{"id":785,"date":"2026-09-16T09:00:00","date_gmt":"2026-09-16T09:00:00","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=785"},"modified":"2026-09-25T15:51:57","modified_gmt":"2026-09-25T15:51:57","slug":"zadachi-na-algoritmy","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/zadachi-na-algoritmy\/","title":{"rendered":"\u0417\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u0441 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u0440\u0430\u0437\u0431\u043e\u0440\u043e\u043c"},"content":{"rendered":"<p><strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b<\/strong> &#8212; \u044d\u0442\u043e \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u0433\u0434\u0435 \u043d\u0443\u0436\u043d\u043e \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0442\u0432\u0435\u0442, \u0430 \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u0441\u043f\u043e\u0441\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0438 \u043e\u0446\u0435\u043d\u0438\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0448\u0430\u0433\u043e\u0432 \u0438 \u043f\u0430\u043c\u044f\u0442\u0438 \u043e\u043d \u043f\u043e\u0442\u0440\u0435\u0431\u0443\u0435\u0442. \u0418\u043c\u0435\u043d\u043d\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u0430 \u043d\u0435 \u044f\u0437\u044b\u043a, \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0437\u0430 \u0441\u0435\u043a\u0443\u043d\u0434\u0443 \u043e\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043d\u0435 \u0434\u043e\u0436\u0434\u0430\u0442\u044c\u0441\u044f. \u041d\u0438\u0436\u0435 &#8212; \u0440\u0430\u0437\u0431\u043e\u0440 \u0442\u0438\u043f\u043e\u0432\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043f\u043e \u0442\u0435\u043c\u0430\u043c: \u043f\u043e\u0438\u0441\u043a, \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430, \u0441\u0442\u0440\u043e\u043a\u0438, \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u0433\u0440\u0430\u0444\u044b.<\/p>\n<div class=\"oj-toc\" style=\"background:#f6f6f6;border-radius:8px;padding:14px 20px;margin:20px 0\">\n<p><strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/strong><\/p>\n<ol>\n<li><a href=\"#s1\">\u041a\u0430\u043a \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442\u044c \u043a \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435<\/a><\/li>\n<li><a href=\"#s2\">\u041f\u043e\u0438\u0441\u043a: \u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u0432 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u043c\u0430\u0441\u0441\u0438\u0432\u0435<\/a><\/li>\n<li><a href=\"#s3\">\u0421\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430: \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430 \u0432\u0441\u0442\u0430\u0432\u043a\u0430\u043c\u0438<\/a><\/li>\n<li><a href=\"#s4\">\u0421\u0442\u0440\u043e\u043a\u0438: \u043f\u0430\u043b\u0438\u043d\u0434\u0440\u043e\u043c \u0438 \u0430\u043d\u0430\u0433\u0440\u0430\u043c\u043c\u0430<\/a><\/li>\n<li><a href=\"#s5\">\u0414\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435: \u0424\u0438\u0431\u043e\u043d\u0430\u0447\u0447\u0438 \u0438 \u0440\u0430\u0437\u043c\u0435\u043d \u043c\u043e\u043d\u0435\u0442<\/a><\/li>\n<li><a href=\"#s6\">\u0413\u0440\u0430\u0444\u044b: \u043e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 (BFS)<\/a><\/li>\n<li><a href=\"#s7\">\u0422\u0438\u043f\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430: \u043d\u0435\u0432\u0435\u0440\u043d\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0446\u0438\u043a\u043b\u0430 \u0432 \u0431\u0438\u043d\u0430\u0440\u043d\u043e\u043c \u043f\u043e\u0438\u0441\u043a\u0435<\/a><\/li>\n<li><a href=\"#s8\">\u0412\u044b\u0432\u043e\u0434\u044b<\/a><\/li>\n<li><a href=\"#s9\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/a><\/li>\n<li><a href=\"#s10\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<p>\u041a\u0430\u0436\u0434\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0438\u0434\u0435\u0442 \u043f\u043e \u043e\u0434\u043d\u043e\u0439 \u0441\u0445\u0435\u043c\u0435: \u0443\u0441\u043b\u043e\u0432\u0438\u0435, \u0438\u0434\u0435\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u0433\u043e\u0442\u043e\u0432\u044b\u0439 \u043a\u043e\u0434 \u0438 \u043e\u0446\u0435\u043d\u043a\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 O(). \u041a\u043e\u0434 \u043d\u0430 Python &#8212; \u043f\u043e\u043b\u043d\u044b\u0435 \u0444\u0440\u0430\u0433\u043c\u0435\u043d\u0442\u044b, \u0438\u0445 \u043c\u043e\u0436\u043d\u043e \u0441\u043a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0438 \u0437\u0430\u043f\u0443\u0441\u0442\u0438\u0442\u044c, \u0432\u044b\u0432\u043e\u0434 \u0443\u043a\u0430\u0437\u0430\u043d \u0432 \u043a\u043e\u043c\u043c\u0435\u043d\u0442\u0430\u0440\u0438\u0438 \u0440\u044f\u0434\u043e\u043c. \u0412 \u043a\u043e\u043d\u0446\u0435 \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c \u0442\u0438\u043f\u0438\u0447\u043d\u0443\u044e \u043e\u0448\u0438\u0431\u043a\u0443, \u0438\u0437-\u0437\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043d\u0430 \u0432\u0438\u0434 \u043a\u043e\u0434 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u043d\u0435\u0432\u0435\u0440\u043d\u044b\u0439 \u043e\u0442\u0432\u0435\u0442.<\/p>\n<h2 id=\"s1\">\u041a\u0430\u043a \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442\u044c \u043a \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435<\/h2>\n<p>\u041f\u0435\u0440\u0435\u0434 \u0442\u0435\u043c \u043a\u0430\u043a \u043f\u0438\u0441\u0430\u0442\u044c \u043a\u043e\u0434, \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u043f\u0440\u043e\u0439\u0442\u0438 \u0447\u0435\u0442\u044b\u0440\u0435 \u0448\u0430\u0433\u0430: \u043f\u043e\u043d\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u0438\u0435, \u043f\u0440\u0438\u0434\u0443\u043c\u0430\u0442\u044c \u0438\u0434\u0435\u044e (\u043a\u0430\u043a\u0430\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u043a\u0430\u043a\u043e\u0439 \u043f\u0440\u0438\u0435\u043c \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0442), \u043f\u0440\u0438\u043a\u0438\u043d\u0443\u0442\u044c \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u0442\u043e\u043c \u043a\u043e\u0434\u0438\u0440\u043e\u0432\u0430\u0442\u044c. \u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442 \u0447\u0435\u0440\u0435\u0437 O-\u043d\u043e\u0442\u0430\u0446\u0438\u044e: \u043e\u043d\u0430 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u0440\u0430\u0441\u0442\u0435\u0442 \u0447\u0438\u0441\u043b\u043e \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043f\u0440\u0438 \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u0438 \u0440\u0430\u0437\u043c\u0435\u0440\u0430 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 n.