{"id":10809,"date":"2026-09-24T09:00:00","date_gmt":"2026-09-24T09:00:00","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=10809"},"modified":"2026-09-25T15:24:31","modified_gmt":"2026-09-25T15:24:31","slug":"binarnye-dreva","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/binarnye-dreva\/","title":{"rendered":"\u0414\u0432\u043e\u0438\u0447\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f: \u043d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u0432\u0438\u0434\u044b \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435"},"content":{"rendered":"<p><strong>\u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 (\u0431\u0438\u043d\u0430\u0440\u043d\u043e\u0435) \u0434\u0435\u0440\u0435\u0432\u043e<\/strong> &#8212; \u044d\u0442\u043e \u0438\u0435\u0440\u0430\u0440\u0445\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u0430\u043d\u043d\u044b\u0445, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0434\u0432\u0443\u0445 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432, \u043f\u0440\u0438\u0447\u0435\u043c \u043e\u043d\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043a\u0430\u043a <strong>\u043b\u0435\u0432\u044b\u0439<\/strong> \u0438 <strong>\u043f\u0440\u0430\u0432\u044b\u0439<\/strong>. \u041d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 &#8212; \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u0435 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u0432\u044b\u0431\u0438\u0440\u0430\u0442\u044c \u043e\u0434\u043d\u0443 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0432\u0435\u0442\u0432\u0435\u0439: \u044d\u0442\u043e \u0434\u0430\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u043f\u043e \u043a\u043b\u044e\u0447\u0443 (\u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430), \u0431\u044b\u0441\u0442\u0440\u0443\u044e \u0432\u044b\u0434\u0430\u0447\u0443 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 (\u043a\u0443\u0447\u0430) \u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u0438 \u043a\u043e\u0434\u043e\u0432 (\u0434\u0435\u0440\u0435\u0432\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043a\u043e\u0434 \u0425\u0430\u0444\u0444\u043c\u0430\u043d\u0430).<\/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\">\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e: \u0442\u0435\u0440\u043c\u0438\u043d\u044b<\/a><\/li>\n<li><a href=\"#s2\">\u0412\u0438\u0434\u044b \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0445 \u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432<\/a><\/li>\n<li><a href=\"#s3\">\u041a\u0430\u043a \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u0445\u0440\u0430\u043d\u0438\u0442\u0441\u044f \u0432 \u043f\u0430\u043c\u044f\u0442\u0438<\/a><\/li>\n<li><a href=\"#s4\">\u0411\u0438\u043d\u0430\u0440\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430: \u043f\u043e\u0438\u0441\u043a, \u0432\u0441\u0442\u0430\u0432\u043a\u0430, \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0435<\/a><\/li>\n<li><a href=\"#s5\">\u041e\u0431\u0445\u043e\u0434\u044b \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430: \u0432 \u0433\u043b\u0443\u0431\u0438\u043d\u0443 \u0438 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443<\/a><\/li>\n<li><a href=\"#s6\">\u041d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0445 \u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432<\/a><\/li>\n<li><a href=\"#s7\">\u0415\u0441\u043b\u0438 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c<\/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\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/a><\/li>\n<li><a href=\"#s10\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<p>\u0412\u0430\u0436\u043d\u043e \u0441\u0440\u0430\u0437\u0443 \u0440\u0430\u0437\u0432\u0435\u0441\u0442\u0438 \u0442\u0440\u0438 \u0432\u0435\u0449\u0438. \u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e &#8212; \u044d\u0442\u043e \u0444\u043e\u0440\u043c\u0430 (\u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0434\u0432\u0443\u0445 \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0435\u043d\u043d\u044b\u0445 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432). \u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430 &#8212; \u0444\u043e\u0440\u043c\u0430 \u043f\u043b\u044e\u0441 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u043a\u043b\u044e\u0447\u0435\u0439. \u0414\u0432\u043e\u0438\u0447\u043d\u0430\u044f \u043a\u0443\u0447\u0430 &#8212; \u043f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e (\u0431\u0435\u0437 \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u043e\u0432 \u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c) \u043f\u043b\u044e\u0441 \u0434\u0440\u0443\u0433\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: \u0432 min-\u043a\u0443\u0447\u0435 \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432, \u0432 max-\u043a\u0443\u0447\u0435 &#8212; \u043d\u0435 \u043c\u0435\u043d\u044c\u0448\u0435. \u041d\u0438\u0436\u0435 &#8212; \u0432\u0438\u0434\u044b, \u0445\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0432 \u043f\u0430\u043c\u044f\u0442\u0438, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043e\u0431\u0445\u043e\u0434\u044b \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f. \u041a\u043e\u0434 \u043f\u0440\u043e\u0432\u0435\u0440\u0435\u043d \u043d\u0430 Python 3.14.<\/p>\n<h2 id=\"s1\">\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e: \u0442\u0435\u0440\u043c\u0438\u043d\u044b<\/h2>\n<p>\u041a\u043e\u0440\u043e\u0442\u043a\u0438\u0439 \u0441\u043b\u043e\u0432\u0430\u0440\u044c, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0445\u0432\u0430\u0442\u0438\u0442 \u0434\u043b\u044f \u0441\u0442\u0430\u0442\u044c\u0438:<\/p>\n<ul>\n<li><strong>\u041a\u043e\u0440\u0435\u043d\u044c<\/strong> &#8212; \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u0437\u0435\u043b \u0431\u0435\u0437 \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044f.<\/li>\n<li><strong>\u041b\u0438\u0441\u0442<\/strong> &#8212; \u0443\u0437\u0435\u043b \u0431\u0435\u0437 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432; \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0437\u043b\u044b \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u043c\u0438.<\/li>\n<li><strong>\u041f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u043e<\/strong> &#8212; \u0443\u0437\u0435\u043b \u0432\u043c\u0435\u0441\u0442\u0435 \u0441\u043e \u0432\u0441\u0435\u043c\u0438 \u0435\u0433\u043e \u043f\u043e\u0442\u043e\u043c\u043a\u0430\u043c\u0438; \u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u0435\u0441\u0442\u044c \u043b\u0435\u0432\u043e\u0435 \u0438 \u043f\u0440\u0430\u0432\u043e\u0435 \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u043e (\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u043f\u0443\u0441\u0442\u043e\u0435).<\/li>\n<li><strong>\u0412\u044b\u0441\u043e\u0442\u0430<\/strong> &#8212; \u0447\u0438\u0441\u043b\u043e \u0443\u0440\u043e\u0432\u043d\u0435\u0439 \u043e\u0442 \u043a\u043e\u0440\u043d\u044f \u0434\u043e \u0441\u0430\u043c\u043e\u0433\u043e \u0434\u0430\u043b\u044c\u043d\u0435\u0433\u043e \u043b\u0438\u0441\u0442\u0430. \u0415\u0435 \u0441\u0447\u0438\u0442\u0430\u044e\u0442 \u0432 \u0443\u0440\u043e\u0432\u043d\u044f\u0445 \u0438\u043b\u0438 \u0432 \u0440\u0435\u0431\u0440\u0430\u0445; \u0434\u0430\u043b\u044c\u0448\u0435 \u0432 \u043a\u043e\u0434\u0435 &#8212; \u0432 \u0443\u0440\u043e\u0432\u043d\u044f\u0445.<\/li>\n<\/ul>\n<p>\u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e &#8212; \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u00ab\u0434\u0435\u0440\u0435\u0432\u043e \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 2\u00bb. \u0412 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u0443\u0437\u0435\u043b \u0441 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u043b\u0435\u0432\u044b\u043c \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u043c \u0438 \u0443\u0437\u0435\u043b \u0441 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u043f\u0440\u0430\u0432\u044b\u043c &#8212; \u0440\u0430\u0437\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f, \u0430 \u0432 \u043e\u0431\u044b\u0447\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u0442\u0430\u043a\u043e\u0433\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u043d\u0435\u0442. \u041e\u0431\u0449\u0438\u0435 \u0442\u0435\u0440\u043c\u0438\u043d\u044b \u0438 \u0442\u0440\u0438 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u044b\u0445 \u043e\u0431\u0445\u043e\u0434\u0430 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u044b \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"\/journal\/derevo-kak-struktura-dannyh\/\">\u0414\u0435\u0440\u0435\u0432\u043e \u043a\u0430\u043a \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u0430\u043d\u043d\u044b\u0445<\/a>, \u0437\u0434\u0435\u0441\u044c \u0444\u043e\u043a\u0443\u0441 \u043d\u0430 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435.<\/p>\n<h2 id=\"s2\">\u0412\u0438\u0434\u044b \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0445 \u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432<\/h2>\n<p>\u0412 \u0440\u0443\u0441\u0441\u043a\u0438\u0445 \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0430\u0445 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u044f \u0432\u0438\u0434\u043e\u0432 \u043f\u0443\u0442\u0430\u044e\u0442\u0441\u044f: \u00ab\u043f\u043e\u043b\u043d\u044b\u043c\u00bb \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0442\u043e full, \u0442\u043e complete, \u0442\u043e perfect. