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.

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

## Sample Output

```15

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;`
` ``}`
` ``}`