\u200c\u062a\u0631 \u0627\u0632 \u0639\u0631\u0648\u0633\u06a9 \u0627\u0648\u0644 \u0628\u0627\u0634\u062f\u060c \u062f\u0627\u0631\u0627 \u062c\u06cc\u063a \u0645\u06cc\u200c\u06a9\u0634\u062f. \u067e\u0633 \u062f\u0631 \u0647\u0631 \u0635\u0648\u0631\u062a \u06cc\u06a9\u06cc \u0627\u0632 \u0622\u0646\u200c\u0647\u0627 \u0628\u0639\u062f \u0627\u0632 \u0622\u0645\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9 \u062f\u0648\u0645 \u062c\u06cc\u063a \u062e\u0648\u0627\u0647\u062f \u06a9\u0634\u06cc\u062f \u0648 \u062d\u062f\u0627\u0642\u0644 \u0633\u0647 \u062c\u06cc\u063a \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0634\u06cc\u062f.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u0622\u0646\u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u062c\u0648\u0627\u0628 \u0628\u06cc\u0634 \u0627\u0632 \u06f3 \u0646\u06cc\u0633\u062a\u060c \u0645\u062b\u0627\u0644\u06cc \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u06a9\u0647 \u062f\u0627\u0631\u0627 \u0648 \u0633\u0627\u0631\u0627 \u062f\u0642\u06cc\u0642\u0627\u064b \u06f3 \u0628\u0627\u0631 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639 \u062c\u06cc\u063a \u0645\u06cc\u200c\u06a9\u0634\u0646\u062f. \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0639\u0631\u0648\u0633\u06a9 \u0634\u0645\u0627\u0631\u0647 \u06f1\u060c \u0633\u067e\u0633 \u0639\u0631\u0648\u0633\u06a9 \u0634\u0645\u0627\u0631\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0648 \u0633\u067e\u0633 \u0645\u0627\u0628\u0642\u06cc \u0639\u0631\u0648\u0633\u06a9\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628\u06cc \u062f\u0644\u062e\u0648\u0627\u0647 \u0628\u06cc\u0627\u06cc\u0646\u062f. \u062f\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u062f\u0642\u06cc\u0642\u0627\u064b \u062f\u0648 \u062c\u06cc\u063a \u0628\u0639\u062f \u0627\u0632 \u062f\u06cc\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9 \u0627\u0648\u0644 \u0648 \u06cc\u06a9 \u062c\u06cc\u063a \u0628\u0639\u062f \u0627\u0632 \u062f\u06cc\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9 \u062f\u0648\u0645 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a \u0648 \u0628\u0639\u062f \u0627\u0632 \u062f\u06cc\u062f\u0646 \u0639\u0631\u0648\u0633\u06a9\u200c\u0647\u0627\u06cc \u0628\u0639\u062f\u06cc \u0647\u06cc\u0686 \u062c\u06cc\u063a\u06cc \u0648\u062c\u0648\u062f \u0646\u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.<\/p>\n\n\n\n<p>\u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">n&gt;1<\/span> \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0631\u0627\u0628\u0631 \u06f3 \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}(1)<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u062a\u0631\u062f\u0633\u062a\u06cc\"><span class=\"ez-toc-section\" id=\"%D8%AA%D8%B1%D8%AF%D8%B3%D8%AA%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175188\/\"><strong>\u062a\u0631\u062f\u0633\u062a\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0647 \u06cc\u06a9 \u0628\u0627\u0632\u0647 \u0627\u0632 \u06a9\u0627\u0631\u062a\u200c\u0647\u0627 \u0628\u0644\u0648\u06a9 \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u0627\u06af\u0631 \u0647\u0645\u0647 \u06a9\u0627\u0631\u062a\u200c\u0647\u0627 \u0648\u0636\u0639\u06cc\u062a \u0645\u0634\u0627\u0628\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f \u0648 \u0628\u0627\u0632\u0647 \u0627\u0632 \u0647\u06cc\u0686 \u0637\u0631\u0641\u06cc \u0642\u0627\u0628\u0644 \u06af\u0633\u062a\u0631\u0634 \u0646\u0628\u0627\u0634\u062f (\u0645\u0627\u06a9\u0633\u06cc\u0645\u0627\u0644 \u0628\u0627\u0634\u062f). \u0645\u062b\u0644\u0627\u064b 0110111000 \u0627\u0632 \u06f5 \u0628\u0644\u0648\u06a9 \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u062f\u0639\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u0628\u0631 \u062a\u0639\u062f\u0627\u062f \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc \u0628\u0647 \u067e\u0634\u062a\u200c \u0627\u0633\u062a. \u0645\u0634\u062e\u0635\u0627\u064b \u0686\u0648\u0646 \u0647\u0631 \u0628\u0644\u0648\u06a9 \u06cc\u06a9 \u0628\u0627\u0632\u0647 \u0647\u0633\u062a \u067e\u0633 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9\u06cc \u06cc\u06a9\u06cc \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc \u067e\u0634\u062a \u0631\u0627 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u06cc\u0645 \u062a\u0627 \u0647\u0645\u0647 \u06a9\u0627\u0631\u062a\u200c\u0647\u0627 \u0631\u0648 \u0634\u0648\u0646\u062f. \u0627\u0632 \u0637\u0631\u0641\u06cc \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0628\u0627 \u06cc\u06a9 \u062d\u0631\u06a9\u062a \u062a\u0639\u062f\u0627\u062f \u0628\u0644\u0648\u06a9\u200c\u0647\u0627\u06cc \u067e\u0634\u062a \u062d\u062f\u0627\u06a9\u062b\u0631 \u06cc\u06a9\u06cc \u06a9\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u067e\u0633 \u0627\u062f\u0639\u0627 \u062b\u0627\u0628\u062a \u0645\u06cc\u200c\u0634\u0648\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}(T \\times CountCards)<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u062c\u0632\u0648\u0647-\u062f\u0631\u0633\u06cc\"><span class=\"ez-toc-section\" id=\"%D8%AC%D8%B2%D9%88%D9%87_%D8%AF%D8%B1%D8%B3%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175189\/\"><strong>\u062c\u0632\u0648\u0647 \u062f\u0631\u0633\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u0648\u0644\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u062f\u0631 \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0642\u0637\u0639\u0627\u064b \u0641\u0627\u06cc\u0644 \u0628\u0627 \u0628\u06cc\u0634\u062a\u0631\u06cc\u0646 \u062d\u062c\u0645 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u067e\u0627\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0627\u0633\u062a. \u062f\u0644\u06cc\u0644 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0645\u062d\u062a\u0648\u0627\u06cc \u0647\u0645\u0647\u200c\u06cc \u0641\u0627\u06cc\u0644\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0632\u06cc\u0631\u0645\u062c\u0645\u0648\u0639\u0647\u200c\u06cc \u067e\u0627\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0647\u0633\u062a\u0646\u062f\u060c \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u0645\u06a9\u0627\u0646 \u0646\u062f\u0627\u0631\u062f \u062d\u062c\u0645 \u0622\u0646\u200c\u0647\u0627 \u0627\u0632 \u062d\u062c\u0645 \u067e\u0627\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627\u0634\u062f.<\/p>\n\n\n\n<p>\u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u062c\u0645 \u0641\u0627\u06cc\u0644 \u067e\u0627\u06cc\u0627\u0646\u062a\u0631\u0645 \u0631\u0627 \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645. \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u062d\u062c\u0645 \u0627\u06cc\u0646 \u0641\u0627\u06cc\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0648 \u0645\u062c\u0645\u0648\u0639 \u062d\u062c\u0645 \u0645\u0627\u0628\u0642\u06cc \u0641\u0627\u06cc\u0644\u200c\u0647\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0627\u0633\u062a. \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> (\u06a9\u0647 \u0647\u0645\u0627\u0646 \u062d\u062c\u0645 \u0641\u0627\u06cc\u0644 \u067e\u0627\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0627\u0633\u062a) \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639 \u062d\u062c\u0645 \u062a\u0645\u0627\u0645 \u062c\u0644\u0633\u0627\u062a \u06a9\u0644\u0627\u0633 \u0627\u0633\u062a. \u0647\u0645\u06cc\u0646\u0637\u0648\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639 \u062d\u062c\u0645 \u062a\u0645\u0627\u0645 \u062c\u0644\u0633\u0627\u062a \u06a9\u0644\u0627\u0633 \u0648 \u0641\u0627\u06cc\u0644 \u0645\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0627\u0633\u062a. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u062c\u0645 \u0641\u0627\u06cc\u0644 \u0645\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">B-A<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u062c\u0645 \u067e\u0627\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u067e\u0631 \u062d\u062c\u0645\u200c\u062a\u0631\u06cc\u0646 \u0641\u0627\u06cc\u0644 \u0648\u0631\u0648\u062f\u06cc\u060c \u0648 \u062d\u062c\u0645 \u0645\u06cc\u0627\u0646\u200c\u062a\u0631\u0645 \u0628\u0631\u0627\u0628\u0631 \u0645\u062c\u0645\u0648\u0639 \u062d\u062c\u0645 \u0628\u0642\u06cc\u0647\u200c\u06cc \u0641\u0627\u06cc\u0644\u200c\u0647\u0627 \u0645\u0646\u0647\u0627\u06cc \u0622\u0646 \u0641\u0627\u06cc\u0644 \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)<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0686\u0634\u0645-\u0646\u0648\u0627\u0632\"><span class=\"ez-toc-section\" id=\"%DA%86%D8%B4%D9%85%E2%80%8C%D9%86%D9%88%D8%A7%D8%B2\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175182\/\"><strong>\u0686\u0634\u0645\u200c\u0646\u0648\u0627\u0632<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u0628\u062a\u062f\u0627 \u0645\u0633\u0627\u0644\u0647 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0634\u0631\u06a9\u062a \u062d\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0646\u06cc\u0632 \u0628\u062f\u0648\u0646 \u0627\u0632 \u062f\u0633\u062a \u062f\u0627\u062f\u0646 \u06a9\u0644\u06cc\u062a \u0645\u0633\u0627\u0644\u0647 \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">n \\le m<\/span> \u062d\u0627\u0644:<\/p>\n\n\n\n<p>\u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n = 1<\/span> \u0628\u0627\u0634\u062f \u067e\u0627\u0633\u062e \u0645\u0633\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">4 \\times 3 ^ {m-1}<\/span> \u0627\u0633\u062a \u0686\u0631\u0627 \u06a9\u0647 \u0627\u06af\u0631 \u067e\u0646\u062c\u0631\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0627\u0632 \u0686\u067e \u0628\u0647 \u0631\u0627\u0633\u062a \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u06a9\u0646\u06cc\u0645 \u0622\u0646\u06af\u0627\u0647 \u067e\u0646\u062c\u0631\u0647 \u0627\u0648\u0644 \u06f4 \u062d\u0627\u0644\u062a \u0648 \u0628\u0642\u06cc\u0647 \u06f3 \u062d\u0627\u0644\u062a \u062f\u0627\u0631\u0646\u062f.