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0435 \u0440\u044f\u0434\u043e\u043c \u0434\u0430\u043d \u0430\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u0438\u0439 \u0442\u0435\u0440\u043c\u0438\u043d \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0412\u0438\u0434<\/th>\n<th>\u0410\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u0438\u0439 \u0442\u0435\u0440\u043c\u0438\u043d<\/th>\n<th>\u0423\u0441\u043b\u043e\u0432\u0438\u0435<\/th>\n<th>\u0413\u0434\u0435 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0421\u0442\u0440\u043e\u0433\u043e\u0435 (\u043f\u043e\u043b\u043d\u043e\u0435)<\/td>\n<td>full, strict<\/td>\n<td>\u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 0 \u0438\u043b\u0438 2 \u043f\u043e\u0442\u043e\u043c\u043a\u0430<\/td>\n<td>\u0434\u0435\u0440\u0435\u0432\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0434\u0435\u0440\u0435\u0432\u043e \u0425\u0430\u0444\u0444\u043c\u0430\u043d\u0430<\/td>\n<\/tr>\n<tr>\n<td>\u041f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0435 (\u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e\u0435)<\/td>\n<td>complete<\/td>\n<td>\u0432\u0441\u0435 \u0443\u0440\u043e\u0432\u043d\u0438 \u0437\u0430\u043f\u043e\u043b\u043d\u0435\u043d\u044b, \u043a\u0440\u043e\u043c\u0435 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e; \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u0437\u0430\u043f\u043e\u043b\u043d\u0435\u043d \u0441\u043b\u0435\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043e \u0431\u0435\u0437 \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u043e\u0432<\/td>\n<td>\u0434\u0432\u043e\u0438\u0447\u043d\u0430\u044f \u043a\u0443\u0447\u0430, \u0445\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0432 \u043c\u0430\u0441\u0441\u0438\u0432\u0435<\/td>\n<\/tr>\n<tr>\n<td>\u0421\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e\u0435<\/td>\n<td>perfect<\/td>\n<td>\u0432\u0441\u0435 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0435 \u0443\u0437\u043b\u044b \u0438\u043c\u0435\u044e\u0442 2 \u043f\u043e\u0442\u043e\u043c\u043a\u0430, \u0432\u0441\u0435 \u043b\u0438\u0441\u0442\u044c\u044f \u043d\u0430 \u043e\u0434\u043d\u043e\u043c \u0443\u0440\u043e\u0432\u043d\u0435<\/td>\n<td>\u0438\u0434\u0435\u0430\u043b\u044c\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043e\u043a<\/td>\n<\/tr>\n<tr>\n<td>\u0421\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435<\/td>\n<td>balanced<\/td>\n<td>\u0432\u044b\u0441\u043e\u0442\u0430 \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f O(log n): \u0432 AVL \u0432\u044b\u0441\u043e\u0442\u044b \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432 \u043b\u044e\u0431\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0447\u0435\u043c \u043d\u0430 1, \u0432 \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u043e\u043c \u0441\u0430\u043c\u044b\u0439 \u0434\u043b\u0438\u043d\u043d\u044b\u0439 \u043f\u0443\u0442\u044c \u043e\u0442 \u0443\u0437\u043b\u0430 \u0434\u043e \u043b\u0438\u0441\u0442\u0430 \u043d\u0435 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c \u0432\u0434\u0432\u043e\u0435 \u0434\u043b\u0438\u043d\u043d\u0435\u0435 \u0441\u0430\u043c\u043e\u0433\u043e \u043a\u043e\u0440\u043e\u0442\u043a\u043e\u0433\u043e<\/td>\n<td>AVL, \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f<\/td>\n<\/tr>\n<tr>\n<td>\u0412\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u0435<\/td>\n<td>degenerate<\/td>\n<td>\u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u043e\u0434\u043d\u043e\u0433\u043e \u043f\u043e\u0442\u043e\u043c\u043a\u0430<\/td>\n<td>\u043f\u043e \u0441\u0443\u0442\u0438 \u0441\u0432\u044f\u0437\u043d\u044b\u0439 \u0441\u043f\u0438\u0441\u043e\u043a, \u0445\u0443\u0434\u0448\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0422\u0440\u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u044b\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u044e\u0442\u0441\u044f \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u043e\u043c:<\/p>\n<ul>\n<li>\u0412 \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u0438\u0437 h \u0443\u0440\u043e\u0432\u043d\u0435\u0439 \u0440\u043e\u0432\u043d\u043e 2^h &#8212; 1 \u0443\u0437\u043b\u043e\u0432 \u0438 2^(h-1) \u043b\u0438\u0441\u0442\u044c\u0435\u0432: \u043f\u0440\u0438 h = 3 \u044d\u0442\u043e 7 \u0443\u0437\u043b\u043e\u0432 \u0438 4 \u043b\u0438\u0441\u0442\u0430.<\/li>\n<li>\u0412 \u0441\u0442\u0440\u043e\u0433\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u043b\u0438\u0441\u0442\u044c\u0435\u0432 \u043d\u0430 \u043e\u0434\u0438\u043d \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0443\u0437\u043b\u043e\u0432.<\/li>\n<li>\u041c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0443\u0440\u043e\u0432\u043d\u0435\u0439 \u0434\u043b\u044f n \u0443\u0437\u043b\u043e\u0432 &#8212; \u2308log2(n + 1)\u2309: \u0434\u043b\u044f 1000 \u0443\u0437\u043b\u043e\u0432 \u044d\u0442\u043e 10 \u0443\u0440\u043e\u0432\u043d\u0435\u0439, \u0430 \u0443 \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 &#8212; \u0432\u0441\u0435 1000.<\/li>\n<\/ul>\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 10 \u0438 1000 \u0443\u0440\u043e\u0432\u043d\u044f\u043c\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442, \u0437\u0430\u0447\u0435\u043c \u043d\u0443\u0436\u043d\u044b \u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f.<\/p>\n<h2 id=\"s3\">\u041a\u0430\u043a \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u0445\u0440\u0430\u043d\u0438\u0442\u0441\u044f \u0432 \u043f\u0430\u043c\u044f\u0442\u0438<\/h2>\n<p>\u0415\u0441\u0442\u044c \u0434\u0432\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430. \u041f\u0435\u0440\u0432\u044b\u0439 &#8212; \u0443\u0437\u043b\u044b \u0441\u043e \u0441\u0441\u044b\u043b\u043a\u0430\u043c\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\">left<\/code> \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\">right<\/code>: \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0439 \u0444\u043e\u0440\u043c\u044b \u0434\u0435\u0440\u0435\u0432\u0430. \u0412\u0442\u043e\u0440\u043e\u0439 &#8212; \u043c\u0430\u0441\u0441\u0438\u0432 \u0431\u0435\u0437 \u0441\u0441\u044b\u043b\u043e\u043a: \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u0434\u043b\u044f \u043f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0432 \u043d\u0435\u043c \u043d\u0435\u0442 \u00ab\u0434\u044b\u0440\u00bb. \u0423 \u0443\u0437\u043b\u0430 \u0441 \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c i \u043b\u0435\u0432\u044b\u0439 \u043f\u043e\u0442\u043e\u043c\u043e\u043a \u043b\u0435\u0436\u0438\u0442 \u0432 2i + 1, \u043f\u0440\u0430\u0432\u044b\u0439 &#8212; \u0432 2i + 2, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c &#8212; \u0432 (i &#8212; 1) \/\/ 2.<\/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\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">heapq<\/span>\n\n<span style=\"color: #7F848E\"># \u041f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0435 (complete) \u0434\u0435\u0440\u0435\u0432\u043e \u0432 \u043c\u0430\u0441\u0441\u0438\u0432\u0435: \u043f\u043e\u0442\u043e\u043c\u043a\u0438 \u0443\u0437\u043b\u0430 i \u043b\u0435\u0436\u0430\u0442 \u0432 2*i+1 \u0438 2*i+2<\/span>\n<span style=\"color: #E06C75\">tree<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">8<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">10<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">6<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">9<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">14<\/span><span style=\"color: #ABB2BF\">]<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">children<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">i<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">kids<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">i<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">2<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">i<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">tree<\/span><span style=\"color: #ABB2BF\">)]<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">tree<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">j<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">j<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">kids<\/span><span style=\"color: #ABB2BF\">]<\/span>\n\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">i<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">value<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">enumerate<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">tree<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">parent<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">tree<\/span><span style=\"color: #ABB2BF\">[(<\/span><span style=\"color: #E06C75\">i<\/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: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">i<\/span> <span style=\"color: #56B6C2\">&gt;<\/span> <span style=\"color: #D19A66\">0<\/span> <span style=\"color: #C678DD\">else<\/span> <span style=\"color: #E5C07B\">None<\/span>\n    <span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"\u0438\u043d\u0434\u0435\u043a\u0441 {<\/span><span style=\"color: #E06C75\">i<\/span><span style=\"color: #98C379\">}: \u0443\u0437\u0435\u043b {<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #98C379\">}, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c {<\/span><span style=\"color: #E06C75\">parent<\/span><span style=\"color: #98C379\">}, \u0434\u0435\u0442\u0438 {<\/span><span style=\"color: #E06C75\">children<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">i<\/span><span style=\"color: #ABB2BF\">)<\/span><span style=\"color: #98C379\">}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #7F848E\"># heapq \u0445\u0440\u0430\u043d\u0438\u0442 \u0434\u0432\u043e\u0438\u0447\u043d\u0443\u044e \u043a\u0443\u0447\u0443 \u0432 \u043e\u0431\u044b\u0447\u043d\u043e\u043c \u0441\u043f\u0438\u0441\u043a\u0435 \u043f\u043e \u0442\u043e\u0439 \u0436\u0435 \u0441\u0445\u0435\u043c\u0435 \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u0432<\/span>\n<span style=\"color: #E06C75\">tasks<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[(<\/span><span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"\u043e\u0442\u0447\u0435\u0442\"<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"\u0430\u0432\u0430\u0440\u0438\u044f\"<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"\u0440\u0435\u0432\u044c\u044e\"<\/span><span style=\"color: #ABB2BF\">)]<\/span>\n<span style=\"color: #E06C75\">heapq<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">heapify<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">tasks<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043a\u043e\u0440\u0435\u043d\u044c \u043a\u0443\u0447\u0438:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">tasks<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">])<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0432\u044b\u0434\u0430\u0447\u0438:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">heapq<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">heappop<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">tasks<\/span><span style=\"color: #ABB2BF\">)[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">]<\/span> <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: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">)])<\/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\">\u0438\u043d\u0434\u0435\u043a\u0441 0: \u0443\u0437\u0435\u043b 8, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c None, \u0434\u0435\u0442\u0438 [3, 10]\n\u0438\u043d\u0434\u0435\u043a\u0441 1: \u0443\u0437\u0435\u043b 3, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 8, \u0434\u0435\u0442\u0438 [1, 6]\n\u0438\u043d\u0434\u0435\u043a\u0441 2: \u0443\u0437\u0435\u043b 10, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 8, \u0434\u0435\u0442\u0438 [9, 14]\n\u0438\u043d\u0434\u0435\u043a\u0441 3: \u0443\u0437\u0435\u043b 1, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 3, \u0434\u0435\u0442\u0438 []\n\u0438\u043d\u0434\u0435\u043a\u0441 4: \u0443\u0437\u0435\u043b 6, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 3, \u0434\u0435\u0442\u0438 []\n\u0438\u043d\u0434\u0435\u043a\u0441 5: \u0443\u0437\u0435\u043b 9, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 10, \u0434\u0435\u0442\u0438 []\n\u0438\u043d\u0434\u0435\u043a\u0441 6: \u0443\u0437\u0435\u043b 14, \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c 10, \u0434\u0435\u0442\u0438 []\n\u043a\u043e\u0440\u0435\u043d\u044c \u043a\u0443\u0447\u0438: (1, &#x27;\u0430\u0432\u0430\u0440\u0438\u044f&#x27;)\n\u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0432\u044b\u0434\u0430\u0447\u0438: [&#x27;\u0430\u0432\u0430\u0440\u0438\u044f&#x27;, &#x27;\u0440\u0435\u0432\u044c\u044e&#x27;, &#x27;\u043e\u0442\u0447\u0435\u0442&#x27;]\n<\/code><\/pre>\n<p>\u041c\u043e\u0434\u0443\u043b\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\">heapq<\/code> &#8212; \u0433\u043e\u0442\u043e\u0432\u0430\u044f \u0434\u0432\u043e\u0438\u0447\u043d\u0430\u044f \u043a\u0443\u0447\u0430: \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0431\u043e\u0442\u0430\u044e\u0442 \u0441 min-\u043a\u0443\u0447\u0435\u0439, \u0432 \u043a\u043e\u0440\u043d\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\">tasks[0]<\/code>) \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0437\u0430\u0434\u0430\u0447\u0430 \u0441 \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u043e\u043c 1 \u0432\u044b\u0434\u0430\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u043e\u0439. \u0421 Python 3.14 \u0432 \u043c\u043e\u0434\u0443\u043b\u0435 \u0435\u0441\u0442\u044c \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 max-\u043a\u0443\u0447\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\">heapify_max<\/code>, <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\">heappush_max<\/code>, <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\">heappop_max<\/code>); \u0432 \u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u043d\u043d\u0438\u0445 \u0432\u0435\u0440\u0441\u0438\u044f\u0445 \u0434\u043b\u044f max-\u043a\u0443\u0447\u0438 \u043a\u043b\u044e\u0447\u0438 \u0445\u0440\u0430\u043d\u044f\u0442 \u0441 \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u043c \u0437\u043d\u0430\u043a\u043e\u043c. \u0412\u0441\u0442\u0430\u0432\u043a\u0430 \u0438 \u0438\u0437\u0432\u043b\u0435\u0447\u0435\u043d\u0438\u0435 \u0441\u0442\u043e\u044f\u0442 O(log n), \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u00ab\u0432\u0441\u043f\u043b\u044b\u0432\u0430\u0435\u0442\u00bb \u0438\u043b\u0438 \u00ab\u0442\u043e\u043d\u0435\u0442\u00bb \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e \u043e\u0434\u043d\u043e\u0439 \u0432\u0435\u0442\u0432\u0438.<\/p>\n<h2 id=\"s4\">\u0411\u0438\u043d\u0430\u0440\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430: \u043f\u043e\u0438\u0441\u043a, \u0432\u0441\u0442\u0430\u0432\u043a\u0430, \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0435<\/h2>\n<p>\u0412 <strong>\u0434\u0432\u043e\u0438\u0447\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u043f\u043e\u0438\u0441\u043a\u0430<\/strong> (BST) \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u0432\u0441\u0435 \u043a\u043b\u044e\u0447\u0438 \u043b\u0435\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430 \u043c\u0435\u043d\u044c\u0448\u0435 \u043a\u043b\u044e\u0447\u0430 \u0443\u0437\u043b\u0430, \u0430 \u0432\u0441\u0435 \u043a\u043b\u044e\u0447\u0438 \u043f\u0440\u0430\u0432\u043e\u0433\u043e &#8212; \u0431\u043e\u043b\u044c\u0448\u0435. \u041f\u043e\u0438\u0441\u043a \u0438 \u0432\u0441\u0442\u0430\u0432\u043a\u0430 \u0438\u0434\u0443\u0442 \u043e\u0442 \u043a\u043e\u0440\u043d\u044f \u0432\u043d\u0438\u0437: \u043c\u0435\u043d\u044c\u0448\u0435 &#8212; \u0432\u043b\u0435\u0432\u043e, \u0431\u043e\u043b\u044c\u0448\u0435 &#8212; \u0432\u043f\u0440\u0430\u0432\u043e. \u0421\u043b\u043e\u0436\u043d\u0435\u0435 \u0432\u0441\u0435\u0433\u043e \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0435, \u0443 \u043d\u0435\u0433\u043e \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u044f:<\/p>\n<ol>\n<li>\u0423 \u0443\u0437\u043b\u0430 \u043d\u0435\u0442 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432 &#8212; \u043f\u0440\u043e\u0441\u0442\u043e \u0443\u0431\u0438\u0440\u0430\u0435\u043c \u0435\u0433\u043e.<\/li>\n<li>\u041e\u0434\u0438\u043d \u043f\u043e\u0442\u043e\u043c\u043e\u043a &#8212; \u0441\u0442\u0430\u0432\u0438\u043c \u043f\u043e\u0442\u043e\u043c\u043a\u0430 \u043d\u0430 \u043c\u0435\u0441\u0442\u043e \u0443\u0437\u043b\u0430.<\/li>\n<li>\u0414\u0432\u0430 \u043f\u043e\u0442\u043e\u043c\u043a\u0430 &#8212; \u0431\u0435\u0440\u0435\u043c \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 \u043f\u0440\u0430\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430 (\u043f\u0440\u0435\u0435\u043c\u043d\u0438\u043a\u0430), \u043a\u043e\u043f\u0438\u0440\u0443\u0435\u043c \u0435\u0433\u043e \u0432 \u0443\u0437\u0435\u043b \u0438 \u0443\u0434\u0430\u043b\u044f\u0435\u043c \u043f\u0440\u0435\u0435\u043c\u043d\u0438\u043a\u0430 \u0438\u0437 \u043f\u0440\u0430\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430. \u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 \u0432\u0430\u0440\u0438\u0430\u043d\u0442 &#8212; \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u043b\u0435\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430.<\/li>\n<\/ol>\n<p>\u041f\u043e\u043b\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440: \u0432\u0441\u0442\u0430\u0432\u043a\u0430 \u0431\u0435\u0437 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0438, \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0435 \u0432\u0441\u0435\u0445 \u0442\u0440\u0435\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u0432\u044b\u0441\u043e\u0442\u044b \u043f\u0440\u0438 \u0440\u0430\u0437\u043d\u043e\u043c \u043f\u043e\u0440\u044f\u0434\u043a\u0435 \u0432\u0441\u0442\u0430\u0432\u043a\u0438.<\/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\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">random<\/span>\n\n<span style=\"color: #C678DD\">class<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E5C07B\">Node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n    <span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2; font-weight: bold\">__init__<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">self<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">):<\/span>\n        <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">None<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">insert<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">):<\/span>\n<span style=\"color: #ABB2BF\">    <\/span><span style=\"color: #98C379\">\"\"\"\u0418\u0442\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u0430\u044f \u0432\u0441\u0442\u0430\u0432\u043a\u0430: \u043d\u0435 \u0443\u043f\u0438\u0440\u0430\u0435\u0442\u0441\u044f \u0432 \u043b\u0438\u043c\u0438\u0442 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0438.