{"id":5335,"date":"2020-12-02T22:57:43","date_gmt":"2020-12-02T19:57:43","guid":{"rendered":"http:\/\/java.mazurok.com\/?p=5335"},"modified":"2020-12-06T15:58:42","modified_gmt":"2020-12-06T12:58:42","slug":"e-olimp-8536-%d0%b7%d0%b0%d0%bf%d0%be%d0%b2%d0%bd%d0%b5%d0%bd%d0%bd%d1%8f-%d1%81%d0%bc%d1%83%d0%b3%d0%b8-3-times-n","status":"publish","type":"post","link":"https:\/\/java.mazurok.com\/?p=5335","title":{"rendered":"e-olimp 8536. \u0417\u0430\u043f\u043e\u0432\u043d\u0435\u043d\u043d\u044f \u0441\u043c\u0443\u0433\u0438 $3 \\times n$"},"content":{"rendered":"<blockquote><p><strong>\u0412\u043d\u0438\u043c\u0430\u043d\u0438\u0435<\/strong>: \u0417\u0430\u0434\u0430\u0447\u0430 \u043d\u0430 \u0441\u0430\u0439\u0442\u0435 e-olymp \u0431\u044b\u043b\u0430 \u0437\u0430\u043c\u0435\u043d\u0435\u043d\u0430 \u043d\u0430 \u0434\u0440\u0443\u0433\u0443\u044e. \u0422\u0435\u043f\u0435\u0440\u044c \u0442\u0430\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u0442\u0430\u043c \u043d\u0435\u0442.<\/p><\/blockquote>\n<h1>\u0417\u0430\u0434\u0430\u0447\u0430<\/h1>\n<p>\u0421\u043c\u0443\u0433\u0443 \u0432\u0438\u0441\u043e\u0442\u043e\u044e $3$ \u0441\u043c \u0456 \u0448\u0438\u0440\u0438\u043d\u043e\u044e $n$ \u0441\u043c \u0441\u0443\u0446\u0456\u043b\u044c\u043d\u043e \u0437\u0430\u043f\u043e\u0432\u043d\u0435\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0438\u043a\u0430\u043c\u0438 $3 \\times 1$ \u0442\u0430 $1 \\times 3$ \u0441\u043c. \u0421\u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u043c\u043e\u0436\u043d\u0430 \u0457\u0457 \u0437\u0430\u043f\u043e\u0432\u043d\u0438\u0442\u0438? \u0420\u0456\u0437\u043d\u0456 \u0441\u043f\u043e\u0441\u043e\u0431\u0438 \u2013 \u0446\u0435 \u0440\u0456\u0437\u043d\u0456 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456 \u0432\u043a\u0430\u0437\u0430\u043d\u0438\u0445 \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0438\u043a\u0456\u0432 \u0442\u0430 \u0457\u0445 \u0440\u0456\u0437\u043d\u0456 \u0440\u043e\u0437\u0442\u0430\u0448\u0443\u0432\u0430\u043d\u043d\u044f.<\/p>\n<h1>\u0412\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456<\/h1>\n<p>\u041e\u0434\u043d\u0435 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u0435 \u0447\u0438\u0441\u043b\u043e $n$ $(1 \\leqslant n \\leqslant 50)$.<\/p>\n<h1>\u0412\u0438\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456<\/h1>\n<p>\u0412\u0438\u0432\u0435\u0441\u0442\u0438 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0441\u043f\u043e\u0441\u043e\u0431\u0456\u0432, \u044f\u043a\u0438\u043c\u0438 \u043c\u043e\u0436\u043d\u0430 \u0437\u0430\u043f\u043e\u0432\u043d\u0438\u0442\u0438 \u0441\u043c\u0443\u0433\u0443.<\/p>\n<h1>\u0422\u0435\u0441\u0442\u0438<\/h1>\n<table>\n<tbody>\n<tr>\n<th>\u0412\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456<\/th>\n<th>\u0412\u0438\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456<\/th>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>60<\/td>\n<\/tr>\n<tr>\n<td>50<\/td>\n<td>122106097<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>\u041a\u043e\u0434 \u2116 1<\/h1>\n<pre class=\"lang:java decode:true \" title=\"e-olymp 8536\">import java.util.Scanner;\r\n\r\nclass Main {\r\n\tpublic static void main (String[] args) {\r\n\t    