最大子矩阵和

题目链接：http://acm.hust.edu.cn/vjudge/contest/view.action?cid=87125#problem/F

题目：

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

题意：
求矩阵中和最大的小矩阵，输出该和。
分析：
   把第j列前i个数的和放入a[i][j]中，求第i行到第j行之间的最大和矩阵的时候，就以i行和j行之间的同一列的数字的和为累加数字进行比较，然后dp求这个数列的最大和连续子序列。

 1 #include<iostream> 
 2 #include<cstring>  
 3 using namespace std;
 4 int a[105][105];
 5 int main()
 6 {
 7     int n,i,j,x,Max;
 8    while(cin>>n)
 9    {  
10       Max=0;
11     memset(a,0,sizeof(a));
12     for(i=1;i<=n;i++)
13     {
14         for(j=1;j<=n;j++)
15         {   
16             cin>>x;
17          a[i][j]=a[i-1][j]+x;
18         }
19     }
20     for(i=1;i<=n;i++)
21     {  
22         for(j=i;j<=n;j++)
23         {
24            int    sum=0;
25             for(int k=1;k<=n;k++)
26             {
27               x=a[j][k]-a[i-1][k];
28               sum=sum+x;
29               if(sum>Max)
30                   Max=sum;
31               if(sum<0)  sum=0;
32             }
33           }    
34     }
35    cout<<Max<<endl;
36 }
37     return 0;
38  }

最大子矩阵和

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