\"\"\"<\/span>\n    <span style=\"color: #E06C75\">new<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">new<\/span>\n    <span style=\"color: #E06C75\">cur<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">root<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E5C07B\">True<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n                <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">new<\/span>\n                <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">root<\/span>\n            <span style=\"color: #E06C75\">cur<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span>\n        <span style=\"color: #C678DD\">elif<\/span> <span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">&gt;<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n                <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">new<\/span>\n                <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">root<\/span>\n            <span style=\"color: #E06C75\">cur<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span>\n        <span style=\"color: #C678DD\">else<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">root<\/span>  <span style=\"color: #7F848E\"># \u0434\u0443\u0431\u043b\u0438\u043a\u0430\u0442 \u043d\u0435 \u0432\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">node<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E5C07B\">None<\/span>                      <span style=\"color: #7F848E\"># \u043a\u043b\u044e\u0447\u0430 \u043d\u0435\u0442 - \u0434\u0435\u0440\u0435\u0432\u043e \u043d\u0435 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">&lt;<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">elif<\/span> <span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">&gt;<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">else<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>            <span style=\"color: #7F848E\"># \u0441\u043b\u0443\u0447\u0430\u0438 1 \u0438 2: \u043d\u043e\u043b\u044c \u0438\u043b\u0438 \u043e\u0434\u0438\u043d \u043f\u043e\u0442\u043e\u043c\u043e\u043a<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span>\n        <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span>\n        <span style=\"color: #E06C75\">succ<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span>                <span style=\"color: #7F848E\"># \u0441\u043b\u0443\u0447\u0430\u0439 3: \u0434\u0432\u0430 \u043f\u043e\u0442\u043e\u043c\u043a\u0430<\/span>\n        <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">succ<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #56B6C2\">not<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>     <span style=\"color: #7F848E\"># \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u043f\u0440\u0430\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430<\/span>\n            <span style=\"color: #E06C75\">succ<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">succ<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span>\n        <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">succ<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span>\n        <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">succ<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">node<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">inorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">):<\/span>\n<span style=\"color: #ABB2BF\">    <\/span><span style=\"color: #98C379\">\"\"\"\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434 \u0431\u0435\u0437 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0438, \u0447\u0435\u0440\u0435\u0437 \u044f\u0432\u043d\u044b\u0439 \u0441\u0442\u0435\u043a.\"\"\"<\/span>\n    <span style=\"color: #E06C75\">stack<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[],<\/span> <span style=\"color: #ABB2BF\">[]<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">stack<\/span> <span style=\"color: #56B6C2\">or<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n            <span style=\"color: #E06C75\">stack<\/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: #E06C75\">node<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span>\n        <span style=\"color: #E06C75\">node<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">stack<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">pop<\/span><span style=\"color: #ABB2BF\">()<\/span>\n        <span style=\"color: #E06C75\">out<\/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: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n        <span style=\"color: #E06C75\">node<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">out<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">height<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">):<\/span>\n<span style=\"color: #ABB2BF\">    <\/span><span style=\"color: #98C379\">\"\"\"\u0412\u044b\u0441\u043e\u0442\u0430 \u0432 \u0443\u0440\u043e\u0432\u043d\u044f\u0445, \u043e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443.\"\"\"<\/span>\n    <span style=\"color: #E06C75\">level<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">node<\/span> <span style=\"color: #C678DD\">else<\/span> <span style=\"color: #ABB2BF\">[],<\/span> <span style=\"color: #D19A66\">0<\/span>\n    <span style=\"color: #C678DD\">while<\/span> <span style=\"color: #E06C75\">level<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">+=<\/span> <span style=\"color: #D19A66\">1<\/span>\n        <span style=\"color: #E06C75\">level<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">c<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">n<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">level<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">c<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">c<\/span><span style=\"color: #ABB2BF\">]<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">h<\/span>\n\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">None<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">k<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">8<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">10<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">6<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">14<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">13<\/span><span style=\"color: #ABB2BF\">]:<\/span>\n    <span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">insert<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">k<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">)<\/span>    <span style=\"color: #7F848E\"># \u0443 3 \u0434\u0432\u0430 \u043f\u043e\u0442\u043e\u043c\u043a\u0430: \u0435\u0435 \u043c\u0435\u0441\u0442\u043e \u0437\u0430\u0439\u043c\u0435\u0442 4<\/span>\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">14<\/span><span style=\"color: #ABB2BF\">)<\/span>   <span style=\"color: #7F848E\"># \u0443 14 \u043e\u0434\u0438\u043d \u043f\u043e\u0442\u043e\u043c\u043e\u043a: 13 \u043f\u043e\u0434\u043d\u0438\u043c\u0435\u0442\u0441\u044f<\/span>\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">)<\/span>    <span style=\"color: #7F848E\"># 7 - \u043b\u0438\u0441\u0442: \u043f\u0440\u043e\u0441\u0442\u043e \u0438\u0441\u0447\u0435\u0437\u0430\u0435\u0442<\/span>\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">delete<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">99<\/span><span style=\"color: #ABB2BF\">)<\/span>   <span style=\"color: #7F848E\"># \u0442\u0430\u043a\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 \u043d\u0435\u0442<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043f\u043e\u0441\u043b\u0435 \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0439:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">inorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043a\u043e\u0440\u0435\u043d\u044c \u043b\u0435\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">root<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E06C75\">n<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">1000<\/span>\n<span style=\"color: #E06C75\">chain<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">None<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">k<\/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\">n<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">):<\/span>          <span style=\"color: #7F848E\"># \u043a\u043b\u044e\u0447\u0438 \u043f\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044e<\/span>\n    <span style=\"color: #E06C75\">chain<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">insert<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">chain<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">k<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">keys<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">list<\/span><span style=\"color: #ABB2BF\">(<\/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\">n<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">seed<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">42<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">shuffle<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">keys<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">mixed<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">None<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">k<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">keys<\/span><span style=\"color: #ABB2BF\">:<\/span>                     <span style=\"color: #7F848E\"># \u0442\u0435 \u0436\u0435 \u043a\u043b\u044e\u0447\u0438 \u0432 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u043c \u043f\u043e\u0440\u044f\u0434\u043a\u0435<\/span>\n    <span style=\"color: #E06C75\">mixed<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">insert<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">mixed<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">k<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0432\u044b\u0441\u043e\u0442\u0430, \u0432\u0441\u0442\u0430\u0432\u043a\u0430 \u043f\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0443:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">height<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">chain<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0432\u044b\u0441\u043e\u0442\u0430, \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u043f\u043e\u0440\u044f\u0434\u043e\u043a:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">height<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">mixed<\/span><span style=\"color: #ABB2BF\">))<\/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\">\u043f\u043e\u0441\u043b\u0435 \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0439: [1, 4, 6, 8, 10, 13]\n\u043a\u043e\u0440\u0435\u043d\u044c \u043b\u0435\u0432\u043e\u0433\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u0430: 4\n\u0432\u044b\u0441\u043e\u0442\u0430, \u0432\u0441\u0442\u0430\u0432\u043a\u0430 \u043f\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0443: 1000\n\u0432\u044b\u0441\u043e\u0442\u0430, \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u043f\u043e\u0440\u044f\u0434\u043e\u043a: 21\n<\/code><\/pre>\n<p>\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434 \u0432\u044b\u0434\u0430\u043b \u043a\u043b\u044e\u0447\u0438 \u043f\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044e &#8212; \u0437\u043d\u0430\u0447\u0438\u0442, \u043f\u043e\u0441\u043b\u0435 \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0439 \u043f\u0440\u0430\u0432\u0438\u043b\u043e BST \u043d\u0435 \u043d\u0430\u0440\u0443\u0448\u0435\u043d\u043e. \u0427\u0438\u0441\u043b\u043e 21 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0432 \u043e\u0434\u043d\u043e\u043c \u043f\u0440\u043e\u0433\u043e\u043d\u0435 \u0441 <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\">random.seed(42)<\/code>, \u043f\u0440\u0438 \u0434\u0440\u0443\u0433\u043e\u043c \u043f\u043e\u0440\u044f\u0434\u043a\u0435 \u043e\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0434\u0440\u0443\u0433\u0438\u043c, \u043d\u043e \u0431\u043b\u0438\u0437\u043a\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430.<\/p>\n<p>\u0413\u043b\u0430\u0432\u043d\u044b\u0439 \u0432\u044b\u0432\u043e\u0434 \u0438\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0445 \u0434\u0432\u0443\u0445 \u0441\u0442\u0440\u043e\u043a: \u043e\u0446\u0435\u043d\u043a\u0430 O(log n) \u0434\u043b\u044f BST \u0432\u0435\u0440\u043d\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430. \u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0441\u0442\u043e\u044f\u0442 O(h), \u0433\u0434\u0435 h &#8212; \u0432\u044b\u0441\u043e\u0442\u0430, \u0438 \u0432 \u0445\u0443\u0434\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 h = n. \u041e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435 \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u044e\u0442 BST \u0432 \u0441\u043f\u0438\u0441\u043e\u043a. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0430\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442 \u0441\u0430\u043c\u043e\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u0443\u044e\u0449\u0438\u0435\u0441\u044f \u0434\u0435\u0440\u0435\u0432\u044c\u044f: \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <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\">java.util.TreeMap<\/code> \u043f\u043e \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0430\u0446\u0438\u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d \u043d\u0430 \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435. \u0423\u0434\u0430\u043b\u0435\u043d\u0438\u0435 \u0432 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u043e\u0435: \u0434\u043b\u044f \u0443\u0447\u0435\u0431\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e, \u043d\u0430 \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435 \u0435\u0433\u043e \u0441\u0442\u043e\u0438\u0442 \u043f\u0435\u0440\u0435\u043f\u0438\u0441\u0430\u0442\u044c \u0446\u0438\u043a\u043b\u043e\u043c \u0442\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0432\u0441\u0442\u0430\u0432\u043a\u0443.<\/p>\n<h2 id=\"s5\">\u041e\u0431\u0445\u043e\u0434\u044b \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430: \u0432 \u0433\u043b\u0443\u0431\u0438\u043d\u0443 \u0438 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443<\/h2>\n<p>\u041e\u0431\u0445\u043e\u0434 &#8212; \u043f\u043e\u0441\u0435\u0449\u0435\u043d\u0438\u0435 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u0440\u043e\u0432\u043d\u043e \u043e\u0434\u0438\u043d \u0440\u0430\u0437. \u041f\u043e\u0440\u044f\u0434\u043a\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043c\u043e\u043c\u0435\u043d\u0442\u043e\u043c, \u043a\u043e\u0433\u0434\u0430 \u043e\u0431\u0440\u0430\u0431\u0430\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u0430\u043c \u0443\u0437\u0435\u043b.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u041e\u0431\u0445\u043e\u0434<\/th>\n<th>\u041f\u043e\u0440\u044f\u0434\u043e\u043a<\/th>\n<th>\u0427\u0435\u043c \u0440\u0435\u0430\u043b\u0438\u0437\u0443\u044e\u0442<\/th>\n<th>\u0422\u0438\u043f\u0438\u0447\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u041f\u0440\u044f\u043c\u043e\u0439 (pre-order)<\/td>\n<td>\u0443\u0437\u0435\u043b -&gt; \u043b\u0435\u0432\u043e\u0435 -&gt; \u043f\u0440\u0430\u0432\u043e\u0435<\/td>\n<td>\u0440\u0435\u043a\u0443\u0440\u0441\u0438\u044f \u0438\u043b\u0438 \u0441\u0442\u0435\u043a<\/td>\n<td>\u043a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u0441\u0435\u0440\u0438\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0434\u0435\u0440\u0435\u0432\u0430, \u043f\u0440\u0435\u0444\u0438\u043a\u0441\u043d\u0430\u044f \u0437\u0430\u043f\u0438\u0441\u044c<\/td>\n<\/tr>\n<tr>\n<td>\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 (in-order)<\/td>\n<td>\u043b\u0435\u0432\u043e\u0435 -&gt; \u0443\u0437\u0435\u043b -&gt; \u043f\u0440\u0430\u0432\u043e\u0435<\/td>\n<td>\u0440\u0435\u043a\u0443\u0440\u0441\u0438\u044f \u0438\u043b\u0438 \u0441\u0442\u0435\u043a<\/td>\n<td>\u043a\u043b\u044e\u0447\u0438 BST \u043f\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044e<\/td>\n<\/tr>\n<tr>\n<td>\u041e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 (post-order)<\/td>\n<td>\u043b\u0435\u0432\u043e\u0435 -&gt; \u043f\u0440\u0430\u0432\u043e\u0435 -&gt; \u0443\u0437\u0435\u043b<\/td>\n<td>\u0440\u0435\u043a\u0443\u0440\u0441\u0438\u044f \u0438\u043b\u0438 \u0441\u0442\u0435\u043a<\/td>\n<td>\u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u0435 \u0434\u0435\u0440\u0435\u0432\u0430, \u0440\u0430\u0437\u043c\u0435\u0440\u044b \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432<\/td>\n<\/tr>\n<tr>\n<td>\u0412 \u0448\u0438\u0440\u0438\u043d\u0443 (level-order)<\/td>\n<td>\u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c, \u0441\u043b\u0435\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043e<\/td>\n<td>\u043e\u0447\u0435\u0440\u0435\u0434\u044c<\/td>\n<td>\u043a\u0440\u0430\u0442\u0447\u0430\u0439\u0448\u0438\u0439 \u043f\u0443\u0442\u044c \u0434\u043e \u0443\u0437\u043b\u0430, \u043f\u0435\u0447\u0430\u0442\u044c \u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u041f\u0435\u0440\u0432\u044b\u0435 \u0442\u0440\u0438 &#8212; \u043e\u0431\u0445\u043e\u0434\u044b \u0432 \u0433\u043b\u0443\u0431\u0438\u043d\u0443. \u041e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043e\u0447\u0435\u0440\u0435\u0434\u044c: \u0443\u0437\u0435\u043b \u0438\u0437\u0432\u043b\u0435\u043a\u0430\u0435\u0442\u0441\u044f \u0438\u0437 \u043d\u0430\u0447\u0430\u043b\u0430, \u0435\u0433\u043e \u043f\u043e\u0442\u043e\u043c\u043a\u0438 \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432 \u043a\u043e\u043d\u0435\u0446. \u0423\u0434\u043e\u0431\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440, \u0433\u0434\u0435 \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u043e\u0431\u0445\u043e\u0434\u0430 \u043c\u0435\u043d\u044f\u0435\u0442 \u0441\u043c\u044b\u0441\u043b, &#8212; \u0434\u0435\u0440\u0435\u0432\u043e \u0432\u044b\u0440\u0430\u0436\u0435\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\">class<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E5C07B\">Node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n    <span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2; font-weight: bold\">__init__<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">self<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">left<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">right<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">):<\/span>\n        <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">right<\/span>\n\n<span style=\"color: #7F848E\"># \u0414\u0435\u0440\u0435\u0432\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f (2 + 3) * (7 - 4): \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0432\u043e \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0443\u0437\u043b\u0430\u0445, \u0447\u0438\u0441\u043b\u0430 \u0432 \u043b\u0438\u0441\u0442\u044c\u044f\u0445<\/span>\n<span style=\"color: #E06C75\">expr<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"*\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"+\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">)),<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"-\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">)))<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">preorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #ABB2BF\">[]<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">n<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span> <span style=\"color: #C678DD\">else<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">]<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">preorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">preorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">postorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #ABB2BF\">[]<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">n<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span> <span style=\"color: #C678DD\">else<\/span> <span style=\"color: #E06C75\">postorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">postorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">]<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">by_levels<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">queue<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[],<\/span> <span style=\"color: #E06C75\">deque<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #E06C75\">root<\/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\">n<\/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>\n        <span style=\"color: #E06C75\">out<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">append<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">)<\/span>\n        <span style=\"color: #E06C75\">queue<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">extend<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">c<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">c<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">c<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">out<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">evaluate<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">):<\/span>\n<span style=\"color: #ABB2BF\">    <\/span><span style=\"color: #98C379\">\"\"\"\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 = \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043e\u043f\u0435\u0440\u0430\u043d\u0434\u044b, \u043f\u043e\u0442\u043e\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f.\"\"\"<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span> <span style=\"color: #56B6C2\">and<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">is<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/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\">evaluate<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">evaluate<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #ABB2BF\">{<\/span><span style=\"color: #98C379\">\"+\"<\/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: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"-\"<\/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: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"*\"<\/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: #ABB2BF\">}[<\/span><span style=\"color: #E06C75\">n<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">value<\/span><span style=\"color: #ABB2BF\">]<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043f\u0440\u044f\u043c\u043e\u0439:  \"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\" \"<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">join<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">map<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">str<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">preorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">expr<\/span><span style=\"color: #ABB2BF\">))))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\" \"<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">join<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">map<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">str<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">postorder<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">expr<\/span><span style=\"color: #ABB2BF\">))))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0432 \u0448\u0438\u0440\u0438\u043d\u0443:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\" \"<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">join<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">map<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">str<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">by_levels<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">expr<\/span><span style=\"color: #ABB2BF\">))))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">evaluate<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">expr<\/span><span style=\"color: #ABB2BF\">))<\/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\">\u043f\u0440\u044f\u043c\u043e\u0439:   * + 2 3 - 7 4\n\u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439: 2 3 + 7 4 - *\n\u0432 \u0448\u0438\u0440\u0438\u043d\u0443: * + - 2 3 7 4\n\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435: 15\n<\/code><\/pre>\n<p>\u041f\u0440\u044f\u043c\u043e\u0439 \u043e\u0431\u0445\u043e\u0434 \u0434\u0430\u043b \u043f\u043e\u043b\u044c\u0441\u043a\u0443\u044e (\u043f\u0440\u0435\u0444\u0438\u043a\u0441\u043d\u0443\u044e) \u0437\u0430\u043f\u0438\u0441\u044c, \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 &#8212; \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u043f\u043e\u043b\u044c\u0441\u043a\u0443\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044e\u0442 \u0441\u0442\u0435\u043a\u043e\u043c. \u042d\u0442\u043e \u0434\u0435\u0440\u0435\u0432\u043e \u0441\u0442\u0440\u043e\u0433\u043e\u0435: \u0443 \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0440\u043e\u0432\u043d\u043e \u0434\u0432\u0430 \u043e\u043f\u0435\u0440\u0430\u043d\u0434\u0430. \u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434 \u0437\u0434\u0435\u0441\u044c \u0434\u0430\u043b \u0431\u044b <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 + 3 * 7 - 4<\/code> &#8212; \u0431\u0435\u0437 \u0441\u043a\u043e\u0431\u043e\u043a \u043e\u043d \u0442\u0435\u0440\u044f\u0435\u0442 \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441\u043a\u043e\u0431\u043a\u0438 \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u044e\u0442 \u043f\u0440\u0438 \u043e\u0431\u0445\u043e\u0434\u0435.<\/p>\n<h2 id=\"s6\">\u041d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0445 \u0434\u0435\u0440\u0435\u0432\u044c\u0435\u0432<\/h2>\n<p>\u0412\u044b\u0431\u043e\u0440 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b \u0438\u0434\u0435\u0442 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438, \u0430 \u043d\u0435 \u043e\u0442 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u044f \u0434\u0435\u0440\u0435\u0432\u0430:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0417\u0430\u0434\u0430\u0447\u0430<\/th>\n<th>\u0427\u0442\u043e \u0432\u0437\u044f\u0442\u044c<\/th>\n<th>\u041f\u0440\u0438\u043c\u0435\u0440<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0411\u044b\u0441\u0442\u0440\u043e \u0434\u043e\u0441\u0442\u0430\u0432\u0430\u0442\u044c \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c<\/td>\n<td>\u0434\u0432\u043e\u0438\u0447\u043d\u0430\u044f \u043a\u0443\u0447\u0430<\/td>\n<td><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\">heapq<\/code> \u0432 Python, <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\">PriorityQueue<\/code> \u0432 Java, \u043f\u043b\u0430\u043d\u0438\u0440\u043e\u0432\u0449\u0438\u043a\u0438 \u0437\u0430\u0434\u0430\u0447<\/td>\n<\/tr>\n<tr>\n<td>\u0425\u0440\u0430\u043d\u0438\u0442\u044c \u043a\u043b\u044e\u0447\u0438 \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0435\u043d\u043d\u043e, \u0438\u0441\u043a\u0430\u0442\u044c \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u044b<\/td>\n<td>\u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435 BST<\/td>\n<td><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\">TreeMap<\/code> \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\">TreeSet<\/code> \u0432 Java, <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\">std::map<\/code> \u0432 C++ (\u043e\u0431\u044b\u0447\u043d\u043e \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e)<\/td>\n<\/tr>\n<tr>\n<td>\u0420\u0430\u0437\u0431\u0438\u0440\u0430\u0442\u044c \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f<\/td>\n<td>\u0434\u0435\u0440\u0435\u0432\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f<\/td>\n<td>\u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u044b, \u043a\u043e\u043c\u043f\u0438\u043b\u044f\u0442\u043e\u0440\u044b (\u0441\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u0431\u044b\u0432\u0430\u0435\u0442 \u0438 \u043d\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u043c)<\/td>\n<\/tr>\n<tr>\n<td>\u0421\u0436\u0438\u043c\u0430\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u0435 \u043f\u0440\u0435\u0444\u0438\u043a\u0441\u043d\u044b\u043c \u043a\u043e\u0434\u043e\u043c<\/td>\n<td>\u0434\u0435\u0440\u0435\u0432\u043e \u0425\u0430\u0444\u0444\u043c\u0430\u043d\u0430<\/td>\n<td>\u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u0432\u043b\u0435\u0432\u043e &#8212; 0, \u0432\u043f\u0440\u0430\u0432\u043e &#8212; 1; \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0432 DEFLATE (zip, gzip, PNG)<\/td>\n<\/tr>\n<tr>\n<td>\u041f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430\u043c<\/td>\n<td>\u0434\u0435\u0440\u0435\u0432\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0439<\/td>\n<td>\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c CART \u0441\u0442\u0440\u043e\u0438\u0442 \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0435 \u0440\u0430\u0437\u0431\u0438\u0435\u043d\u0438\u044f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0415\u0441\u043b\u0438 \u043a\u043b\u044e\u0447\u0438 \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u0434\u0438\u0441\u043a\u0435, \u0430 \u043d\u0435 \u0432 \u043f\u0430\u043c\u044f\u0442\u0438, \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043e\u0431\u044b\u0447\u043d\u043e \u043f\u0440\u043e\u0438\u0433\u0440\u044b\u0432\u0430\u0435\u0442: \u0438\u043d\u0434\u0435\u043a\u0441\u044b \u0421\u0423\u0411\u0414 \u0441\u0442\u0440\u043e\u044f\u0442 \u043d\u0430 B-\u0434\u0435\u0440\u0435\u0432\u044c\u044f\u0445, \u0443 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443 \u0443\u0437\u043b\u0430 \u043c\u043d\u043e\u0433\u043e \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432 \u0438 \u043c\u0435\u043d\u044c\u0448\u0435 \u0447\u0442\u0435\u043d\u0438\u0439 \u0441 \u0434\u0438\u0441\u043a\u0430. \u0414\u043b\u044f \u0442\u043e\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u0438\u0441\u043a\u0430 \u043f\u043e \u043a\u043b\u044e\u0447\u0443 \u0431\u0435\u0437 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0447\u0430\u0449\u0435 \u0445\u0432\u0430\u0442\u0430\u0435\u0442 \u0445\u0435\u0448-\u0442\u0430\u0431\u043b\u0438\u0446\u044b (<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\">dict<\/code>), \u0434\u0435\u0440\u0435\u0432\u043e \u043d\u0443\u0436\u043d\u043e, \u043a\u043e\u0433\u0434\u0430 \u0432\u0430\u0436\u043d\u044b \u043f\u043e\u0440\u044f\u0434\u043e\u043a, \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u0438\u043b\u0438 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u044b.<\/p>\n<h2 id=\"s7\">\u0415\u0441\u043b\u0438 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c<\/h2>\n<p>\u0422\u0438\u043f\u0438\u0447\u043d\u044b\u0435 \u0441\u0438\u043c\u043f\u0442\u043e\u043c\u044b \u0438 \u043f\u0440\u0438\u0447\u0438\u043d\u044b:<\/p>\n<ul>\n<li><strong>RecursionError \u043d\u0430 \u0431\u043e\u043b\u044c\u0448\u043e\u043c \u0434\u0435\u0440\u0435\u0432\u0435.<\/strong> \u0420\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434 \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 \u0443\u0445\u043e\u0434\u0438\u0442 \u043d\u0430 \u0433\u043b\u0443\u0431\u0438\u043d\u0443 n.<\/li>\n<li><strong>\u041a\u043b\u044e\u0447\u0438 \u0442\u0435\u0440\u044f\u044e\u0442\u0441\u044f \u043f\u0440\u0438 \u0432\u0441\u0442\u0430\u0432\u043a\u0435.<\/strong> \u041d\u0435\u0442 \u0432\u0435\u0442\u043a\u0438 \u0434\u043b\u044f \u0440\u0430\u0432\u043d\u044b\u0445 \u043a\u043b\u044e\u0447\u0435\u0439 \u0438\u043b\u0438 \u043d\u0435 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/li>\n<li><strong>\u041f\u043e\u0441\u043b\u0435 \u0443\u0434\u0430\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u043f\u0430\u043b\u043e \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u043e.<\/strong> \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u043e\u0442\u043e\u043c\u043a\u0430\u043c\u0438 \u0443\u0437\u0435\u043b \u0443\u0434\u0430\u043b\u0435\u043d \u0446\u0435\u043b\u0438\u043a\u043e\u043c \u0432\u043c\u0435\u0441\u0442\u043e \u0437\u0430\u043c\u0435\u043d\u044b \u043f\u0440\u0435\u0435\u043c\u043d\u0438\u043a\u043e\u043c.<\/li>\n<\/ul>\n<p>\u041f\u0435\u0440\u0432\u044b\u0439 \u0441\u0438\u043c\u043f\u0442\u043e\u043c \u043b\u0435\u0433\u043a\u043e \u0432\u043e\u0441\u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0441\u0442\u0438 &#8212; \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u044b\u0439 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0439 \u043e\u0431\u0445\u043e\u0434 \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0438\u0437 5000 \u0443\u0437\u043b\u043e\u0432:<\/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\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sys<\/span>\n\n<span style=\"color: #C678DD\">class<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E5C07B\">Node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n    <span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2; font-weight: bold\">__init__<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">self<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">):<\/span>\n        <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">self<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">None<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">None<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">inorder_rec<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">node<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">inorder_rec<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">left<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n        <span style=\"color: #E06C75\">out<\/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: #56B6C2\">.<\/span><span style=\"color: #E06C75\">key<\/span><span style=\"color: #ABB2BF\">)<\/span>\n        <span style=\"color: #E06C75\">inorder_rec<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">node<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E06C75\">root<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">cur<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">k<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5001<\/span><span style=\"color: #ABB2BF\">):<\/span>   <span style=\"color: #7F848E\"># \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e-\u00ab\u0446\u0435\u043f\u043e\u0447\u043a\u0430\u00bb \u0438\u0437 5000 \u0443\u0437\u043b\u043e\u0432<\/span>\n    <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">Node<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">k<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">cur<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">cur<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">right<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u043b\u0438\u043c\u0438\u0442 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0438:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">sys<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">getrecursionlimit<\/span><span style=\"color: #ABB2BF\">())<\/span>\n<span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">[]<\/span>\n<span style=\"color: #E06C75\">inorder_rec<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">root<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043d\u0430 Python 3.14 (\u0444\u0440\u0430\u0433\u043c\u0435\u043d\u0442):<\/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\">\u043b\u0438\u043c\u0438\u0442 \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0438: 1000\nTraceback (most recent call last):\n  ...\nRecursionError: maximum recursion depth exceeded\n<\/code><\/pre>\n<p>\u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 &#8212; \u043d\u0435 \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u0442\u044c \u043b\u0438\u043c\u0438\u0442, \u0430 \u043e\u0431\u0445\u043e\u0434\u0438\u0442\u044c \u0438\u0442\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u043e: \u0444\u0443\u043d\u043a\u0446\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\">inorder<\/code> \u0441\u043e \u0441\u0442\u0435\u043a\u043e\u043c \u0438\u0437 \u0440\u0430\u0437\u0434\u0435\u043b\u0430 \u043f\u0440\u043e BST \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0442\u0435 \u0436\u0435 5000 \u0443\u0437\u043b\u043e\u0432 \u0431\u0435\u0437 \u043e\u0448\u0438\u0431\u043a\u0438. \u041b\u0443\u0447\u0448\u0430\u044f \u0437\u0430\u0449\u0438\u0442\u0430 &#8212; \u043d\u0435 \u0434\u043e\u043f\u0443\u0441\u043a\u0430\u0442\u044c \u0432\u044b\u0440\u043e\u0436\u0434\u0435\u043d\u0438\u044f: \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u0432\u044b\u0441\u043e\u0442\u0430 \u0434\u043b\u044f 5000 \u0443\u0437\u043b\u043e\u0432 &#8212; 13 \u0443\u0440\u043e\u0432\u043d\u0435\u0439, \u0438 \u0443 AVL \u0438\u043b\u0438 \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 \u043e\u043d\u0430 \u0442\u043e\u0433\u043e \u0436\u0435 \u043f\u043e\u0440\u044f\u0434\u043a\u0430, \u0430 \u043d\u0435 5000.