<\/p>\n\n\n\n<p>\u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u06cc\u0627 \u062c\u062f\u0648\u0644 (\u0646\u0645\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062c\u062f\u0648\u0644 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f) \u0633\u0637\u0631\u06cc \u0631\u0646\u06af \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u06cc\u0627 \u0633\u062a\u0648\u0646\u06cc. \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u062c\u062f\u0648\u0644 \u0633\u0637\u0631\u06cc \u0631\u0646\u06af \u0634\u062f\u0647 \u0627\u06af\u0631 \u0633\u0637\u0631\u0647\u0627\u06cc \u0641\u0631\u062f \u062a\u0646\u0647\u0627 \u0627\u0632 \u062f\u0648 \u0631\u0646\u06af \u0645\u0634\u062e\u0635 \u0631\u0646\u06af \u0634\u062f\u0647 \u0628\u0627\u0634\u0646\u062f. \u0633\u062a\u0648\u0646\u06cc \u0631\u0646\u06af \u0634\u062f\u0646 \u0647\u0645 \u0645\u0634\u0627\u0628\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u0627\u062b\u0628\u0627\u062a: \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u062c\u062f\u0648\u0644 \u0633\u0637\u0631\u06cc \u0631\u0646\u06af \u0646\u0634\u062f\u0647 \u0628\u0627\u0634\u062f \u067e\u0633 \u0628\u0627 \u06a9\u0645\u06cc \u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u0634\u0648\u062f \u06f3 \u062e\u0627\u0646\u0647 \u06a9\u0646\u0627\u0631 \u0647\u0645 \u06cc\u0627\u0641\u062a \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0631\u0646\u06af\u200c\u0647\u0627\u06cc \u0645\u062a\u0645\u0627\u06cc\u0632\u06cc \u062f\u0627\u0631\u0646\u062f. \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0631\u0646\u06af\u200c\u0647\u0627 \u0627\u0632 \u0686\u067e \u0628\u0647 \u0631\u0627\u0633\u062a \u06f1 \u0648 \u06f2 \u0648 \u06f3 \u0628\u0627\u0634\u0646\u062f \u062f\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0633\u062a\u0648\u0646\u200c\u0647\u0627\u06cc \u0628\u0627\u0644\u0627 \u0648 \u067e\u0627\u06cc\u06cc\u0646 \u0622\u0646 \u06cc\u06a9\u062a\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1 2 3\n\\\\\n3 4 1\n\\\\\n1 2 3\n\\\\\n3 4 1<\/pre><\/div>\n\n\n\n<p>\u0648 \u0628\u0627\u0632 \u0628\u0627 \u06a9\u0645\u06cc \u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0646\u062a\u06cc\u062c\u0647 \u0628\u06af\u06cc\u0631\u06cc\u062f \u0627\u06af\u0631 \u0633\u0637\u0631\u06cc \u0631\u0646\u06af \u0646\u0634\u062f\u0647 \u0628\u0627\u0634\u062f \u067e\u0633 \u0633\u062a\u0648\u0646\u06cc \u0631\u0646\u06af \u0634\u062f\u0647.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u06af\u0631 \u062c\u062f\u0648\u0644 \u0633\u0637\u0631\u06cc \u0631\u0646\u06af \u0634\u062f\u0647 \u0628\u0627\u0634\u062f \u067e\u0627\u0633\u062e $6 \\times 2^n$ \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u0686\u0631\u0627 \u06a9\u0647 \u0627\u0646\u062a\u062e\u0627\u0628 \u0631\u0646\u06af\u200c\u0647\u0627\u06cc \u0633\u0637\u0631 \u0627\u0648\u0644 \u06f6 \u062d\u0627\u0644\u062a \u0648 \u0627\u06cc\u0646\u06a9\u0647 \u0627\u0648\u0644\u06cc\u0646 \u062e\u0627\u0646\u0647 \u0647\u0631 \u0633\u0637\u0631 \u0686\u0647 \u0631\u0646\u06af\u06cc \u0628\u0627\u0634\u062f \u06f2 \u062d\u0627\u0644\u062a \u062f\u0627\u0631\u062f.<\/p>\n\n\n\n<p>\u067e\u0633 \u062c\u0648\u0627\u0628 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc\u200c\u0647\u0627\u06cc \u0633\u0637\u0631\u06cc \u0628\u0647 \u0639\u0644\u0627\u0648\u0647 \u062a\u0639\u062f\u0627\u062f \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc\u200c\u0647\u0627\u06cc \u0633\u062a\u0648\u0646\u06cc \u0645\u0646\u0647\u0627\u06cc \u062a\u0639\u062f\u0627\u062f \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u0645 \u0633\u0637\u0631\u06cc \u0648 \u0647\u0645 \u0633\u062a\u0648\u0646\u06cc \u0647\u0633\u062a\u0646\u062f.