Scanner sc = new Scanner(System.in);\r\n        int n = sc.nextInt();\r\n\t    int[] F = new int[51];\r\n\t    F[0] = 0;\r\n\t    F[1] = 1;\r\n\t    F[2] = 1;\r\n\t    F[3] = 2;\r\n\t    F[4] = 3;\r\n\t    for(int i = 5; i &lt;= n; i++) {\r\n\t       F[i] = F[i-2] + F[i-3] + F[i-4];\r\n\t    }\r\n\t    System.out.println(F[n]);\r\n\t}\r\n}<\/pre>\n<h1>\u0420\u0456\u0448\u0435\u043d\u043d\u044f 1<\/h1>\n<p>\u0426\u0435 \u0437\u0430\u0432\u0434\u0430\u043d\u043d\u044f \u043d\u0430 \u0434\u0438\u043d\u0430\u043c\u0456\u0447\u043d\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443\u0432\u0430\u043d\u043d\u044f, \u0442\u043e\u043c\u0443 \u0441\u043f\u043e\u0447\u0430\u0442\u043a\u0443 \u043d\u0430\u043c \u043f\u043e\u0442\u0440\u0456\u0431\u043d\u043e \u0440\u043e\u0437\u0431\u0438\u0442\u0438 \u0446\u044e \u0437\u0430\u0434\u0430\u0447\u0443 \u043d\u0430 \u0434\u0435\u043a\u0456\u043b\u044c\u043a\u0430 \u043f\u0440\u043e\u0441\u0442\u0438\u0445. \u0422\u0440\u0435\u0431\u0430 \u043f\u043e\u0440\u0430\u0445\u0443\u0432\u0430\u0442\u0438 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0441\u043f\u043e\u0441\u043e\u0431\u0456\u0432 \u0434\u043b\u044f \u0447\u043e\u0442\u0438\u0440\u044c\u043e\u0445 \u043f\u0435\u0440\u0448\u0438\u0445 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0456\u0432 \u043c\u0430\u0441\u0438\u0432\u0443. \u042f\u043a\u0449\u043e \u0440\u0430\u0445\u0443\u0432\u0430\u0442\u0438 \u0434\u0430\u043b\u0456, \u0442\u043e \u043c\u0438 \u043f\u043e\u043c\u0456\u0442\u0438\u043c\u043e, \u0449\u043e \u043a\u043e\u0436\u043d\u0435 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043e\u0442\u0440\u0438\u043c\u0443\u0454\u0442\u044c\u0441\u044f \u0437\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u044e  <span class=\"lang:java decode:true  crayon-inline \">F[i] = F[i-2] + F[i-3] + F[i-4]<\/span>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/java.mazurok.com\/wp-content\/uploads\/5836-e-olymp.svg\" alt=\"\" width=\"800\" height=\"400\" class=\"alignnone size-medium wp-image-5337\" role=\"img\" \/><\/p>\n<h1>\u041a\u043e\u0434 \u2116 2<\/h1>\n<pre class=\"lang:java decode:true   \" title=\"e-olymp 8536\">import java.util.Scanner;\r\n\r\npublic class Main {\r\n\tpublic static int[] F = new int[51];\r\n\tpublic static int numberOfWays(int n){\r\n\t\tF[0] = 0;\r\n\t\tF[1] = 1;\r\n\t\tF[2] = 1;\r\n\t\tF[3] = 2;\r\n\t\tF[4] = 3;\r\n\t    if(F[n] &gt; 0) {\r\n    \t\treturn F[n];\r\n\t\t} else {\r\n    \t\tF[n] = numberOfWays(n-2) + numberOfWays(n-3) + numberOfWays(n-4);\r\n\t\t}\r\n\t\treturn F[n];\r\n\t}\r\n\tpublic static void main (String[] args){\r\n\t    Scanner sc = new Scanner(System.in);\r\n        int n = sc.nextInt();\r\n\t    System.out.println(numberOfWays(n));\r\n\t}\r\n}<\/pre>\n<h1>\u0420\u0456\u0448\u0435\u043d\u043d\u044f 2<\/h1>\n<p>\u0422\u0430\u043a\u043e\u0436 \u0434\u043b\u044f \u0440\u0456\u0448\u0435\u043d\u043d\u044f \u0446\u0456\u0454\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u043c\u043e\u0436\u043d\u0430 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u0440\u0435\u043a\u0443\u0440\u0441\u0456\u044e. \u041f\u0440\u0438 \u0432\u0438\u043a\u043b\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 \u043c\u0438 