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  • TO THE MAX

    http://acm.sdibt.edu.cn/JudgeOnline/problem.php?

    id=1207

    Time Limit: 1 Sec  Memory Limit: 64 MB
    Submit: 6  Solved: 6
    [Submit][STATUS][DISCUSS]

    Description

    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. As an example, the maximal sub-rectangle of the array: 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2 is in the lower left corner: 9 2 -4 1 -1 8 and has a sum of 15.

    Input

    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].

    Output

    Output the sum of the maximal sub-rectangle.

    Sample Input

    4
    0 -2 -7 0
    9 2 -6 2
    -4 1 -4  1
    -1 8  0 -2

    Sample Output

    15
    
    题目大意:
    从一个输入的矩阵中找出一个子矩阵,这个子矩阵的和是该矩阵的全部子矩阵中最大的
    
    解题思路:
    1.最大子矩阵问题,能够转换为最大子段和问题
    2.设置一个大小为N的一维数组,然后将矩阵中同一列的若干数合并到该一维数组的相应项中
      问题就转换成求该一维数组的最大子段和问题
    3.最大子段和问题核心代码:
    for(k=1;k<=n;k++)
    {
    if(sum+dp[k]<0)
    sum=0;
    else
    {
    sum+=dp[k];
    if(max<sum)
    max=sum;
    }
    }
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  • 原文地址:https://www.cnblogs.com/jzssuanfa/p/6757853.html
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