{"id":1106,"date":"2009-11-25T17:01:25","date_gmt":"2009-11-25T09:01:25","guid":{"rendered":"http:\/\/www.slyar.com\/blog\/?p=1106"},"modified":"2022-07-03T15:47:00","modified_gmt":"2022-07-03T22:47:00","slug":"poj-2533-cpp","status":"publish","type":"post","link":"http:\/\/www.slyar.com\/blog\/poj-2533-cpp.html","title":{"rendered":"POJ 2533 Longest Ordered Subsequence C++\u7248"},"content":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a<span style=\"color: #0000ff;\">\u59dc\u5357(Slyar) <\/span>\u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (<a title=\"Slyar\" href=\"http:\/\/www.slyar.com\" target=\"_blank\" rel=\"noopener\">www.slyar.com<\/a>) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002<\/p>\n<p>\u7ea0\u7ed3DP\uff0c\u4ece\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u5f00\u59cb\u3002<\/p>\n<p><!--more--><\/p>\n<p><span style=\"color: #0000ff;\">Description<\/span><\/p>\n<p>A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1, a2, ..., aN) be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).\n\nYour program, when given the numeric sequence, must find the length of its longest ordered subsequence.\n\n<span style=\"color: #0000ff;\">Input<\/span><\/p>\n<p>The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 &lt;= N &lt;= 1000<\/p>\n<p><span style=\"color: #0000ff;\">Output<\/span><\/p>\n<p>Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.<\/p>\n<p><span style=\"color: #0000ff;\">Sample Input<\/span><\/p>\n<p>7<br \/>\n1 7 3 5 9 4 8<\/p>\n<p><span style=\"color: #0000ff;\">Sample Output<\/span><\/p>\n<p>4<\/p>\n<p><span style=\"color: #ff0000;\">Slyar:\u5c5e\u4e8e\u7b80\u5355\u7684\u7ecf\u5178\u7684DP\uff0c\u6c42\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217(LIS)\u3002\u5148\u7814\u7a76\u4e86O(n^2)\u7684\u601d\u8def\u3002<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u4ee4A[i]\u8868\u793a\u8f93\u5165\u7b2ci\u4e2a\u5143\u7d20\uff0cD[i]\u8868\u793a\u4eceA[1]\u5230A[i]\u4e2d\u4ee5A[i]\u7ed3\u5c3e\u7684\u6700\u957f\u5b50\u5e8f\u5217\u957f\u5ea6\u3002\u5bf9\u4e8e\u4efb\u610f\u76840 &lt;\u00a0 j &lt;= i-1\uff0c\u5982\u679cA(j) &lt; A(i)\uff0c\u5219A(i)\u53ef\u4ee5\u63a5\u5728A(j)\u540e\u9762\u5f62\u6210\u4e00\u4e2a\u4ee5A(i)\u7ed3\u5c3e\u7684\u65b0\u7684\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u3002\u5bf9\u4e8e\u6240\u6709\u7684 0 &lt;\u00a0 j &lt;= i-1\uff0c\u6211\u4eec\u9700\u8981\u627e\u51fa\u5176\u4e2d\u7684\u6700\u5927\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #ff0000;\">DP\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b:<\/span><\/p>\n<p><span style=\"color: #ff0000;\">D[i] = max{1, D[j] + 1} (j = 1, 2, 3, ..., i-1 \u4e14 A[j] &lt; A[i])<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u89e3\u91ca\u4e00\u4e0b\u8fd9\u4e2a\u65b9\u7a0b\uff0ci\uff0c j\u5728\u8303\u56f4\u5185:<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u5982\u679c A[j] &lt; A[i] \uff0c\u5219D[i] = D[j] + 1<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u5982\u679c A[j] &gt;= A[i] \uff0c\u5219D[i] = 1<\/span><\/p>\n<pre lang=\"c\" line=\"1\">\r\n#include <iostream>\r\n#define SIZE 1001\r\n\r\nusing namespace std;\r\n\r\nint main()\r\n{\r\n    int i, j, n, max;\r\n    \/* a[i]\u8868\u793a\u8f93\u5165\u7b2ci\u4e2a\u5143\u7d20 *\/\r\n    int a[SIZE];\r\n    \/* d[i]\u8868\u793a\u4ee5a[i]\u7ed3\u5c3e\u7684\u6700\u957f\u5b50\u5e8f\u5217\u957f\u5ea6 *\/\r\n    int d[SIZE];\r\n    \r\n    cin >> n;\r\n    for (i = 1; i <= n; i++)\r\n    {\r\n        cin >> a[i];\r\n    }\r\n    \r\n    max = 0;\r\n    for (i = 1; i <= n; i++)\r\n    {\r\n        d[i] = 1;\r\n        for (j = 1; j <= i - 1; j++)\r\n        {\r\n            if (a[j] < a[i] && d[i] < d[j] + 1)\r\n            {\r\n                d[i] = d[j] + 1;\r\n            }\r\n        }\r\n        \/* \u8bb0\u5f55\u6700\u957f\u5b50\u5e8f\u5217 *\/\r\n        if (d[i] > max) max = d[i];\r\n    }\r\n    \r\n    cout << max << endl;\r\n    \r\n    \/\/system(\"pause\");\r\n    return 0;\r\n}\r\n<\/pre>\n<p>\u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1a<a href=\"http:\/\/www.slyar.com\/blog\">Slyar Home<\/a> &raquo; <a href=\"http:\/\/www.slyar.com\/blog\/poj-2533-cpp.html\">POJ 2533 Longest Ordered Subsequence C++\u7248<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a\u59dc\u5357(Slyar) \u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (www.slyar.com) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002 \u7ea0\u7ed3DP\uff0c\u4ece\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u5f00\u59cb\u3002 \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1aSlyar Home &raquo; POJ 2533 Longest Ordered [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1103],"tags":[1006],"class_list":["post-1106","post","type-post","status-publish","format-standard","hentry","category-acm-oj-solution","tag-poj"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - 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