<\/p>\n<p>\u041e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u044b \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438: O(1) &#8212; \u0447\u0438\u0441\u043b\u043e \u0448\u0430\u0433\u043e\u0432 \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 n; O(log n) &#8212; \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0442\u0431\u0440\u0430\u0441\u044b\u0432\u0430\u0435\u043c \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0443 \u0434\u0430\u043d\u043d\u044b\u0445 (\u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a); O(n) &#8212; \u043e\u0434\u0438\u043d \u043f\u0440\u043e\u0445\u043e\u0434 \u043f\u043e \u0434\u0430\u043d\u043d\u044b\u043c; O(n log n) &#8212; \u0445\u043e\u0440\u043e\u0448\u0438\u0435 \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0438; O(n^2) &#8212; \u0432\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440 \u043f\u0430\u0440; O(2^n) &#8212; \u043f\u043e\u043b\u043d\u044b\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u043b\u0438\u0448\u044c \u043d\u0430 \u043c\u0430\u043b\u044b\u0445 n. \u041c\u0435\u043d\u044c\u0448\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0432\u0430\u0436\u043d\u0430 \u043d\u0430 \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445: \u043f\u0440\u0438 n = 1 000 000 \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 O(n) \u0438 O(n^2) &#8212; \u044d\u0442\u043e \u0441\u0435\u043a\u0443\u043d\u0434\u0430 \u043f\u0440\u043e\u0442\u0438\u0432 \u043d\u0435\u0434\u0435\u043b\u0438.<\/p>\n<h2 id=\"s2\">\u041f\u043e\u0438\u0441\u043a: \u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u0432 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u043c\u0430\u0441\u0441\u0438\u0432\u0435<\/h2>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435: \u0432 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u043f\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044e \u043c\u0430\u0441\u0441\u0438\u0432\u0435 \u043d\u0430\u0439\u0442\u0438 \u0438\u043d\u0434\u0435\u043a\u0441 \u0447\u0438\u0441\u043b\u0430. \u0412\u0435\u0440\u043d\u0443\u0442\u044c -1, \u0435\u0441\u043b\u0438 \u0447\u0438\u0441\u043b\u0430 \u043d\u0435\u0442.<\/p>\n<p>\u0418\u0434\u0435\u044f: \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0446\u0435\u043b\u044c \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u043c. \u0415\u0441\u043b\u0438 \u0446\u0435\u043b\u044c \u043c\u0435\u043d\u044c\u0448\u0435 &#8212; \u0438\u0449\u0435\u043c \u0432 \u043b\u0435\u0432\u043e\u0439 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435, \u0435\u0441\u043b\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 &#8212; \u0432 \u043f\u0440\u0430\u0432\u043e\u0439. \u041a\u0430\u0436\u0434\u044b\u0439 \u0448\u0430\u0433 \u0432\u0434\u0432\u043e\u0435 \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u0435\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u0430\u0441\u0441\u0438\u0432 \u043e\u0431\u044f\u0437\u0430\u043d \u0431\u044b\u0442\u044c \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">binary_search<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">lo<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">\/\/<\/span> <span style=\"color: #D19A66\">2<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">mid<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span>     <span style=\"color: #7F848E\"># \u0446\u0435\u043b\u044c \u043f\u0440\u0430\u0432\u0435\u0435 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b<\/span>\n        <span style=\"color: #C678DD\">else<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>     <span style=\"color: #7F848E\"># \u0446\u0435\u043b\u044c \u043b\u0435\u0432\u0435\u0435 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E06C75\">nums<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">9<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">11<\/span><span style=\"color: #ABB2BF\">]<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">binary_search<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">nums<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">))<\/span>   <span style=\"color: #7F848E\"># 3<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">binary_search<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">nums<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">8<\/span><span style=\"color: #ABB2BF\">))<\/span>   <span style=\"color: #7F848E\"># -1<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">3\n-1\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(log n): \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430 \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u0435\u0442\u0441\u044f \u0432\u0434\u0432\u043e\u0435 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0438. \u0414\u043b\u044f \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440 \u043f\u043e \u043c\u0430\u0441\u0441\u0438\u0432\u0443 \u0434\u0430\u043b \u0431\u044b O(n). \u0415\u0441\u043b\u0438 \u043c\u0430\u0441\u0441\u0438\u0432 \u043d\u0435 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d, \u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u043d\u0435\u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c &#8212; \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u0438\u0448\u043b\u043e\u0441\u044c \u0431\u044b \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/p>\n<h2 id=\"s3\">\u0421\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430: \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430 \u0432\u0441\u0442\u0430\u0432\u043a\u0430\u043c\u0438<\/h2>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435: \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043c\u0430\u0441\u0441\u0438\u0432 \u043f\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044e \u0441\u0432\u043e\u0438\u043c\u0438 \u0440\u0443\u043a\u0430\u043c\u0438, \u0431\u0435\u0437 \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u043e\u0439 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">sorted<\/code>.