{"id":34724,"date":"2022-04-22T11:14:38","date_gmt":"2022-04-22T11:14:38","guid":{"rendered":"https:\/\/quera.org\/blog\/?p=34724"},"modified":"2022-06-09T08:01:58","modified_gmt":"2022-06-09T08:01:58","slug":"algo-39-solutions","status":"publish","type":"post","link":"https:\/\/quera.org\/blog\/algo-39-solutions\/","title":{"rendered":"\u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u0634\u0645\u0627\u0631\u0647 \u06f3\u06f9 + \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\" style=\"font-size:18px\"><strong>\u0633\u0644\u0627\u0645!<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u06f3\u06f9\u0627\u0645\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u06a9\u0648\u0626\u0631\u0627 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062a\u0627\u06a9\u0646\u0648\u0646 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href=\"https:\/\/quera.org\/blog\/algo-39-solutions\/#%D9%BE%DB%8C%E2%80%8C%D9%86%D9%88%D8%B4%D8%AA_%D8%B1%D8%A7%D9%87%E2%80%8C%D8%AD%D9%84%E2%80%8C%D9%87%D8%A7\" >\u067e\u06cc\u200c\u0646\u0648\u0634\u062a: \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627<\/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\/algo-39-solutions\/#%D8%B3%DB%8C%D8%A8%D9%84_%D8%AA%DB%8C%D8%B1%D8%A7%D9%86%D8%AF%D8%A7%D8%B2%DB%8C\" >\u0633\u06cc\u0628\u0644 \u062a\u06cc\u0631\u0627\u0646\u062f\u0627\u0632\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\/algo-39-solutions\/#%D8%AD%D9%82%D9%88%D9%82_%D8%B3%D8%B9%DB%8C%D8%AF\" >\u062d\u0642\u0648\u0642 \u0633\u0639\u06cc\u062f<\/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\/algo-39-solutions\/#%D8%A7%D9%86%D8%AA%D8%B3%D8%A7%D8%A8_%D8%A2%D8%B1%D8%A7%DB%8C%D9%87\" >\u0627\u0646\u062a\u0633\u0627\u0628 \u0622\u0631\u0627\u06cc\u0647<\/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\/algo-39-solutions\/#%D8%B9%D8%AF%D8%AF%DA%AF%D8%B0%D8%A7%D8%B1%DB%8C_%DA%AF%D8%B1%D8%A7%D9%81\" >\u0639\u062f\u062f\u06af\u0630\u0627\u0631\u06cc \u06af\u0631\u0627\u0641<\/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\/algo-39-solutions\/#%D8%AF%D9%86%D8%A8%D8%A7%D9%84%D9%87_%D8%AF%D9%84%D8%AE%D9%88%D8%A7%D9%87\" >\u062f\u0646\u0628\u0627\u0644\u0647 \u062f\u0644\u062e\u0648\u0627\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/quera.org\/blog\/algo-39-solutions\/#%D8%AF%D9%86%D8%A8%D8%A7%D9%84%D9%87_%D8%BA%D8%B1%DB%8C%D8%A8\" >\u062f\u0646\u0628\u0627\u0644\u0647 \u063a\u0631\u06cc\u0628<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%AC%D9%88%D8%A7%DB%8C%D8%B2_%D9%85%D8%B3%D8%A7%D8%A8%D9%82%D9%87\"><\/span><strong>\u062c\u0648\u0627\u06cc\u0632 \u0645\u0633\u0627\u0628\u0642\u0647<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>\u067e\u0646\u062c \u0646\u0641\u0631 \u0627\u0648\u0644: \u06cc\u06a9 \u062a\u06cc\u0634\u0631\u062a \u06a9\u0648\u0626\u0631\u0627\u06cc\u06cc<\/li><li>\u0628\u0647 \u067e\u0646\u062c \u0646\u0641\u0631 \u0627\u0632 \u0646\u0641\u0631\u0627\u062a \u0628\u0631\u062a\u0631: \u0628\u0647 \u0642\u06cc\u062f \u0642\u0631\u0639\u0647 \u06cc\u06a9 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id=\"%D9%BE%DB%8C%E2%80%8C%D9%86%D9%88%D8%B4%D8%AA_%D8%B1%D8%A7%D9%87%E2%80%8C%D8%AD%D9%84%E2%80%8C%D9%87%D8%A7\"><\/span><strong>\u067e\u06cc\u200c\u0646\u0648\u0634\u062a: \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u0645\u06cc\u062f\u0648\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0627\u0632 <a href=\"https:\/\/quera.org\/events\/algo-39\" target=\"_blank\" rel=\"noreferrer noopener\">\u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u0634\u0645\u0627\u0631\u0647 \u06f3\u06f9<\/a> \u0644\u0630\u062a \u0628\u0631\u062f\u0647 \u0628\u0627\u0634\u06cc\u062f. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0645\u0633\u0627\u0628\u0642\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647\u200c\u0627\u0646\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\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\u0627\u0646\u06cc\u062f \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a \u0633\u0624\u0627\u0644\u0627\u062a \u0648 \u0627\u0628\u0647\u0627\u0645\u200c\u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0645\u0637\u0631\u062d \u06a9\u0646\u06cc\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u06af\u0631 \u0631\u0627\u0647\u200c\u062d\u0644 \u062f\u06cc\u06af\u0631\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\u0648\u06cc\u0645 \u06a9\u0647 \u0631\u0627\u0647\u200c\u062d\u0644 \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a \u0628\u0627 \u0645\u0627 \u0648 \u062f\u0648\u0633\u062a\u0627\u0646\u062a\u0627\u0646 \u0628\u0647 \u0627\u0634\u062a\u0631\u0627\u06a9 \u0628\u06af\u0630\u0627\u0631\u06cc\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%B3%DB%8C%D8%A8%D9%84_%D8%AA%DB%8C%D8%B1%D8%A7%D9%86%D8%AF%D8%A7%D8%B2%DB%8C\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141570\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0633\u06cc\u0628\u0644 \u062a\u06cc\u0631\u0627\u0646\u062f\u0627\u0632\u06cc<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0633\u0647 \u062d\u0627\u0644\u062a \u062e\u0648\u0627\u0633\u062a\u0647\u200c\u0634\u062f\u0647 \u0631\u0627 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%AD%D9%82%D9%88%D9%82_%D8%B3%D8%B9%DB%8C%D8%AF\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141574\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u062d\u0642\u0648\u0642 \u0633\u0639\u06cc\u062f<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">sum<\/span> \u0631\u0627 \u0645\u062c\u0645\u0648\u0639 \u062d\u0642\u0648\u0642 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u0645\u0646\u062f \u062f\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0645\u0627\u0647 \u0627\u0648\u0644 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645. \u06cc\u0639\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>sum=a_{1}+a_{2}+ ...+a_{n}<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u06a9\u0647 \u062d\u0642\u0648\u0642 \u0627\u06cc\u0646 \u0634\u062e\u0635 \u062f\u0631 \u0645\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>\u0627\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">(n+1 \\leq k)<\/span> \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>2^{k-n-1}\\times sum<\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%A7%D9%86%D8%AA%D8%B3%D8%A7%D8%A8_%D8%A2%D8%B1%D8%A7%DB%8C%D9%87\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141572\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0627\u0646\u062a\u0633\u0627\u0628 \u0622\u0631\u0627\u06cc\u0647<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06af\u0631 \u0639\u062f\u062f\u06cc \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0628\u0627\u0634\u062f \u06a9\u0647 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0647\u062f\u0641 \u0645\u0645\u06a9\u0646 \u0646\u06cc\u0633\u062a. (\u0686\u0648\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u0646\u062a\u0633\u0627\u0628 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0631\u0627 \u06af\u0633\u062a\u0631\u0634 \u0646\u0645\u06cc\u200c\u062f\u0647\u062f.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u067e\u0633 \u062a\u0646\u0647\u0627 \u062d\u0627\u0644\u062a\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627\u0642\u06cc\u200c\u0645\u0627\u0646\u062f\u0647 \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0632\u06cc\u0631\u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06af\u0631 \u0647\u0645\u0647 \u0627\u0639\u062f\u0627\u062f \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0645\u062a\u0645\u0627\u06cc\u0632 \u0628\u0627\u0634\u0646\u062f\u060c \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0627\u0632 \u0647\u0645\u0627\u0646 \u0627\u0628\u062a\u062f\u0627 \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0628\u0627\u0634\u062f. (\u0686\u0648\u0646 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u0646 \u0647\u0631 \u0639\u0645\u0644\u06cc\u0627\u062a\u06cc \u0628\u0627\u0639\u062b \u0627\u06cc\u062c\u0627\u062f \u0634\u062f\u0646 \u0639\u062f\u062f \u062a\u06a9\u0631\u0627\u0631\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u067e\u0633 \u062d\u0627\u0644\u062a\u200c\u0647\u0627\u06cc\u06cc \u0628\u0627\u0642\u06cc\u200c\u0645\u0627\u0646\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u06cc\u06a9 \u0639\u062f\u062f \u062d\u062f\u0627\u0642\u0644 \u06f2 \u0628\u0627\u0631 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u0647\u0645\u0648\u0627\u0631\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u0627\u062a \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0631\u0633\u06cc\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u062d\u0627\u0644\u062a \u0627\u0648\u0644:<\/strong> \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0639\u062f\u062f\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0646\u06cc\u0627\u0645\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u062c\u0627\u06cc\u06af\u0627\u0647 \u0627\u06cc\u0646 \u0639\u062f\u062f \u0645\u062b\u0644 \u0645\u062a\u063a\u06cc\u0631 \u06a9\u0645\u06a9\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u0648 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0631\u0627 \u06a9\u0627\u0645\u0644\u0627\u064b \u0628\u0633\u0627\u0632\u06cc\u0645 \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0645\u0642\u062f\u0627\u0631 \u0645\u0637\u0644\u0648\u0628 \u0631\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u062e\u0627\u0646\u0647 \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u062d\u0627\u0644\u062a \u062f\u0648\u0645:<\/strong> \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0639\u062f\u062f\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0648 \u0628\u0627\u0631 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0627\u0639\u062f\u0627\u062f \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u062a\u063a\u06cc\u0631 \u06a9\u0645\u06a9\u06cc \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a \u0648 \u062f\u0633\u062a \u0628\u0647 \u06a9\u067e\u06cc \u062f\u06cc\u06af\u0631 \u0622\u0646 \u0646\u0632\u0646\u06cc\u0645 \u0648 \u062c\u0627\u06cc \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u062f\u06cc\u06af\u0631 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0631 \u062c\u0627\u06cc\u06af\u0634\u062a\u06cc \u0631\u0627 \u062f\u0631\u0633\u062a \u06a9\u0646\u06cc\u0645 \u0648 \u06cc\u0627 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631\u0647\u0627\u06cc \u06cc\u06a9 \u0639\u062f\u062f \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0631\u0627 \u0632\u06cc\u0627\u062f \u0648 \u06a9\u0645 \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%B9%D8%AF%D8%AF%DA%AF%D8%B0%D8%A7%D8%B1%DB%8C_%DA%AF%D8%B1%D8%A7%D9%81\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141573\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0639\u062f\u062f\u06af\u0630\u0627\u0631\u06cc \u06af\u0631\u0627\u0641<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u0628\u0631\u0631\u0633\u06cc \u06cc\u06a9 \u0631\u0623\u0633 \u0628\u0647 \u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0631\u0633\u06cc\u062f \u06a9\u0647 \u0627\u06af\u0631 \u062f\u0631\u062c\u0647 \u06cc\u06a9 \u0631\u0623\u0633 \u0628\u06cc\u0634 \u0627\u0632 \u06f2 \u0628\u0627\u0634\u062f\u060c \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0634\u062f\u0646\u06cc \u0646\u06cc\u0633\u062a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u067e\u0633 \u0627\u06af\u0631 \u062f\u0631 \u06af\u0631\u0627\u0641 \u062f\u0627\u062f\u0647\u200c\u0634\u062f\u0647 \u062f\u0631\u062c\u0647 \u0647\u0645\u0647 \u0631\u0623\u0633\u200c\u0647\u0627 \u062d\u062f\u0627\u06a9\u062b\u0631 \u06f2 \u0628\u0627\u0634\u062f\u061b \u0645\u0648\u0644\u0641\u0647\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u06af\u0631\u0627\u0641 \u062a\u0639\u062f\u0627\u062f\u06cc \u0645\u0633\u06cc\u0631 \u0647\u0633\u062a\u0646\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06af\u0631 \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u0637\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0639\u062f\u062f\u200c\u06af\u0630\u0627\u0631\u06cc \u0631\u0648\u06cc \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u0628\u0627\u06cc\u062f \u06cc\u06a9 \u062f\u0646\u0628\u0627\u0644\u0647 \u0645\u062a\u0648\u0627\u0644\u06cc \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0628\u0627\u0634\u062f. (\u0686\u0647 \u0635\u0639\u0648\u062f\u06cc\u060c \u0686\u0647 \u0646\u0632\u0648\u0644\u06cc)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0627\u06af\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>&nbsp;\u06a9\u0645\u062a\u0631 \u0627\u0632&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">l<\/span>&nbsp;\u0628\u0627\u0634\u062f\u060c \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0686\u0646\u06cc\u0646 \u0639\u062f\u062f\u200c\u06af\u0630\u0627\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f.<\/li><li>\u0627\u06af\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>&nbsp;\u0628\u06cc\u0634\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">l<\/span>&nbsp;\u0628\u0627\u0634\u062f \u0648&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">l<\/span>&nbsp;\u0628\u0632\u0631\u06af\u200c\u062a\u0631 \u0627\u0632 \u06f1 \u0628\u0627\u0634\u062f\u060c \u0627\u06cc\u0646 \u0639\u062f\u062f\u06af\u0630\u0627\u0631\u06cc \u0628\u0647&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">2(k+1-l)<\/span>&nbsp;\u0631\u0648\u0634 \u0645\u0645\u06a9\u0646 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/li><li>\u0627\u06af\u0631&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">l<\/span>&nbsp;\u0628\u0631\u0627\u0628\u0631 \u06f1 \u0628\u0627\u0634\u062f\u060c \u0627\u06cc\u0646 \u0639\u062f\u062f\u06af\u0630\u0627\u0631\u06cc \u0628\u0647&nbsp;<span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>&nbsp;\u0631\u0648\u0634 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0627\u06af\u0631 \u0639\u062f\u062f\u06af\u0630\u0627\u0631\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u0645\u0624\u0644\u0641\u0647 \u0647\u0645\u0628\u0646\u062f\u06cc \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645\u060c \u067e\u0627\u0633\u062e \u06a9\u0644\u06cc \u0645\u0633\u0626\u0644\u0647 \u0628\u0646\u0627\u0628\u0631 \u0627\u0635\u0644 \u0636\u0631\u0628\u060c \u0628\u0631\u0627\u0628\u0631 \u0636\u0631\u0628 \u062a\u0639\u062f\u0627\u062f \u062d\u0627\u0644\u062a\u200c\u0647\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0624\u0644\u0641\u0647\u200c\u0647\u0627 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%AF%D9%86%D8%A8%D8%A7%D9%84%D9%87_%D8%AF%D9%84%D8%AE%D9%88%D8%A7%D9%87\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141568\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u062f\u0646\u0628\u0627\u0644\u0647 \u062f\u0644\u062e\u0648\u0627\u0647<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06cc\u0646 \u0633\u0624\u0627\u0644 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u06a9\u0647 \u0647\u0645\u06af\u06cc \u062f\u0631\u0633\u062a \u0647\u0633\u062a\u0646\u062f. \u0627\u0645\u0627 \u06cc\u06a9 \u0631\u0627\u0647\u200c\u062d\u0644 \u0642\u0627\u0628\u0644\u200c\u0642\u0628\u0648\u0644 \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u0627\u0644\u0627\u0646 \u0639\u062f\u062f \u06f2 \u062a\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0631\u0627 \u0646\u0648\u0634\u062a\u0647\u200c\u0627\u06cc\u0645 \u0648\u0644\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">k+1<\/span> \u0631\u0627 \u0646\u0646\u0648\u0634\u062a\u0647\u200c\u0627\u06cc\u0645. \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0639\u062f\u062f <span class=\"katex-eq\" data-katex-display=\"false\">k+1<\/span> \u0631\u0627 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u06cc\u06a9 \u0645\u0636\u0631\u0628 \u0645\u0634\u062a\u0631\u06a9 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">k+1<\/span> \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647 \u062a\u0627 \u0627\u0644\u0627\u0646 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0646\u06cc\u0627\u0645\u062f\u0647 \u0627\u0633\u062a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u06cc\u0646 \u0639\u062f\u062f \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> \u0628\u0646\u0627\u0645\u06cc\u0645. \u0628\u0639\u062f \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> (\u06a9\u0647 \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0642\u0628\u0644 \u0646\u0648\u0634\u062a\u06cc\u0645) \u0639\u062f\u062f <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> \u0648 \u0633\u067e\u0633 \u0639\u062f\u062f <span class=\"katex-eq\" data-katex-display=\"false\">k+1<\/span> \u0631\u0627 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0646\u062d\u0648\u0647 \u0627\u0646\u062a\u062e\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span> \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u0647\u0631 \u062f\u0648 \u0639\u062f\u062f \u0645\u062c\u0627\u0648\u0631 \u0646\u0633\u0628\u062a \u0628\u0647 \u0647\u0645 \u0627\u0648\u0644 \u0646\u06cc\u0633\u062a\u0646\u062f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0627 \u0627\u062f\u0627\u0645\u0647 \u062f\u0627\u062f\u0646 \u0627\u06cc\u0646 \u0631\u0648\u0646\u062f \u0647\u0645\u0647 \u0627\u0639\u062f\u0627\u062f \u0627\u0632 \u06f2 \u062a\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0638\u0627\u0647\u0631 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0637\u0648\u0644 \u062f\u0646\u0628\u0627\u0644\u0647 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">2n<\/span> \u0628\u06cc\u0634\u062a\u0631 \u0646\u0645\u06cc\u200c\u0634\u0648\u062f\u061b \u0627\u0645\u0627 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u06a9\u0645\u062a\u0631 \u0634\u0648\u062f. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0637\u0648\u0644 \u062f\u0646\u0628\u0627\u0644\u0647 \u0631\u0627 \u062f\u0642\u06cc\u0642\u0627\u064b \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">2n<\/span> \u06a9\u0646\u06cc\u0645\u060c \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0645\u0636\u0627\u0631\u0628 \u0639\u062f\u062f \u0622\u062e\u0631 \u06a9\u0647 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0638\u0627\u0647\u0631 \u0646\u0634\u062f\u0647\u200c\u0627\u0646\u062f \u0631\u0627 \u0628\u0647 \u0627\u0646\u062a\u0647\u0627\u06cc \u0622\u0646 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062a\u062d\u0642\u06cc\u0642 \u06a9\u0631\u062f \u06a9\u0647 \u0631\u0648\u0634 \u0641\u0648\u0642 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>\u0647\u0627\u06cc \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u06f1\u06f0\u060c\u06f0\u06f0\u06f0 \u0647\u06cc\u0686\u0648\u0642\u062a \u0639\u062f\u062f\u06cc \u0628\u06cc\u0634\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u06f1\u06f0\u06f0\u06f0\u060c\u06f0\u06f0\u06f0\u060c\u06f0\u06f0\u06f0 \u062f\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u0642\u0631\u0627\u0631 \u0646\u0645\u06cc\u200c\u062f\u0647\u062f. \u067e\u0633 \u0631\u0648\u0634 \u0641\u0648\u0642 \u0642\u0627\u0628\u0644\u200c\u0642\u0628\u0648\u0644 \u0627\u0633\u062a.