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u044f\u0454\u043c\u043e, \u0447\u0438 \u0454 \u0432 \u043f\u0430\u043c&#8217;\u044f\u0442\u0456 \u0446\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f. \u042f\u043a\u0449\u043e \u0442\u0430\u043a\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043d\u0435 \u043c\u0430\u0454, \u0442\u043e \u043c\u0438 \u0439\u043e\u0433\u043e \u0440\u0430\u0445\u0443\u0454\u043c\u043e. \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c \u043c\u0438 \u0443\u043d\u0438\u043a\u0430\u0454\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f \u0437\u0430\u0439\u0432\u043e\u0457 \u043f\u0430\u043c&#8217;\u044f\u0442\u0456.<\/p>\n<h1>\u041f\u043e\u0441\u0438\u043b\u0430\u043d\u043d\u044f<\/h1>\n<p>\u041a\u043e\u0434 \u0437\u0430\u0434\u0430\u0447\u0456 \u2116 1 \u043d\u0430 <a href=\"https:\/\/ideone.com\/s7c53r\">Ideone<\/a><br \/>\n\u041a\u043e\u0434 \u0437\u0430\u0434\u0430\u0447\u0456 \u2116 2 \u043d\u0430 <a href=\"https:\/\/ideone.com\/SutVZt\">Ideone<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412\u043d\u0438\u043c\u0430\u043d\u0438\u0435: \u0417\u0430\u0434\u0430\u0447\u0430 \u043d\u0430 \u0441\u0430\u0439\u0442\u0435 e-olymp \u0431\u044b\u043b\u0430 \u0437\u0430\u043c\u0435\u043d\u0435\u043d\u0430 \u043d\u0430 \u0434\u0440\u0443\u0433\u0443\u044e. \u0422\u0435\u043f\u0435\u0440\u044c \u0442\u0430\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u0442\u0430\u043c \u043d\u0435\u0442. \u0417\u0430\u0434\u0430\u0447\u0430 \u0421\u043c\u0443\u0433\u0443 \u0432\u0438\u0441\u043e\u0442\u043e\u044e $3$ \u0441\u043c \u0456 \u0448\u0438\u0440\u0438\u043d\u043e\u044e $n$ \u0441\u043c \u0441\u0443\u0446\u0456\u043b\u044c\u043d\u043e \u0437\u0430\u043f\u043e\u0432\u043d\u0435\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0438\u043a\u0430\u043c\u0438 $3 \\times 1$ \u0442\u0430 $1 \\times 3$ \u0441\u043c. \u0421\u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u043c\u043e\u0436\u043d\u0430 \u0457\u0457 \u0437\u0430\u043f\u043e\u0432\u043d\u0438\u0442\u0438? \u0420\u0456\u0437\u043d\u0456 \u0441\u043f\u043e\u0441\u043e\u0431\u0438 \u2013 \u0446\u0435 \u0440\u0456\u0437\u043d\u0456 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456 \u0432\u043a\u0430\u0437\u0430\u043d\u0438\u0445 \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0438\u043a\u0456\u0432 \u0442\u0430 \u0457\u0445 \u0440\u0456\u0437\u043d\u0456 \u0440\u043e\u0437\u0442\u0430\u0448\u0443\u0432\u0430\u043d\u043d\u044f. \u0412\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456 \u041e\u0434\u043d\u0435 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u0435 &hellip; <a href=\"https:\/\/java.mazurok.com\/?p=5335\" class=\"more-link\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":146,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,25],"tags":[348,517,565],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/5335"}],"collection":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5335"}],"version-history":[{"count":8,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/5335\/revisions"}],"predecessor-version":[{"id":5387,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/5335\/revisions\/5387"}],"wp:attachment":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}