<\/p>\n\n\n\n<p>\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u062a\u0639\u062f\u0627\u062f \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u0645 \u0633\u0637\u0631\u06cc \u0648 \u0647\u0645 \u0633\u062a\u0648\u0646\u06cc \u0647\u0633\u062a\u0646\u062f \u06f2\u06f4 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u067e\u0627\u0633\u062e \u062f\u0627\u062f\u0646 \u0628\u0647 \u062a\u0633\u062a\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u06cc\u06a9 \u0628\u0627\u0631 \u0628\u0631\u0627\u06cc \u0647\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">1 \\le x \\le N<\/span> \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">3^x<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">2^x<\/span> \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\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 + T)<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0645\u0647\u0631\u0647-\u062f\u0631-\u06af\u0648\u0646\u06cc\"><span class=\"ez-toc-section\" id=\"%D9%85%D9%87%D8%B1%D9%87_%D8%AF%D8%B1_%DA%AF%D9%88%D9%86%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175183\/\"><strong>\u0645\u0647\u0631\u0647 \u062f\u0631 \u06af\u0648\u0646\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0627\u0639\u062f\u0627\u062f\u06cc \u06a9\u0647 \u062f\u0631 \u06a9\u06cc\u0633\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>\u0627\u0645 \u0647\u0633\u062a\u0646\u062f \u0631\u0627 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0627\u0632 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647 \u06a9\u0645\u06a9\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">add<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">del<\/span> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0647\u0631 \u062e\u0627\u0646\u0647 \u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627 \u062e\u0648\u062f\u0634 \u0644\u06cc\u0633\u062a \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u06cc\u06a9 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">l\\space r\\space x<\/span> \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f. \u0628\u0647 \u0644\u06cc\u0633\u062a\u200c\u0647\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">add[l]<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">rem[r+1]<\/span> \u0639\u062f\u062f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0631\u0627 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u062d\u0627\u0644 \u0627\u06af\u0631 \u0627\u0639\u062f\u0627\u062f \u06a9\u06cc\u0633\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>\u0627\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">G_i<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u0622\u0646\u06af\u0627\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>G_i = G_{i-1}+add[i]-rem[i]<\/pre><\/div>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u0648\u0627\u0644 \u0627\u0632 \u062f\u0648 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u06cc\u06a9 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u06a9\u0647 \u0627\u0639\u062f\u0627\u062f\u06cc \u06a9\u0647 \u0646\u062f\u0627\u0631\u06cc\u0645 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f \u0648 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631\u06cc \u062f\u06cc\u06af\u0631 \u06a9\u0647 \u0627\u0639\u062f\u0627\u062f\u06cc \u06a9\u0647 \u0627\u0636\u0627\u0641\u0647 \u062f\u0627\u0631\u06cc\u0645 \u06cc\u0639\u0646\u06cc \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9\u06cc \u0627\u0632 \u0622\u0646 \u062f\u0627\u0631\u06cc\u0645 \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u062f. \u0628\u0631\u0627\u06cc \u067e\u0627\u0633\u062e \u0633\u0648\u0627\u0644 \u0627\u0628\u062a\u062f\u0627 \u062c\u0648\u0627\u0628 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06af\u0648\u0646\u06cc \u06f1 \u062d\u0633\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0633\u067e\u0633 \u06f2 \u0648&#8230; \u062c\u0648\u0627\u0628 \u0647\u0645\u06cc\u0634\u0647 \u06a9\u0645\u062a\u0631\u06cc\u0646 \u0639\u0636\u0648 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u0627\u0648\u0644\u06cc\u0633\u062a.<\/p>\n\n\n\n<p>\u0628\u0627\u06cc\u062f \u062f\u0631 \u0647\u0631 \u062f\u0648 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631 \u0632\u0645\u0627\u0646 \u062e\u0648\u0628\u06cc (\u0645\u062b\u0644 <span class=\"katex-eq\" data-katex-display=\"false\"> \\mathcal{O}(\\log N) <\/span>) \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9 \u0639\u0636\u0648 \u062d\u0630\u0641 \u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u0627 \u06cc\u06a9 \u0639\u0636\u0648 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u0627 \u0648\u062c\u0648\u062f \u06cc\u06a9 \u0639\u0636\u0648 \u0631\u0627 \u0628\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645. \u062f\u0631 \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u0627\u0648\u0644 \u0628\u0627\u06cc\u062f \u0642\u0627\u0628\u0644\u06cc\u062a \u06af\u0631\u0641\u062a\u0646 \u06a9\u0645\u06cc\u0646\u0647 \u0627\u0639\u0636\u0627 \u0647\u0645 \u062f\u0627\u062f\u0647 \u0628\u0627\u0634\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0627\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 <em>segment tree<\/em> , <em>red-black tree<\/em> \u0648 <em>Trie<\/em> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\n\n\n\n<p>\u062a\u0648\u062c\u0647: \u062f\u0631 <em>C++<\/em> \u062f\u0627\u062f\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 set \u0646\u0648\u0639\u06cc <em>red-black tree<\/em> \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 \\log N) <\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0641\u06cc\u0644-\u0647\u0627\u06cc-\u062f\u0639\u0648\u0627\u06cc\u06cc\"><span class=\"ez-toc-section\" id=\"%D9%81%DB%8C%D9%84%E2%80%8C%D9%87%D8%A7%DB%8C_%D8%AF%D8%B9%D9%88%D8%A7%DB%8C%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175184\/\"><strong>\u0641\u06cc\u0644\u200c\u0647\u0627\u06cc \u062f\u0639\u0648\u0627\u06cc\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0647 \u062a\u0639\u062f\u0627\u062f\u06cc \u062e\u0627\u0646\u0647 \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u062a\u0627\u06cc\u06cc \u0627\u0632 \u0622\u0646\u200c\u0647\u0627 (\u062f\u0631 \u0635\u0648\u0631\u062a \u0648\u062c\u0648\u062f \u0641\u06cc\u0644 \u062f\u0631 \u0622\u0646\u200c\u0647\u0627) \u0647\u0645\u062f\u06cc\u06af\u0631 \u0631\u0627 \u062a\u0647\u062f\u06cc\u062f \u06a9\u0646\u0646\u062f \u0648 \u0646\u06cc\u0632 \u0645\u0627\u06a9\u0633\u06cc\u0645\u0627\u0644 \u0628\u0627\u0634\u0646\u062f (\u06cc\u0639\u0646\u06cc \u0646\u062a\u0648\u0627\u0646 \u062e\u0627\u0646\u0647\u200c\u0627\u06cc \u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u062f \u0646\u0638\u0631 \u0628\u0627 \u062d\u0641\u0638 \u062e\u0627\u0635\u06cc\u062a \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f) \u0628\u0644\u0648\u06a9 \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645. \u0648 \u0646\u06cc\u0632 \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u0646\u0648\u0639 \u0628\u0644\u0648\u06a9 \u0645\u0648\u062c\u0648\u062f \u0627\u0633\u062a. \u06cc\u06a9\u06cc \u0628\u0644\u0648\u06a9 \u0627\u0635\u0644\u06cc \u06a9\u0647 \u0645\u0648\u0627\u0632\u06cc \u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u0642\u0637\u0631 \u0627\u0635\u0644\u06cc \u0627\u0633\u062a \u0648 \u06cc\u06a9\u06cc \u0628\u0644\u0648\u06a9 \u0641\u0631\u0639\u06cc \u06a9\u0647 \u0645\u0648\u0627\u0632\u06cc \u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u0642\u0637\u0631 \u0641\u0631\u0639\u06cc \u0627\u0633\u062a. \u0645\u062b\u0644\u0627\u064b \u062c\u062f\u0648\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>123\\#\n\\\\\n4\\#23\n\\\\\n54\\#2\n\\\\\n654\\#<\/pre><\/div>\n\n\n\n<p>\u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u0647\u0645 \u0634\u0645\u0627\u0631\u0647 \u062f\u0631 \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u0647\u0633\u062a\u0646\u062f. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0647\u0631 \u062e\u0627\u0646\u0647\u200c\u06cc \u062e\u0627\u0644\u06cc \u0645\u062a\u0639\u0644\u0642 \u0628\u0647 \u062f\u0642\u06cc\u0642\u0627\u064b \u062f\u0648 \u0628\u0644\u0648\u06a9 \u0627\u0633\u062a \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u0641\u0631\u0639\u06cc \u0648 \u06cc\u06a9 \u0628\u0644\u0648\u06a9 \u0627\u0635\u0644\u06cc.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u062c\u062f\u0648\u0644 \u0631\u0627 \u0628\u0647 \u06af\u0631\u0627\u0641 \u062f\u0648 \u0628\u062e\u0634\u06cc \u0645\u062f\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0644\u0648\u06a9\u200c\u0647\u0627 \u0647\u0645\u0627\u0646 \u0631\u0627\u0633\u200c\u0647\u0627 \u0647\u0633\u062a\u0646\u062f \u0648 \u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u062e\u0627\u0644\u06cc \u0647\u0645\u0627\u0646 \u06cc\u0627\u0644\u200c\u0647\u0627 \u06a9\u0647 \u062f\u0648 \u0628\u0644\u0648\u06a9 \u0631\u0627 \u0628\u0647 \u0647\u0645 \u0648\u0635\u0644 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f.<\/p>\n\n\n\n<p>\u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062a\u0637\u0627\u0628\u0642 \u06af\u0631\u0627\u0641 \u0647\u0645\u0627\u0646 \u062c\u0648\u0628 \u0645\u0633\u0627\u0644\u0647 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u0627\u0648\u0644\u0627\u064b \u0627\u06af\u0631 \u062f\u0631 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u0628\u06cc\u0634\u06cc\u0646\u0647 \u062a\u0637\u0627\u0628\u0642 \u0641\u06cc\u0644\u200c\u0647\u0627 \u0631\u0627 \u0628\u06af\u0630\u0627\u0631\u06cc\u0645 \u0647\u06cc\u0686 \u062f\u0648 \u0641\u06cc\u0644\u06cc \u0647\u0645\u062f\u06cc\u06af\u0631 \u0631\u0627 \u062a\u0647\u062f\u06cc\u062f \u0646\u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0686\u0648\u0646 \u0647\u06cc\u0686 \u062f\u0648 \u06cc\u0627\u0644\u06cc \u0633\u0631 \u0645\u0634\u062a\u0631\u06a9 \u0646\u062f\u0627\u0631\u0646\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0647\u0631 \u0686\u06cc\u062f\u0645\u0627\u0646\u06cc \u0627\u0632 \u0641\u06cc\u0644\u200c\u0647\u0627 \u06a9\u0647 \u0645\u0639\u062a\u0628\u0631 \u0628\u0627\u0634\u062f \u0646\u06cc\u0632 \u0645\u0634\u062e\u0635\u0627\u064b \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u06cc\u06a9 \u062a\u0637\u0627\u0628\u0642 \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 m + (n \\times m)^2)<\/span><\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0628\u06cc\u0634\u06cc\u0646\u0647 \u062a\u0637\u0627\u0628\u0642 \u0645\u0627 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 <a href=\"https:\/\/cp-algorithms.com\/graph\/kuhn_maximum_bipartite_matching.html\">kuhn<\/a> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u06cc\u0645. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0647\u0645 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0622\u0646\u200c\u0647\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0633\u0648\u0627\u0644 \u0646\u06cc\u0633\u062a.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u0631\u0646\u06af-\u0622\u0645\u06cc\u0632\u06cc\"><span class=\"ez-toc-section\" id=\"%D8%B1%D9%86%DA%AF%E2%80%8C%D8%A2%D9%85%DB%8C%D8%B2%DB%8C\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175185\/\"><strong>\u0631\u0646\u06af\u200c\u0622\u0645\u06cc\u0632\u06cc<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp[i]<\/span> \u0631\u0627 \u0628\u0647 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u062d\u0627\u0644\u0627\u062a \u0631\u0646\u06af\u200c\u0622\u0645\u06cc\u0632\u06cc \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u0635\u062d\u06cc\u062d \u06a9\u0647 \u0645\u0636\u0631\u0628\u06cc \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0647 \u0637\u0648\u0631\u06cc\u06a9\u0647 \u0645\u0627\u0628\u0642\u06cc \u0646\u0642\u0627\u0637 \u0645\u062d\u0648\u0631 \u0645\u062e\u062a\u0635\u0627\u062a \u0631\u0646\u06af \u0646\u0634\u0648\u0646\u062f. \u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u0637\u0628\u0642 \u0627\u06cc\u0646 \u062a\u0639\u0631\u06cc\u0641 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">dp[1]<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0647\u0645\u06cc\u0646\u0637\u0648\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">cnt[i]<\/span> \u0631\u0627 \u062a\u0639\u062f\u0627\u062f \u0631\u0646\u06af\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628\u0634\u0627\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u0627\u0633\u062a \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0645\u0642\u0627\u062f\u06cc\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp<\/span> \u0631\u0627 \u0627\u0632 \u0622\u062e\u0631 \u0628\u0647 \u0627\u0648\u0644 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u0648\u0631\u06cc\u0645. \u0641\u0631\u0636 \u06a9\u0646\u06cc\u0645 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp[x]<\/span> \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645. \u0642\u0637\u0639\u0627 \u0641\u0642\u0637 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0631\u0646\u06af\u200c\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628\u0634\u0627\u0646 \u0645\u0636\u0631\u0628\u06cc \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0628\u0627\u0634\u062f. \u06cc\u06a9 \u062d\u0627\u0644\u062a \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0627 \u06cc\u06a9 \u0631\u0646\u06af \u0628\u0627 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0631\u0646\u06af \u06a9\u0646\u06cc\u0645\u060c \u062f\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u0627\u0632 \u06cc\u06a9 \u0631\u0646\u06af \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u062a\u0645\u0627\u0645\u06cc \u0646\u0642\u0627\u0637 \u067e\u0648\u0634\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u062a\u0639\u062f\u0627\u062f \u0627\u06cc\u0646 \u062d\u0627\u0644\u0627\u062a <span class=\"katex-eq\" data-katex-display=\"false\">cnt[x]<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062d\u0627\u0644\u062a \u062f\u06cc\u06af\u0631 \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0641\u0642\u0637 \u0627\u0632 \u0631\u0646\u06af\u200c\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628\u0634\u0627\u0646 \u0645\u0636\u0631\u0628\u06cc \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0648 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u062e\u0648\u062f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0627\u0633\u062a. \u0627\u06af\u0631 \u0628.\u0645.