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><span class=\"ez-toc-section\" id=\"%D8%AF%D9%86%D8%A8%D8%A7%D9%84%D9%87_%D8%BA%D8%B1%DB%8C%D8%A8\"><\/span><span style=\"color:#ff6900\" class=\"tadv-color\"><a href=\"https:\/\/quera.org\/problemset\/141571\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u062f\u0646\u0628\u0627\u0644\u0647 \u063a\u0631\u06cc\u0628<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f \u06a9\u0647 \u0647\u0645\u0648\u0627\u0631\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>n^{2}+1 \\leq f_{n} \\leq n^{2}+n<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0628\u0627\u0644\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u0645\u062b\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span> \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u06a9\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>f_{p}=p^{2}+1<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u067e\u0633 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">f_{n}<\/span>\u200b \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0631\u0648\u0646\u062f \u0628\u0627\u0632\u06af\u0634\u062a \u0631\u0627 \u062a\u0627 \u0645\u0631\u062d\u0644\u0647\u200c\u0627\u06cc \u0628\u0647 \u0639\u0642\u0628 \u0628\u0631\u06af\u0631\u062f\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u06cc\u06a9 \u0639\u062f\u062f \u0627\u0648\u0644 \u0628\u0631\u0633\u06cc\u0645 \u0648 \u062c\u0648\u0627\u0628 \u0631\u0627 \u0627\u0632 \u0631\u0648\u06cc \u0622\u0646 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0628\u0647 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u0632 \u0647\u0631 \u0639\u062f\u062f \u0645\u062b\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0627\u06af\u0631 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b <span class=\"katex-eq\" data-katex-display=\"false\">log(n)<\/span> \u0639\u062f\u062f \u0628\u0647 \u0639\u0642\u0628 \u0628\u0631\u06af\u0631\u062f\u06cc\u0645\u060c \u062d\u062a\u0645\u0627\u064b \u06cc\u06a9 \u0639\u062f\u062f \u0627\u0648\u0644 \u0645\u06cc\u200c\u0628\u06cc\u0646\u06cc\u0645.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0627\u0648\u0644 \u0628\u0648\u062f\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>\u06cc \u06a9\u0647 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0622\u0646 \u0647\u0633\u062a\u06cc\u0645\u060c \u0628\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u0650 \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u06a9\u0627\u0641\u06cc \u0633\u0631\u06cc\u0639 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u0644\u0627\u0645! \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u06f3\u06f9\u0627\u0645\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u06a9\u0648\u0626\u0631\u0627 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062a\u0627\u06a9\u0646\u0648\u0646 \u0627\u0633\u062a \u0648 \u062d\u0644 \u0633\u0648\u0627\u0644\u0627\u062a \u0622\u0646 \u0631\u0648\u06cc \u0627\u0645\u062a\u06cc\u0627\u0632 \u06a9\u0648\u0626\u0631\u0627\u06cc\u06cc \u0634\u0645\u0627 \u062a\u0623\u062b\u06cc\u0631&#8230;<\/p>\n","protected":false},"author":22,"featured_media":34670,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[141,46,50],"tags":[],"class_list":["post-34724","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contests-and-events","category-developer","category-quera-developer"],"_links":{"self":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/34724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/comments?post=34724"}],"version-history":[{"count":41,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/34724\/revisions"}],"predecessor-version":[{"id":36202,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/posts\/34724\/revisions\/36202"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/media\/34670"}],"wp:attachment":[{"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/media?parent=34724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/categories?post=34724"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quera.org\/blog\/wp-json\/wp\/v2\/tags?post=34724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}