To The Max

　　Problem Description

　　Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 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 x 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

　　题目我起先用暴力法来解答，不过，通不过，超时，后来参考了一下别人的思想吧！没想到这道题还可以用动归的方法解答，很吃惊啊！

　　代码如下：

　　[cpp]

　　//这个程序可以求出m*n的矩阵某一块的最大值

　　//这种搜索算法没有错误！但是超时，因此还要进一步优化算法！