<\/p>\n<p>\u0418\u0434\u0435\u044f: \u0438\u0434\u0435\u043c \u0441\u043b\u0435\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043e \u0438 \u043a\u0430\u0436\u0434\u044b\u0439 \u043d\u043e\u0432\u044b\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u0432\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0430 \u043d\u0443\u0436\u043d\u043e\u0435 \u043c\u0435\u0441\u0442\u043e \u0441\u0440\u0435\u0434\u0438 \u0443\u0436\u0435 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0441\u043b\u0435\u0432\u0430. \u041f\u043e\u043b\u0435\u0437\u043d\u043e \u043f\u0440\u043e\u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c \u043f\u0440\u043e\u0445\u043e\u0434\u044b \u043d\u0430 \u043c\u0430\u0441\u0441\u0438\u0432\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[5, 2, 4, 1, 3]<\/code> \u0434\u043e \u043a\u043e\u0434\u0430:<\/p>\n<ul>\n<li>\u0431\u0435\u0440\u0435\u043c 2, \u0432\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043f\u0435\u0440\u0435\u0434 5: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[2, 5, 4, 1, 3]<\/code><\/li>\n<li>\u0431\u0435\u0440\u0435\u043c 4, \u043c\u0435\u0436\u0434\u0443 2 \u0438 5: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[2, 4, 5, 1, 3]<\/code><\/li>\n<li>\u0431\u0435\u0440\u0435\u043c 1, \u0432 \u043d\u0430\u0447\u0430\u043b\u043e: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[1, 2, 4, 5, 3]<\/code><\/li>\n<li>\u0431\u0435\u0440\u0435\u043c 3, \u043c\u0435\u0436\u0434\u0443 2 \u0438 4: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[1, 2, 3, 4, 5]<\/code><\/li>\n<\/ul>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">insertion_sort<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">i<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">)):<\/span>\n        <span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">i<\/span><span style=\"color: #ABB2BF\">]<\/span>\n        <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">i<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n        <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">&gt;=<\/span> <span style=\"color: #D19A66\">0<\/span> <span style=\"color: #56B6C2\">and<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">&gt;<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">:<\/span>  <span style=\"color: #7F848E\"># \u0441\u0434\u0432\u0438\u0433\u0430\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0438\u0435 \u0432\u043f\u0440\u0430\u0432\u043e<\/span>\n            <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span><span style=\"color: #ABB2BF\">]<\/span>\n            <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #D19A66\">1<\/span>\n        <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">key<\/span>                <span style=\"color: #7F848E\"># \u0441\u0442\u0430\u0432\u0438\u043c key \u043d\u0430 \u043e\u0441\u0432\u043e\u0431\u043e\u0434\u0438\u0432\u0448\u0435\u0435\u0441\u044f \u043c\u0435\u0441\u0442\u043e<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">arr<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">insertion_sort<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">]))<\/span>  <span style=\"color: #7F848E\"># [1, 2, 3, 4, 5]<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">[1, 2, 3, 4, 5]\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(n^2) \u0432 \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0438 \u0445\u0443\u0434\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 (\u0434\u043b\u044f \u043f\u043e\u0447\u0442\u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0441\u0434\u0432\u0438\u0433\u043e\u0432 \u043c\u043d\u043e\u0433\u043e), \u043d\u043e O(n) \u043d\u0430 \u0443\u0436\u0435 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u043c\u0430\u0441\u0441\u0438\u0432\u0435: \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0439 \u0446\u0438\u043a\u043b \u0441\u0440\u0430\u0437\u0443 \u0437\u0430\u0432\u0435\u0440\u0448\u0430\u0435\u0442\u0441\u044f. \u0421\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430 \u0432\u0441\u0442\u0430\u0432\u043a\u0430\u043c\u0438 &#8212; \u0443\u0447\u0435\u0431\u043d\u044b\u0439 \u043f\u0440\u0438\u0435\u043c; \u0432 \u0440\u0435\u0430\u043b\u044c\u043d\u043e\u043c \u043a\u043e\u0434\u0435 \u0431\u0435\u0440\u0443\u0442 \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u0443\u044e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">sorted<\/code>, \u0443 \u043d\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c O(n log n).<\/p>\n<h2 id=\"s4\">\u0421\u0442\u0440\u043e\u043a\u0438: \u043f\u0430\u043b\u0438\u043d\u0434\u0440\u043e\u043c \u0438 \u0430\u043d\u0430\u0433\u0440\u0430\u043c\u043c\u0430<\/h2>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435 1: \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u043b\u0438 \u0441\u0442\u0440\u043e\u043a\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e \u0441\u043b\u0435\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043e \u0438 \u0441\u043f\u0440\u0430\u0432\u0430 \u043d\u0430\u043b\u0435\u0432\u043e (\u043f\u0430\u043b\u0438\u043d\u0434\u0440\u043e\u043c).<\/p>\n<p>\u0418\u0434\u0435\u044f: \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u044c \u0441\u0442\u0440\u043e\u043a\u0443 \u0441 \u0435\u0435 \u0440\u0430\u0437\u0432\u043e\u0440\u043e\u0442\u043e\u043c. \u0412 Python \u0440\u0430\u0437\u0432\u043e\u0440\u043e\u0442 \u0434\u0430\u0435\u0442 \u0441\u0440\u0435\u0437 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">s[::-1]<\/code>.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">is_palindrome<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">s<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">s<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">lower<\/span><span style=\"color: #ABB2BF\">()<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">s<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">[::<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">]<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">is_palindrome<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"radar\"<\/span><span style=\"color: #ABB2BF\">))<\/span>   <span style=\"color: #7F848E\"># True<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">is_palindrome<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"python\"<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># False<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">True\nFalse\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(n): \u0440\u0430\u0437\u0432\u043e\u0440\u043e\u0442 \u0438 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u043f\u043e \u0432\u0441\u0435\u043c \u0441\u0438\u043c\u0432\u043e\u043b\u0430\u043c \u043e\u0434\u0438\u043d \u0440\u0430\u0437.<\/p>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435 2: \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438 \u0434\u0432\u0435 \u0441\u0442\u0440\u043e\u043a\u0438 \u0430\u043d\u0430\u0433\u0440\u0430\u043c\u043c\u0430\u043c\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u0441\u043e\u0441\u0442\u043e\u044f\u0442 \u0438\u0437 \u043e\u0434\u043d\u0438\u0445 \u0438 \u0442\u0435\u0445 \u0436\u0435 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u0432 \u0432 \u0440\u0430\u0437\u043d\u043e\u043c \u043f\u043e\u0440\u044f\u0434\u043a\u0435.<\/p>\n<p>\u0418\u0434\u0435\u044f: \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f \u043a\u0430\u0436\u0434\u044b\u0439 \u0441\u0438\u043c\u0432\u043e\u043b, \u0438 \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u044c \u044d\u0442\u0438 \u0441\u0447\u0435\u0442\u0447\u0438\u043a\u0438. \u0413\u043e\u0442\u043e\u0432\u044b\u0439 \u0441\u0447\u0435\u0442\u0447\u0438\u043a \u0434\u0430\u0435\u0442 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">collections.Counter<\/code>.