TO THE MAX

http://acm.sdibt.edu.cn/JudgeOnline/problem.php?id=1207

Time Limit: 1 Sec  Memory Limit: 64 MBSubmit: 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所有子矩阵中最大的

解题思路：

1.最大子矩阵问题，可以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对应项中

  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;
    }
}