<\/p>\n<h2 id=\"s8\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e &#8212; \u0443\u0437\u043b\u044b \u0441 \u043d\u0435 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c \u0434\u0432\u0443\u043c\u044f \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0435\u043d\u043d\u044b\u043c\u0438 \u043f\u043e\u0442\u043e\u043c\u043a\u0430\u043c\u0438; \u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430 \u0438 \u043a\u0443\u0447\u0430 &#8212; \u044d\u0442\u043e \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f \u0441 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u043f\u0440\u0430\u0432\u0438\u043b\u043e\u043c \u043f\u043e\u0440\u044f\u0434\u043a\u0430.<\/li>\n<li>\u041d\u0430\u0437\u0432\u0430\u043d\u0438\u044f \u0432\u0438\u0434\u043e\u0432 \u043f\u0443\u0442\u0430\u044e\u0442\u0441\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0439\u0442\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435: \u0441\u0442\u0440\u043e\u0433\u043e\u0435 (0 \u0438\u043b\u0438 2 \u043f\u043e\u0442\u043e\u043c\u043a\u0430), \u043f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0435 (\u0431\u0435\u0437 \u0434\u044b\u0440 \u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c), \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e\u0435, \u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435.<\/li>\n<li>\u041f\u043e\u0447\u0442\u0438 \u043f\u043e\u043b\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u0443\u0434\u043e\u0431\u043d\u043e \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0432 \u043c\u0430\u0441\u0441\u0438\u0432\u0435 \u043f\u043e \u0438\u043d\u0434\u0435\u043a\u0441\u0430\u043c 2i + 1 \u0438 2i + 2 &#8212; \u0442\u0430\u043a \u0443\u0441\u0442\u0440\u043e\u0435\u043d <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\">heapq<\/code>.<\/li>\n<li>\u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 BST \u0441\u0442\u043e\u044f\u0442 O(h): \u043f\u0440\u0438 \u0431\u0430\u043b\u0430\u043d\u0441\u0435 \u044d\u0442\u043e O(log n), \u043f\u0440\u0438 \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u0432\u0441\u0442\u0430\u0432\u043a\u0435 \u0432\u044b\u0441\u043e\u0442\u0430 \u0440\u0430\u0441\u0442\u0435\u0442 \u0434\u043e n.<\/li>\n<li>\u041f\u043e\u0440\u044f\u0434\u043e\u043a \u043e\u0431\u0445\u043e\u0434\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u044e\u0442 \u043f\u043e\u0434 \u0437\u0430\u0434\u0430\u0447\u0443: in-order \u0434\u043b\u044f \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0438 \u043a\u043b\u044e\u0447\u0435\u0439, post-order \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u043e\u0431\u0445\u043e\u0434 \u0432 \u0448\u0438\u0440\u0438\u043d\u0443 &#8212; \u043f\u043e \u0443\u0440\u043e\u0432\u043d\u044f\u043c \u0447\u0435\u0440\u0435\u0437 \u043e\u0447\u0435\u0440\u0435\u0434\u044c.<\/li>\n<\/ul>\n<h2 id=\"s9\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/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>\u0414\u0432\u043e\u0438\u0447\u043d\u044b\u0435 \u0434\u0435\u0440\u0435\u0432\u044c\u044f &#8212; \u0431\u0430\u0437\u0430 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u0441\u043e\u0431\u0435\u0441\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f\u0445 \u0438 \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0445 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a: \u043e\u0447\u0435\u0440\u0435\u0434\u0438 \u0441 \u043f\u0440\u0438\u043e\u0440\u0438\u0442\u0435\u0442\u043e\u043c, \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0435\u043d\u043d\u044b\u0445 \u0441\u043b\u043e\u0432\u0430\u0440\u0435\u0439, \u043f\u0430\u0440\u0441\u0435\u0440\u043e\u0432 \u0438 \u0441\u0436\u0430\u0442\u0438\u044f. \u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0448\u0430\u0433 \u043f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0438 &#8212; \u0441\u0430\u043c\u043e\u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u0443\u044e\u0449\u0438\u0435\u0441\u044f \u0434\u0435\u0440\u0435\u0432\u044c\u044f (AVL, \u043a\u0440\u0430\u0441\u043d\u043e-\u0447\u0435\u0440\u043d\u044b\u0435) \u0438 \u043e\u0446\u0435\u043d\u043a\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0432 \u0445\u0443\u0434\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435. \u0421\u0438\u0441\u0442\u0435\u043c\u043d\u043e \u044d\u0442\u0438 \u0442\u0435\u043c\u044b \u0441 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438 \u0438 \u0440\u0430\u0437\u0431\u043e\u0440\u043e\u043c \u043a\u043e\u0434\u0430 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u043d\u0430 \u043a\u0443\u0440\u0441\u0435 <a href=\"https:\/\/otus.ru\/lessons\/algorithm\/?int_article=binarnye-dreva&amp;int_place=article&amp;int_variant=v1\">\u00ab\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\u00bb<\/a>. \u041e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u0435\u043c\u044b \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 <a href=\"https:\/\/otus.ru\/events\/?int_article=binarnye-dreva&amp;int_place=article&amp;int_variant=v1\">\u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0443\u0440\u043e\u043a\u0430\u0445 Otus<\/a>.<\/p>\n<\/div>\n<h2 id=\"s10\">FAQ<\/h2>\n<p><strong>\u0427\u0435\u043c \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 \u043f\u043e\u0438\u0441\u043a\u0430?<\/strong><br \/>\n\u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 \u0434\u0435\u0440\u0435\u0432\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0432\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0438\u0441\u043b\u043e \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432. \u0412 \u0434\u0435\u0440\u0435\u0432\u0435 \u043f\u043e\u0438\u0441\u043a\u0430 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: \u0441\u043b\u0435\u0432\u0430 \u043c\u0435\u043d\u044c\u0448\u0438\u0435 \u043a\u043b\u044e\u0447\u0438, \u0441\u043f\u0440\u0430\u0432\u0430 \u0431\u043e\u043b\u044c\u0448\u0438\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u043e \u043d\u0435\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043a\u0430\u0442\u044c \u0437\u0430 O(h).<\/p>\n<p><strong>\u041c\u043e\u0436\u043d\u043e \u043b\u0438 \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0432 BST \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435 \u043a\u043b\u044e\u0447\u0438?<\/strong><br \/>\n\u041c\u043e\u0436\u043d\u043e, \u0435\u0441\u043b\u0438 \u0437\u0430\u0440\u0430\u043d\u0435\u0435 \u0434\u043e\u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c\u0441\u044f: \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0440\u0430\u0432\u043d\u044b\u0435 \u043a\u043b\u044e\u0447\u0438 \u043f\u0440\u0430\u0432\u044b\u043c\u0438 (\u0438\u043b\u0438 \u043b\u0435\u0432\u044b\u043c\u0438) \u043f\u043e\u0442\u043e\u043c\u043a\u0430\u043c\u0438 \u043b\u0438\u0431\u043e \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0432 \u0443\u0437\u043b\u0435 \u0441\u0447\u0435\u0442\u0447\u0438\u043a \u043f\u043e\u0432\u0442\u043e\u0440\u043e\u0432. \u0412 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0432\u044b\u0448\u0435 \u0434\u0443\u0431\u043b\u0438\u043a\u0430\u0442\u044b \u043f\u0440\u043e\u0441\u0442\u043e \u0438\u0433\u043d\u043e\u0440\u0438\u0440\u0443\u044e\u0442\u0441\u044f.<\/p>\n<p><strong>\u041a\u0443\u0447\u0430 &#8212; \u044d\u0442\u043e \u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430?<\/strong><br \/>\n\u041d\u0435\u0442. \u0412 \u043a\u0443\u0447\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u0442\u043e\u043b\u044c\u043a\u043e, \u0447\u0442\u043e \u0440\u043e\u0434\u0438\u0442\u0435\u043b\u044c \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432, \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u043c\u0435\u0436\u0434\u0443 \u043b\u0435\u0432\u044b\u043c \u0438 \u043f\u0440\u0430\u0432\u044b\u043c \u043f\u043e\u0434\u0434\u0435\u0440\u0435\u0432\u043e\u043c \u043d\u0435 \u0437\u0430\u0434\u0430\u043d, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0438\u0441\u043a\u0430\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 \u0432 \u043d\u0435\u0439 \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u0435\u0440\u0435\u0431\u043e\u0440\u043e\u043c.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0414\u0432\u043e\u0438\u0447\u043d\u043e\u0435 (\u0431\u0438\u043d\u0430\u0440\u043d\u043e\u0435) \u0434\u0435\u0440\u0435\u0432\u043e &#8212; \u044d\u0442\u043e \u0438\u0435\u0440\u0430\u0440\u0445\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u0430\u043d\u043d\u044b\u0445, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0443 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0443\u0437\u043b\u0430 \u043d\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0434\u0432\u0443\u0445 \u043f\u043e\u0442\u043e\u043c\u043a\u043e\u0432, \u043f\u0440\u0438\u0447\u0435\u043c \u043e\u043d\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043a\u0430\u043a \u043b\u0435\u0432\u044b\u0439 \u0438 \u043f\u0440\u0430\u0432\u044b\u0439. \u041d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0435\u0440\u0435\u0432\u0430 &#8212; \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u0435 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u0432\u044b\u0431\u0438\u0440\u0430\u0442\u044c \u043e\u0434\u043d\u0443 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0432\u0435\u0442\u0432\u0435\u0439: \u044d\u0442\u043e \u0434\u0430\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u043f\u043e \u043a\u043b\u044e\u0447\u0443 (\u0434\u0435\u0440\u0435\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430), \u0431\u044b\u0441\u0442\u0440\u0443\u044e \u0432\u044b\u0434\u0430\u0447\u0443 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 (\u043a\u0443\u0447\u0430) \u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 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