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">collections<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">Counter<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">is_anagram<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">b<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">Counter<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">Counter<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">b<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">is_anagram<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"listen\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"silent\"<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># True<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">is_anagram<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"hello\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"world\"<\/span><span style=\"color: #ABB2BF\">))<\/span>    <span style=\"color: #7F848E\"># False<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">True\nFalse\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(n): \u043f\u043e\u0434\u0441\u0447\u0435\u0442 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0439. \u0421\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430 \u043e\u0431\u0435\u0438\u0445 \u0441\u0442\u0440\u043e\u043a \u0434\u0430\u043b\u0430 \u0431\u044b \u0442\u043e\u0442 \u0436\u0435 \u043e\u0442\u0432\u0435\u0442, \u043d\u043e \u0437\u0430 O(n log n) &#8212; \u0441\u0447\u0435\u0442\u0447\u0438\u043a \u044d\u043a\u043e\u043d\u043e\u043c\u043d\u0435\u0435.<\/p>\n<h2 id=\"s5\">\u0414\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435: \u0424\u0438\u0431\u043e\u043d\u0430\u0447\u0447\u0438 \u0438 \u0440\u0430\u0437\u043c\u0435\u043d \u043c\u043e\u043d\u0435\u0442<\/h2>\n<p>\u0414\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 (\u0414\u041f) &#8212; \u044d\u0442\u043e \u043a\u043e\u0433\u0434\u0430 \u0437\u0430\u0434\u0430\u0447\u0443 \u0440\u0430\u0437\u0431\u0438\u0432\u0430\u044e\u0442 \u043d\u0430 \u043f\u043e\u0434\u0437\u0430\u0434\u0430\u0447\u0438, \u0430 \u043e\u0442\u0432\u0435\u0442\u044b \u043d\u0430 \u043d\u0438\u0445 \u0441\u043e\u0445\u0440\u0430\u043d\u044f\u044e\u0442, \u0447\u0442\u043e\u0431\u044b \u043d\u0435 \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u0434\u0432\u0430\u0436\u0434\u044b.<\/p>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435 1: \u043d\u0430\u0439\u0442\u0438 n-\u0435 \u0447\u0438\u0441\u043b\u043e \u0424\u0438\u0431\u043e\u043d\u0430\u0447\u0447\u0438 (\u043a\u0430\u0436\u0434\u043e\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 &#8212; \u0441\u0443\u043c\u043c\u0430 \u0434\u0432\u0443\u0445 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0445: 0, 1, 1, 2, 3, 5, 8&#8230;).<\/p>\n<p>\u0418\u0434\u0435\u044f: \u043d\u0430\u0438\u0432\u043d\u0430\u044f \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">fib(n) = fib(n-1) + fib(n-2)<\/code> \u043f\u0435\u0440\u0435\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442 \u043e\u0434\u043d\u0438 \u0438 \u0442\u0435 \u0436\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0438 \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0437\u0430 O(2^n). \u0414\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0438\u0434\u0442\u0438 \u0441\u043d\u0438\u0437\u0443 \u0432\u0432\u0435\u0440\u0445, \u0445\u0440\u0430\u043d\u044f \u0434\u0432\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0445 \u0447\u0438\u0441\u043b\u0430 &#8212; \u0442\u043e\u0433\u0434\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c O(n).<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">fib<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">b<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">_<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">):<\/span>\n        <span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">b<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">b<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">a<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b<\/span>   <span style=\"color: #7F848E\"># \u0441\u0434\u0432\u0438\u0433\u0430\u0435\u043c \u043f\u0430\u0440\u0443 \u043d\u0430 \u0448\u0430\u0433 \u0432\u043f\u0435\u0440\u0435\u0434<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">a<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">fib<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">10<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># 55<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">55\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(n) \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u0438 O(1) \u043f\u043e \u043f\u0430\u043c\u044f\u0442\u0438: \u0445\u0440\u0430\u043d\u0438\u043c \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u0432\u0430 \u0447\u0438\u0441\u043b\u0430.<\/p>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435 2: \u043d\u0430\u0431\u0440\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u043d\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u0443 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u043c\u043e\u043d\u0435\u0442 \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u043e\u043c\u0438\u043d\u0430\u043b\u043e\u0432 (\u043d\u043e\u043c\u0438\u043d\u0430\u043b\u044b \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0442\u044c).<\/p>\n<p>\u0418\u0434\u0435\u044f: \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0443\u043c\u043c\u044b \u043e\u0442 1 \u0434\u043e \u043d\u0443\u0436\u043d\u043e\u0439 \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u043c\u043e\u043d\u0435\u0442, \u043e\u043f\u0438\u0440\u0430\u044f\u0441\u044c \u043d\u0430 \u0443\u0436\u0435 \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u044b\u0435 \u043c\u0435\u043d\u044c\u0448\u0438\u0435 \u0441\u0443\u043c\u043c\u044b. \u042d\u0442\u043e \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0414\u041f.