{"id":1111,"date":"2009-11-28T15:08:40","date_gmt":"2009-11-28T07:08:40","guid":{"rendered":"http:\/\/www.slyar.com\/blog\/?p=1111"},"modified":"2022-07-03T15:47:00","modified_gmt":"2022-07-03T22:47:00","slug":"poj-1050-cpp","status":"publish","type":"post","link":"http:\/\/www.slyar.com\/blog\/poj-1050-cpp.html","title":{"rendered":"POJ 1050 To the Max 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>DP\uff0c\u6700\u5927\u5b50\u6bb5\u548c\uff0c\u6700\u5927\u5b50\u77e9\u9635\u548c<\/p>\n<p><!--more--><\/p>\n<p><span style=\"color: #0000ff;\">Description<\/span><\/p>\n<p>Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.<br \/>\nAs an example, the maximal sub-rectangle of the array:<\/p>\n<p>0 -2 -7 0<br \/>\n9 2 -6 2<br \/>\n-4 1 -4 1<br \/>\n-1 8 0 -2<br \/>\nis in the lower left corner:<\/p>\n<p>9 2<br \/>\n-4 1<br \/>\n-1 8<br \/>\nand has a sum of 15.<\/p>\n<p><span style=\"color: #0000ff;\">Input<\/span><\/p>\n<p>The input consists of an N * N array of integers. The input begins with a single positive integer N on a line by itself, indicating the size of the square two-dimensional array. This is followed by N^2 integers separated by whitespace (spaces and newlines). These are the N^2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in the second row, left to right, etc. N may be as large as 100. The numbers in the array will be in the range [-127,127].<\/p>\n<p><span style=\"color: #0000ff;\">Output<\/span><\/p>\n<p>Output the sum of the maximal sub-rectangle.<\/p>\n<p><span style=\"color: #0000ff;\">Sample Input<\/span><\/p>\n<p>4<br \/>\n0 -2 -7 0 9 2 -6 2<br \/>\n-4 1 -4\u00a0 1 -1<br \/>\n8\u00a0 0 -2<\/p>\n<p><span style=\"color: #0000ff;\">Sample Output<\/span><\/p>\n<p>15<\/p>\n<p><span style=\"color: #ff0000;\">Slyar:\u7ed9\u51fan*n\u7684\u77e9\u9635\uff0c\u6c42\u548c\u6700\u5927\u7684\u5b50\u77e9\u9635\u3002<\/span><\/p>\n<p><span style=\"color: #ff0000;\">1\u3001\u9996\u5148\u8003\u8651\u4e00\u7ef4\u7684\u6700\u5927\u5b50\u6bb5\u548c\u95ee\u9898\uff0c\u7ed9\u51fa\u4e00\u4e2a\u5e8f\u5217a[0]\uff0ca[1]\uff0ca[2]...a[n]\uff0c\u6c42\u51fa\u8fde\u7eed\u7684\u4e00\u6bb5\uff0c\u4f7f\u5176\u603b\u548c\u6700\u5927\u3002<\/span><\/p>\n<p><span style=\"color: #ff0000;\">a[i]\u8868\u793a\u7b2ci\u4e2a\u5143\u7d20<br \/>\ndp[i]\u8868\u793a\u4ee5a[i]\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6bb5\u548c<\/span><\/p>\n<p><span style=\"color: #ff0000;\">dp[i] = max{a[i], dp[i-1] + a[i]}<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u89e3\u91ca\u4e00\u4e0b\u65b9\u7a0b:<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u5982\u679cdp[i-1] &gt; 0\uff0c\u5219 dp[i] = dp[i-1] + a[i]<br \/>\n\u5982\u679cdp[i-1] &lt; 0\uff0c\u5219 dp[i] = a[i]<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u56e0\u4e3a\u4e0d\u7528\u8bb0\u5f55\u4f4d\u7f6e\u4fe1\u606f\uff0c\u6240\u4ee5dp[]\u53ef\u4ee5\u7528\u4e00\u4e2a\u53d8\u91cfdp\u4ee3\u66ff:<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u5982\u679cdp &gt; 0\uff0c\u5219dp += a[i]<br \/>\n\u5982\u679cdp &lt; 0\uff0c\u5219dp = a[i]<\/span><\/p>\n<p><span style=\"color: #ff0000;\">2\u3001\u8003\u8651\u4e8c\u7ef4\u7684\u6700\u5927\u5b50\u77e9\u9635\u95ee\u9898<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u77e9\u9635\u538b\u7f29\u628a\u4e8c\u7ef4\u7684\u95ee\u9898\u8f6c\u5316\u4e3a\u4e00\u7ef4\u7684\u6700\u5927\u5b50\u6bb5\u548c\u95ee\u9898\u3002\u56e0\u4e3a\u662f\u77e9\u9635\u548c\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e2a\u77e9\u5f62\u7684\u9ad8\u538b\u7f29\u62101\uff0c\u7528\u52a0\u6cd5\u5c31\u884c\u4e86\u3002<\/span><\/p>\n<p><span style=\"color: #ff0000;\">\u6069\uff0c\u5176\u5b9e\u8fd9\u4e2a\u9700\u8981\u81ea\u5df1\u753b\u56fe\u7406\u89e3\uff0c\u6211\u7684\u6ce8\u91ca\u91cc\u5199\u5f97\u5f88\u8be6\u7ec6\u4e86\uff0c\u81ea\u5df1\u770b\u5427\u3002<\/span><\/p>\n<pre lang=\"c\" line=\"1\">\r\n#include <iostream>\r\n#define SIZE 101\r\n\r\nusing namespace std;\r\n\r\nint a[SIZE][SIZE];\r\n\r\n\/* \u6700\u5927\u5b50\u6bb5\u548c *\/\r\nint MaxSubArray(int n, int* a)\r\n{\r\n    int max = 0;\r\n    int b = 0;\r\n    for (int i = 0; i < n; i++)\r\n    {\r\n        if (b > 0) b += a[i];\r\n        else b = a[i];\r\n        if (b > max) max = b;\r\n    }\r\n    return max;\r\n}\r\n\r\n\/* \u6700\u5927\u5b50\u77e9\u9635\u548c *\/\r\nint MaxSubMatrix(int m, int n)\r\n{\r\n    int i, j, k, sum;\r\n    int max = 0;\r\n    int b[SIZE];\r\n    \/* i\u4e3a\u8d77\u59cb\u884c *\/\r\n    for (i = 0; i < m; i++)\r\n    {\r\n        \/* \u8d77\u59cb\u884c\u6539\u53d8\u624d\u521d\u59cb\u5316b[] *\/\r\n        for (k = 0; k < n; k++)\r\n        {\r\n            b[k] = 0;\r\n        }\r\n        \r\n        \/* \u4ece\u7b2ci\u884c\u52a0\u5230\u6700\u540e\u4e00\u884c *\/\r\n        for (j = i; j < m; j++)\r\n        {\r\n            \/* \u6bcf\u6b21\u628a\u7b2cj\u884c\u7684\u6570\u90fd\u52a0\u8d77\u6765 *\/\r\n            for (k = 0; k < n; k++)\r\n            {\r\n                b[k] += a[j][k];\r\n            }\r\n            \r\n            \/* \u6c42\u51fa\u52a0\u548c\u7684\u6700\u5927\u5b50\u6bb5\u548c *\/\r\n            sum = MaxSubArray(k, b);\r\n            if (sum > max)\r\n            {\r\n                max = sum;\r\n            }\r\n        }\r\n    }\r\n    return max;\r\n}\r\n\r\nint main()\r\n{\r\n    int n;\r\n    cin >> n;\r\n    for (int i = 0; i < n; i++)\r\n    {\r\n        for (int j = 0; j < n; j++)\r\n        {\r\n            cin >> a[i][j];\r\n        }\r\n    }\r\n    cout << MaxSubMatrix(n, n) << endl;\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-1050-cpp.html\">POJ 1050 To the Max 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 DP\uff0c\u6700\u5927\u5b50\u6bb5\u548c\uff0c\u6700\u5927\u5b50\u77e9\u9635\u548c \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1aSlyar Home &raquo; POJ 1050 To the Max C++\u7248<\/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-1111","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 - aioseo.com -->\n\t<meta name=\"description\" content=\"POJ 1050 To the Max C++\u7248\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Slyar\"\/>\n\t<meta name=\"keywords\" content=\"slyar,poj,pku,1050,to the max,c++,\u89e3\u9898\u62a5\u544a,\u9898\u89e3\" \/>\n\t<link rel=\"canonical\" href=\"http:\/\/www.slyar.com\/blog\/poj-1050-cpp.html\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.2.1\" \/>\n\t\t<meta property=\"og:locale\" content=\"zh_CN\" \/>\n\t\t<meta property=\"og:site_name\" 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