\u0645 \u0627\u06cc\u0646 \u0627\u0639\u062f\u0627\u062f \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">d.x<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645\u060c <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0646\u0628\u0627\u06cc\u062f \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06f1 \u0628\u0627\u0634\u062f\u060c \u0632\u06cc\u0631\u0627 \u062f\u0631 \u0622\u0646 \u0635\u0648\u0631\u062a \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u0631\u0646\u06af \u062f\u0627\u0631\u06cc\u0645\u060c \u0637\u0628\u0642 \u0644\u0645 \u0628\u0632\u0648 \u0628\u0647 \u062a\u0646\u0627\u0642\u0636 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0631\u0633\u06cc\u062f (\u06cc\u0639\u0646\u06cc \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0628\u0627\u06cc\u062f \u062f\u0648 \u0631\u0646\u06af \u0645\u062e\u062a\u0644\u0641 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f). \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0631\u0627 \u0641\u06cc\u06a9\u0633 \u06a9\u0646\u06cc\u0645 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u062d\u0627\u0644\u062a \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u062e\u0627\u0635 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">dp[dx]^d<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f\u060c \u0632\u06cc\u0631\u0627 \u0646\u0642\u0627\u0637 \u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u062f\u0633\u062a\u0647 \u0645\u0633\u062a\u0642\u0644 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647\u200c\u0647\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">dp[dx]<\/span> \u062d\u0627\u0644\u062a \u062f\u0627\u0631\u0646\u062f.<\/p>\n\n\n\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639\u060c \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647\u200c\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">dp[x]<\/span> \u0627\u0632 \u0634\u0645\u0648\u0644 \u0648 \u0639\u062f\u0645 \u0634\u0645\u0648\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u0645\u0627\u0646\u0646\u062f <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span> \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp[px]^p<\/span> \u0631\u0627 \u062c\u0645\u0639 \u0645\u06cc\u200c\u0632\u0646\u06cc\u0645. \u0628\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644 \u062d\u0627\u0644\u062a\u06cc \u06a9\u0647 \u0628.\u0645.\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">6x<\/span> \u0628\u0627\u0634\u062f \u0647\u0645 \u062f\u0631 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">p=2<\/span> \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0648 \u0647\u0645 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">p=3<\/span> \u0627\u0633\u062a \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u067e\u0633 \u0628\u0627\u06cc\u062f \u06a9\u0645 \u0634\u0648\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u06a9\u0644\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0627\u0632\u0627\u06cc \u062a\u0645\u0627\u0645 \u0627\u0639\u062f\u0627\u062f square free (\u06cc\u0639\u0646\u06cc \u0627\u0639\u062f\u0627\u062f\u06cc \u06a9\u0647 \u062f\u0631 \u062a\u062c\u0632\u06cc\u0647\u200c\u0634\u0627\u0646 \u0627\u0632 \u0647\u0631 \u0639\u0627\u0645\u0644 \u0627\u0648\u0644\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u06cc\u06a9\u06cc \u062f\u0627\u0631\u0646\u062f) \u0645\u0627\u0646\u0646\u062f <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp[d.x]^d<\/span> \u0631\u0627 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u0648\u0631\u06cc\u0645. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0639\u0648\u0627\u0645\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0641\u0631\u062f \u0628\u0627\u0634\u062f \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u062c\u0648\u0627\u0628 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0639\u0648\u0627\u0645\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0632\u0648\u062c \u0628\u0627\u0634\u062f \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0631\u0627 \u0627\u0632 \u062c\u0648\u0627\u0628 \u06a9\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0645\u0642\u0627\u062f\u06cc\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp<\/span> \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u0646\u062f \u0648 \u062d\u0627\u0635\u0644 \u0646\u0647\u0627\u06cc\u06cc \u0645\u0627 \u0645\u0642\u062f\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">dp[1]<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\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 + L \\log ^2 L)<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-medium-font-size\" id=\"h-\u062a\u0642\u0633\u06cc\u0645-\u0645\u0646\u0635\u0641\u0627\u0646\u0647\"><span class=\"ez-toc-section\" id=\"%D8%AA%D9%82%D8%B3%DB%8C%D9%85_%D9%85%D9%86%D8%B5%D9%81%D8%A7%D9%86%D9%87\"><\/span><a href=\"https:\/\/quera.org\/problemset\/175186\/\"><strong>\u062a\u0642\u0633\u06cc\u0645 \u0645\u0646\u0635\u0641\u0627\u0646\u0647<\/strong><\/a><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u06cc\u06a9 \u062e\u0637 \u0631\u0627 \u062e\u0648\u0628 \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u0627\u06af\u0631 \u0646\u06cc\u0645\u0647 \u0627\u0632 \u0646\u0642\u0627\u0637 \u06cc\u06a9 \u0637\u0631\u0641 \u0622\u0646 \u0628\u0627\u0634\u0646\u062f. \u062b\u0627\u0628\u062a \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u062e\u0637 \u062e\u0648\u0628 \u06cc\u06a9 \u062e\u0637 \u0639\u0627\u0644\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0647 \u0647\u0645\u0627\u0646 \u0634\u06a9\u0644 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0631 \u062f\u0648 \u0646\u0642\u0637\u0647 \u0646\u06cc\u0632 \u0645\u0645\u0627\u0633 \u0627\u0633\u062a(\u0648 \u062d\u062a\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f \u0622\u0646 \u062f\u0648 \u0646\u0642\u0637\u0647 \u062f\u0631 \u06cc\u06a9 \u0633\u0645\u062a \u062e\u0637 \u0647\u0645 \u0646\u06cc\u0633\u062a\u0646\u062f.)<\/p>\n\n\n\n<p>\u062e\u0637\u06cc \u062e\u0648\u0628 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f. \u0627\u06af\u0631 \u0647\u06cc\u0686 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u0628\u0631 \u0622\u0646 \u0645\u0645\u0627\u0633 \u0646\u0628\u0648\u062f (\u062e\u0637 \u0648 \u0646\u0642\u0637\u0647 \u0631\u0627 \u0645\u0645\u0627\u0633 \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0627\u06af\u0631 \u0641\u0627\u0635\u0644\u0647 \u0622\u0646\u0647\u0627 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0648\u0686\u06a9 \u0628\u0627\u0634\u062f.) \u062e\u0637 \u0631\u0627 \u0628\u0627 \u0628\u0631\u062f\u0627\u0631\u06cc \u062f\u0644\u062e\u0648\u0627\u0647(\u0646\u0627\u0645\u0648\u0627\u0632\u06cc \u0628\u0627 \u062e\u0637) \u0622\u0646\u0642\u062f\u0631 \u0627\u0646\u062a\u0642\u0627\u0644 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u062a\u0627 \u0628\u0627 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u0645\u0645\u0627\u0633 \u0634\u0648\u062f. \u062d\u0627\u0644 \u062e\u0637 \u0631\u0627 \u062d\u0648\u0644 \u0622\u0646 \u0646\u0642\u0637\u0647 \u0622\u0646\u0642\u062f\u0631 \u062f\u0648\u0631\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u062a\u0627 \u0645\u0645\u0627\u0633 \u0628\u0631 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u062a\u0639\u062f\u0627\u062f \u062e\u0637\u0648\u0637 \u0639\u0627\u0644\u06cc \u0645\u062d\u062f\u0648\u062f \u0627\u0633\u062a \u0648 \u0628\u0627 \u0628\u0631\u0633\u06cc \u0647\u0631 \u062f\u0648 \u0646\u0642\u0637\u0647 \u0627\u0632 \u0635\u0641\u062d\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f. \u062d\u0627\u0644 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0627\u0644\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u06a9\u062f\u0627\u0645 \u062f\u0648 \u062e\u0637 \u0639\u0627\u0644\u06cc \u067e\u0627\u0633\u062e \u0645\u0633\u0627\u0644\u0647 \u0645\u0627 \u0647\u0633\u062a\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}(T \\times N^3)<\/span><\/p>\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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1 \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":42559,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,50,141],"tags":[],"class_list":["post-42649","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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1 - \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\" href=\"https:\/\/quera.org\/blog\/bye-1401-solutions\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1 - \u06a9\u0648\u0626\u0631\u0627\u200c\u0628\u0644\u0627\u06af\" \/>\n<meta property=\"og:description\" content=\"\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 \u062e\u062f\u0627\u062d\u0627\u0641\u0638 \u06f1\u06f4\u06f0\u06f1 \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...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/quera.org\/blog\/bye-1401-solutions\/\" \/>\n<meta property=\"og:site_name\" content=\"\u06a9\u0648\u0626\u0631\u0627\u200c\u0628\u0644\u0627\u06af\" \/>\n<meta property=\"article:published_time\" content=\"2023-04-25T21:43:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-04-25T21:43:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quera.org\/blog\/wp-content\/uploads\/2023\/03\/khodahafez1401-resize-05.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"800\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"\u0645\u062d\u0645\u062f\u200c\u067e\u0627\u0631\u0633\u0627 \u0627\u0644\u0647\u06cc\u200c\u0645\u0646\u0634\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0646\u0648\u0634\u062a\u0647\u200c\u0634\u062f\u0647 \u0628\u062f\u0633\u062a\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u0645\u062d\u0645\u062f\u200c\u067e\u0627\u0631\u0633\u0627 \u0627\u0644\u0647\u06cc\u200c\u0645\u0646\u0634\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 \u062f\u0642\u06cc\u0642\u0647\" \/>\n<script type=\"application\/ld+json\" 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