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">min_coins<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">coins<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">amount<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">INF<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">amount<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #E06C75\">dp<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">INF<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">amount<\/span>        <span style=\"color: #7F848E\"># dp[s] - \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u043c\u043e\u043d\u0435\u0442 \u043d\u0430 \u0441\u0443\u043c\u043c\u0443 s<\/span>\n    <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">s<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">amount<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">):<\/span>\n        <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">c<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">coins<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">c<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">:<\/span>\n                <span style=\"color: #E06C75\">dp<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">min<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">dp<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #E06C75\">dp<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">s<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">c<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">dp<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">amount<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">dp<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">amount<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">!=<\/span> <span style=\"color: #E06C75\">INF<\/span> <span style=\"color: #C678DD\">else<\/span> <span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">min_coins<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #D19A66\">6<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># 2  (\u044d\u0442\u043e 3 + 3)<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">2\n<\/code><\/pre>\n<p>\u0414\u043b\u044f \u0441\u0443\u043c\u043c\u044b 6 \u0438 \u043d\u043e\u043c\u0438\u043d\u0430\u043b\u043e\u0432 1, 3, 4 \u043e\u0442\u0432\u0435\u0442 &#8212; \u0434\u0432\u0435 \u043c\u043e\u043d\u0435\u0442\u044b (3 + 3), \u0430 \u0436\u0430\u0434\u043d\u044b\u0439 \u0432\u044b\u0431\u043e\u0440 \u0441\u0430\u043c\u043e\u0439 \u043a\u0440\u0443\u043f\u043d\u043e\u0439 \u043c\u043e\u043d\u0435\u0442\u044b \u0434\u0430\u043b \u0431\u044b 4 + 1 + 1 = \u0442\u0440\u0438 \u043c\u043e\u043d\u0435\u0442\u044b. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0437\u0434\u0435\u0441\u044c \u043d\u0443\u0436\u0435\u043d \u0438\u043c\u0435\u043d\u043d\u043e \u043f\u0435\u0440\u0435\u0431\u043e\u0440 \u0447\u0435\u0440\u0435\u0437 \u0414\u041f. \u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(amount * k), \u0433\u0434\u0435 k &#8212; \u0447\u0438\u0441\u043b\u043e \u043d\u043e\u043c\u0438\u043d\u0430\u043b\u043e\u0432.<\/p>\n<h2 id=\"s6\">\u0413\u0440\u0430\u0444\u044b: \u043e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 (BFS)<\/h2>\n<p>\u0423\u0441\u043b\u043e\u0432\u0438\u0435: \u043e\u0431\u043e\u0439\u0442\u0438 \u0432\u0441\u0435 \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u0433\u0440\u0430\u0444\u0430, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439, \u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c \u0431\u043b\u0438\u0437\u043e\u0441\u0442\u0438 \u043a \u0441\u0442\u0430\u0440\u0442\u0443.<\/p>\n<p>\u0418\u0434\u0435\u044f: \u043e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 (breadth-first search, BFS) \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043e\u0447\u0435\u0440\u0435\u0434\u044c. \u0414\u043e\u0441\u0442\u0430\u0435\u043c \u0432\u0435\u0440\u0448\u0438\u043d\u0443, \u043f\u043e\u043c\u0435\u0447\u0430\u0435\u043c \u0435\u0435 \u0441\u043e\u0441\u0435\u0434\u0435\u0439 \u043a\u0430\u043a \u0443\u0432\u0438\u0434\u0435\u043d\u043d\u044b\u0445 \u0438 \u043a\u043b\u0430\u0434\u0435\u043c \u0438\u0445 \u0432 \u043a\u043e\u043d\u0435\u0446 \u043e\u0447\u0435\u0440\u0435\u0434\u0438. \u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">seen<\/code> \u0437\u0430\u0449\u0438\u0449\u0430\u0435\u0442 \u043e\u0442 \u043f\u043e\u0432\u0442\u043e\u0440\u043e\u0432 \u0438 \u0437\u0430\u0446\u0438\u043a\u043b\u0438\u0432\u0430\u043d\u0438\u044f.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">collections<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">deque<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">bfs<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">graph<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">start<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">order<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[]<\/span>\n    <span style=\"color: #E06C75\">seen<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">{<\/span><span style=\"color: #E06C75\">start<\/span><span style=\"color: #ABB2BF\">}<\/span>\n    <span style=\"color: #E06C75\">queue<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">deque<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #E06C75\">start<\/span><span style=\"color: #ABB2BF\">])<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">queue<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">node<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">queue<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">popleft<\/span><span style=\"color: #ABB2BF\">()<\/span>        <span style=\"color: #7F848E\"># \u0431\u0435\u0440\u0435\u043c \u0438\u0437 \u043d\u0430\u0447\u0430\u043b\u0430 \u043e\u0447\u0435\u0440\u0435\u0434\u0438<\/span>\n        <span style=\"color: #E06C75\">order<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">append<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">)<\/span>\n        <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">nb<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">graph<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">]:<\/span>\n            <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">nb<\/span> <span style=\"color: #56B6C2\">not<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">seen<\/span><span style=\"color: #ABB2BF\">:<\/span>\n                <span style=\"color: #E06C75\">seen<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">add<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">nb<\/span><span style=\"color: #ABB2BF\">)<\/span>\n                <span style=\"color: #E06C75\">queue<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">append<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">nb<\/span><span style=\"color: #ABB2BF\">)<\/span>      <span style=\"color: #7F848E\"># \u0441\u043e\u0441\u0435\u0434\u0438 - \u0432 \u043a\u043e\u043d\u0435\u0446 \u043e\u0447\u0435\u0440\u0435\u0434\u0438<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">order<\/span>\n\n<span style=\"color: #E06C75\">graph<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">{<\/span>\n    <span style=\"color: #98C379\">\"A\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"B\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"C\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n    <span style=\"color: #98C379\">\"B\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"A\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"D\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"E\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n    <span style=\"color: #98C379\">\"C\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"A\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"F\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n    <span style=\"color: #98C379\">\"D\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"B\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n    <span style=\"color: #98C379\">\"E\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"B\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"F\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n    <span style=\"color: #98C379\">\"F\"<\/span><span style=\"color: #ABB2BF\">:<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #98C379\">\"C\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"E\"<\/span><span style=\"color: #ABB2BF\">],<\/span>\n<span style=\"color: #ABB2BF\">}<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">bfs<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">graph<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"A\"<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># ['A', 'B', 'C', 'D', 'E', 'F']<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">[&#x27;A&#x27;, &#x27;B&#x27;, &#x27;C&#x27;, &#x27;D&#x27;, &#x27;E&#x27;, &#x27;F&#x27;]\n<\/code><\/pre>\n<p>\u0421\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; O(V + E), \u0433\u0434\u0435 V &#8212; \u0447\u0438\u0441\u043b\u043e \u0432\u0435\u0440\u0448\u0438\u043d, E &#8212; \u0447\u0438\u0441\u043b\u043e \u0440\u0435\u0431\u0435\u0440: \u043a\u0430\u0436\u0434\u0443\u044e \u0432\u0435\u0440\u0448\u0438\u043d\u0443 \u0438 \u043a\u0430\u0436\u0434\u043e\u0435 \u0440\u0435\u0431\u0440\u043e \u043e\u0431\u0440\u0430\u0431\u0430\u0442\u044b\u0432\u0430\u0435\u043c \u043e\u0434\u0438\u043d \u0440\u0430\u0437. BFS \u043d\u0430\u0445\u043e\u0434\u0438\u0442 \u043a\u0440\u0430\u0442\u0447\u0430\u0439\u0448\u0438\u0439 \u043f\u0443\u0442\u044c \u043f\u043e \u0447\u0438\u0441\u043b\u0443 \u0440\u0435\u0431\u0435\u0440 \u0432 \u043d\u0435\u0432\u0437\u0432\u0435\u0448\u0435\u043d\u043d\u043e\u043c \u0433\u0440\u0430\u0444\u0435; \u0434\u043b\u044f \u0432\u0437\u0432\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0433\u0440\u0430\u0444\u043e\u0432 \u0431\u0435\u0440\u0443\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0414\u0435\u0439\u043a\u0441\u0442\u0440\u044b.<\/p>\n<h2 id=\"s7\">\u0422\u0438\u043f\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430: \u043d\u0435\u0432\u0435\u0440\u043d\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0446\u0438\u043a\u043b\u0430 \u0432 \u0431\u0438\u043d\u0430\u0440\u043d\u043e\u043c \u043f\u043e\u0438\u0441\u043a\u0435<\/h2>\n<p>\u0427\u0430\u0441\u0442\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430 \u0432 \u0431\u0438\u043d\u0430\u0440\u043d\u043e\u043c \u043f\u043e\u0438\u0441\u043a\u0435 &#8212; \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">while lo &lt; hi<\/code> \u0432\u043c\u0435\u0441\u0442\u043e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">while lo &lt;= hi<\/code>. \u0422\u043e\u0433\u0434\u0430 \u043f\u0440\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0435\u043d\u0438\u0438 \u0433\u0440\u0430\u043d\u0438\u0446 (<code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">lo == hi<\/code>) \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u043e\u0441\u0442\u0430\u0432\u0448\u0438\u0439\u0441\u044f \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043d\u0435 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u0442\u0441\u044f, \u0438 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043e\u0431\u044a\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c.<\/p>\n<p>\u041d\u0435\u0432\u0435\u0440\u043d\u044b\u0439 \u043a\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">binary_search_bad<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">lo<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">:<\/span>               <span style=\"color: #7F848E\"># \u043e\u0448\u0438\u0431\u043a\u0430: \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0439 lo == hi<\/span>\n        <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">\/\/<\/span> <span style=\"color: #D19A66\">2<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">mid<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span>\n        <span style=\"color: #C678DD\">else<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">binary_search_bad<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># -1, \u0445\u043e\u0442\u044f 5 \u0435\u0441\u0442\u044c \u0432 \u043c\u0430\u0441\u0441\u0438\u0432\u0435<\/span><\/code><\/pre>\n<p>\u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">-1\n<\/code><\/pre>\n<p>\u0420\u0430\u0437\u0431\u043e\u0440: \u0434\u043b\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">[1, 3, 5]<\/code> \u0438 \u0446\u0435\u043b\u0438 5 \u043f\u043e\u0441\u043b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0448\u0430\u0433\u0430 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">lo<\/code> \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0440\u0430\u0432\u0435\u043d 2 \u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">hi<\/code> \u0442\u043e\u0436\u0435 \u0440\u0430\u0432\u0435\u043d 2. \u0423\u0441\u043b\u043e\u0432\u0438\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">2 &lt; 2<\/code> \u043b\u043e\u0436\u043d\u043e, \u0446\u0438\u043a\u043b \u043f\u0440\u0435\u0440\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0438 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u0441 \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c 2 (\u043a\u0430\u043a \u0440\u0430\u0437 \u0447\u0438\u0441\u043b\u043e 5) \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u043e\u0432\u0435\u0440\u0435\u043d\u043d\u044b\u043c.<\/p>\n<p>\u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 &#8212; \u043d\u0435\u0441\u0442\u0440\u043e\u0433\u043e\u0435 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">&lt;=<\/code>, \u043e\u043d\u043e \u0438 \u0441\u0442\u043e\u0438\u0442 \u0432 \u0440\u0430\u0431\u043e\u0447\u0435\u0439 \u0432\u0435\u0440\u0441\u0438\u0438 \u0438\u0437 \u0440\u0430\u0437\u0434\u0435\u043b\u0430 \u043f\u0440\u043e \u043f\u043e\u0438\u0441\u043a:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">binary_search<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">lo<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">:<\/span>             <span style=\"color: #7F848E\"># \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c \u0438 \u0441\u043b\u0443\u0447\u0430\u0439 lo == hi<\/span>\n        <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">hi<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">\/\/<\/span> <span style=\"color: #D19A66\">2<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">mid<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">arr<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">mid<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">target<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">lo<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span>\n        <span style=\"color: #C678DD\">else<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">hi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">mid<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">1<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">binary_search<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">))<\/span>  <span style=\"color: #7F848E\"># 2<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">2\n<\/code><\/pre>\n<h2 id=\"s8\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u0417\u0430\u0434\u0430\u0447\u0430 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0441\u0445\u0435\u043c\u0435: \u0443\u0441\u043b\u043e\u0432\u0438\u0435, \u0438\u0434\u0435\u044f (\u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u043f\u0440\u0438\u0435\u043c), \u043e\u0446\u0435\u043d\u043a\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 O() \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u0442\u043e\u043c \u043a\u043e\u0434.<\/li>\n<li>\u0411\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u0434\u0430\u0435\u0442 O(log n), \u043d\u043e \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0441\u0438\u0432\u0430; \u043e\u0431\u044b\u0447\u043d\u044b\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440 \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0432\u0441\u0435\u0433\u0434\u0430, \u043d\u043e \u0437\u0430 O(n).<\/li>\n<li>\u0421\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430 \u0432\u0441\u0442\u0430\u0432\u043a\u0430\u043c\u0438 &#8212; \u0443\u0447\u0435\u0431\u043d\u044b\u0439 \u043f\u0440\u0438\u0435\u043c \u043d\u0430 O(n^2); \u0432 \u0440\u0435\u0430\u043b\u044c\u043d\u043e\u043c \u043a\u043e\u0434\u0435 \u0431\u0435\u0440\u0443\u0442 \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u0443\u044e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">sorted<\/code> \u0441 O(n log n).<\/li>\n<li>\u0414\u043b\u044f \u0441\u0442\u0440\u043e\u043a \u043f\u043e\u0434\u0441\u0447\u0435\u0442 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u0432 \u0447\u0435\u0440\u0435\u0437 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">Counter<\/code> \u0440\u0435\u0448\u0430\u0435\u0442 \u0437\u0430\u0434\u0430\u0447\u0443 \u0430\u043d\u0430\u0433\u0440\u0430\u043c\u043c \u0437\u0430 O(n) &#8212; \u044d\u043a\u043e\u043d\u043e\u043c\u043d\u0435\u0435 \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0438.<\/li>\n<li>\u0414\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0443\u0431\u0438\u0440\u0430\u0435\u0442 \u043f\u043e\u0432\u0442\u043e\u0440\u043d\u044b\u0439 \u0441\u0447\u0435\u0442: \u043d\u0430\u0438\u0432\u043d\u044b\u0439 \u0424\u0438\u0431\u043e\u043d\u0430\u0447\u0447\u0438 &#8212; O(2^n), \u0438\u0442\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0439 &#8212; O(n); \u0436\u0430\u0434\u043d\u044b\u0439 \u0432\u044b\u0431\u043e\u0440 \u0432 \u0440\u0430\u0437\u043c\u0435\u043d\u0435 \u043c\u043e\u043d\u0435\u0442 \u043d\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u0435\u043d, \u0414\u041f \u043d\u0430\u0434\u0435\u0436\u043d\u0435\u0435.<\/li>\n<li>\u041e\u0431\u0445\u043e\u0434 \u0433\u0440\u0430\u0444\u0430 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 (BFS) \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0437\u0430 O(V + E) \u0438 \u043d\u0430\u0445\u043e\u0434\u0438\u0442 \u043a\u0440\u0430\u0442\u0447\u0430\u0439\u0448\u0438\u0439 \u043f\u0443\u0442\u044c \u043f\u043e \u0447\u0438\u0441\u043b\u0443 \u0440\u0435\u0431\u0435\u0440 \u0432 \u043d\u0435\u0432\u0437\u0432\u0435\u0448\u0435\u043d\u043d\u043e\u043c \u0433\u0440\u0430\u0444\u0435.<\/li>\n<\/ul>\n<h2 id=\"s9\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/h2>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p style=\"margin:0 0 8px\"><strong>\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0442\u0435\u043c\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/strong><\/p>\n<p>\u0423\u043c\u0435\u043d\u0438\u0435 \u043f\u043e\u0434\u043e\u0431\u0440\u0430\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438 \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u0435\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c &#8212; \u043e\u0441\u043d\u043e\u0432\u0430 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u043e\u0431\u0435\u0441\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0439 \u0438 \u043f\u043e\u0432\u0441\u0435\u0434\u043d\u0435\u0432\u043d\u043e\u0439 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0438: \u043e\u0442 \u043f\u043e\u0438\u0441\u043a\u0430 \u043f\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u043c \u0434\u0430\u043d\u043d\u044b\u043c \u0438 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438 \u0442\u0435\u043a\u0441\u0442\u0430 \u0434\u043e \u043c\u0430\u0440\u0448\u0440\u0443\u0442\u043e\u0432 \u0432 \u043a\u0430\u0440\u0442\u0430\u0445 \u0438 \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0430\u0446\u0438\u0439. \u0420\u0430\u0437\u043e\u0431\u0440\u0430\u0442\u044c \u044d\u0442\u0438 \u043f\u0440\u0438\u0435\u043c\u044b \u0441\u0438\u0441\u0442\u0435\u043c\u043d\u043e, \u043e\u0442 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 \u0434\u0430\u043d\u043d\u044b\u0445 \u0434\u043e \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u0432 \u043d\u0430 \u0433\u0440\u0430\u0444\u0430\u0445, \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0441\u0432\u044f\u0437\u044c \u043e\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0443\u044e\u0449\u0438\u0445 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a\u043e\u0432 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u043a\u0443\u0440\u0441 <a href=\"https:\/\/otus.ru\/lessons\/algorithm\/?int_article=zadachi-na-algoritmy&amp;int_place=article&amp;int_variant=v1\">\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b \u0434\u0430\u043d\u043d\u044b\u0445<\/a>.<\/p>\n<\/div>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p style=\"margin:0 0 8px\"><strong>\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0442\u0435\u043c\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/strong><\/p>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u043a\u0430\u043a \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u044e\u0442 \u0442\u0430\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u0436\u0438\u0432\u0443\u044e, \u0438 \u0437\u0430\u0434\u0430\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u044f\u043c \u043c\u043e\u0436\u043d\u043e \u043d\u0430 <a href=\"https:\/\/otus.ru\/events\/?int_article=zadachi-na-algoritmy&amp;int_place=article&amp;int_variant=v1\">\u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0432\u0435\u0431\u0438\u043d\u0430\u0440\u0430\u0445 Otus<\/a> &#8212; \u043e\u043d\u0438 \u0431\u0435\u0441\u043f\u043b\u0430\u0442\u043d\u044b\u0435 \u0438 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u043d\u043e.<\/p>\n<\/div>\n<p>\u0421\u043c\u0435\u0436\u043d\u044b\u0435 \u0442\u0435\u043c\u044b: <a href=\"https:\/\/otus.ru\/journal\/vidy-i-harakteristiki-algoritmov\/\">\u0412\u0438\u0434\u044b \u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u0432<\/a>, <a href=\"https:\/\/otus.ru\/journal\/massivy-v-programmirovanii-opisanie-i-napolnenie-dannymi\/\">\u041c\u0430\u0441\u0441\u0438\u0432\u044b \u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438<\/a>.<\/p>\n<h2 id=\"s10\">FAQ<\/h2>\n<p><strong>\u0421 \u043a\u0430\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043d\u0430\u0447\u0430\u0442\u044c \u043d\u043e\u0432\u0438\u0447\u043a\u0443?<\/strong> \u0421 \u043f\u043e\u0438\u0441\u043a\u0430 \u0438 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043e\u043a: \u043e\u043d\u0438 \u043a\u043e\u0440\u043e\u0442\u043a\u0438\u0435, \u043b\u0435\u0433\u043a\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u044e\u0442\u0441\u044f \u043d\u0430 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u043c \u043c\u0430\u0441\u0441\u0438\u0432\u0435 \u0438 \u0437\u043d\u0430\u043a\u043e\u043c\u044f\u0442 \u0441 \u043e\u0446\u0435\u043d\u043a\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438. \u0414\u0430\u043b\u044c\u0448\u0435 &#8212; \u0441\u0442\u0440\u043e\u043a\u0438, \u0437\u0430\u0442\u0435\u043c \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u0433\u0440\u0430\u0444\u044b.<\/p>\n<p><strong>\u041e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043b\u0438 \u0437\u043d\u0430\u0442\u044c O-\u043d\u043e\u0442\u0430\u0446\u0438\u044e, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0438?<\/strong> \u0414\u043b\u044f \u0440\u0430\u0431\u043e\u0447\u0435\u0433\u043e \u043e\u0442\u0432\u0435\u0442\u0430 &#8212; \u043d\u0435\u0442, \u043d\u043e \u0438\u043c\u0435\u043d\u043d\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043d\u0430 \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445, \u043e\u0442 \u0442\u043e\u0433\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u0430\u0434\u0430\u0435\u0442 \u043f\u043e \u0442\u0430\u0439\u043c\u0430\u0443\u0442\u0443 \u043d\u0430 \u0441\u043e\u0431\u0435\u0441\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0438 \u0438\u043b\u0438 \u0432 \u043f\u0440\u043e\u0434\u0435.<\/p>\n<p><strong>\u041d\u0430 \u043a\u0430\u043a\u043e\u043c \u044f\u0437\u044b\u043a\u0435 \u0440\u0435\u0448\u0430\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438?<\/strong> \u042f\u0437\u044b\u043a \u0432\u0442\u043e\u0440\u0438\u0447\u0435\u043d: \u0442\u0435 \u0436\u0435 \u0438\u0434\u0435\u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043d\u0430 C++, Java, Go. Python \u0443\u0434\u043e\u0431\u0435\u043d \u0434\u043b\u044f \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438\u0437-\u0437\u0430 \u043a\u043e\u0440\u043e\u0442\u043a\u0438\u0445 \u0441\u0440\u0435\u0437\u043e\u0432, <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">collections<\/code> \u0438 \u0447\u0438\u0442\u0430\u0435\u043c\u043e\u0433\u043e \u043a\u043e\u0434\u0430, \u043d\u043e \u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430\u0445 \u0438 \u0432 \u0432\u044b\u0441\u043e\u043a\u043e\u043d\u0430\u0433\u0440\u0443\u0436\u0435\u043d\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u0447\u0430\u0449\u0435 \u0431\u0435\u0440\u0443\u0442 C++ \u0440\u0430\u0434\u0438 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b &#8212; \u044d\u0442\u043e \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u0433\u0434\u0435 \u043d\u0443\u0436\u043d\u043e \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0442\u0432\u0435\u0442, \u0430 \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u0441\u043f\u043e\u0441\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0438 \u043e\u0446\u0435\u043d\u0438\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0448\u0430\u0433\u043e\u0432 \u0438 \u043f\u0430\u043c\u044f\u0442\u0438 \u043e\u043d \u043f\u043e\u0442\u0440\u0435\u0431\u0443\u0435\u0442. \u0418\u043c\u0435\u043d\u043d\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u0430 \u043d\u0435 \u044f\u0437\u044b\u043a, \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0437\u0430 \u0441\u0435\u043a\u0443\u043d\u0434\u0443 \u043e\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043d\u0435 \u0434\u043e\u0436\u0434\u0430\u0442\u044c\u0441\u044f. \u041d\u0438\u0436\u0435 &#8212; \u0440\u0430\u0437\u0431\u043e\u0440 \u0442\u0438\u043f\u043e\u0432\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043f\u043e \u0442\u0435\u043c\u0430\u043c: \u043f\u043e\u0438\u0441\u043a, \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430, \u0441\u0442\u0440\u043e\u043a\u0438, \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u0433\u0440\u0430\u0444\u044b. \u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435 \u041a\u0430\u043a [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":786,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-785","post","type-post","status-publish","format-standard","has-post-thumbnail","","category-polza"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0420\u0430\u0437\u0431\u043e\u0440 \u0442\u0438\u043f\u043e\u0432\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u0441 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u043d\u0430 Python: \u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0439 \u043f\u043e\u0438\u0441\u043a, \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0430, \u0441\u0442\u0440\u043e\u043a\u0438, \u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0430 \u0438 \u043e\u0431\u0445\u043e\u0434 \u0433\u0440\u0430\u0444\u0430. \u0413\u043e\u0442\u043e\u0432\u044b\u0439 \u043a\u043e\u0434, \u0432\u044b\u0432\u043e\u0434 \u0438 \u043e\u0446\u0435\u043d\u043a\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 O().\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"A. 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