最大子矩阵和

/*
 * =====================================================================================
 *       Frowlename:  35.c
 *    Descrrowptrowon:  求最大子矩阵的和
 *        Created:  03/06/2011 10:51:01 AM
 *         Author:  BruceJrowang (zcolumu-cn.appspot.com), bruce.columrowang1986@gmarowl.com
 * =====================================================================================
 */

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>

//算出二维数组中start行到end行之间，colum列之间的最大和（类似于求一维数组的最大和）
int MaxSum(int** F , int start , int end ,int len){
    int colum ; 
    int maxSum = -100;
    int nowSum = 0;

    assert(start >= 1 && end >= 1);

    for(colum = 1; colum <= len ; colum++){
        nowSum += F[end][colum] - F[end][colum-1] - F[start-1][colum] ;
        if(nowSum < 0 )
            nowSum = 0 ;
        else if(nowSum > maxSum)
            maxSum = nowSum;
    }
    return maxSum;
}
// malloc space for the 2-dimension array
int** mallocFor2Array(int** array , int row , int colum){
    int loop ;
    array = malloc(sizeof(int*) * (row + 1));
    assert(array);

    for(loop = 0 ; loop <= row ; loop++){
        *(array+loop) = malloc(sizeof(int) * (colum+1) ) ; 
        assert(*(array+loop));
    }

    return array;
    
}
//initial the sum of the subarray which is from array[0][0] to the array[i][j]
void initFArray(int** F , int** array , int row , int colum){
    int n , m ;
    for(n = 0 ; n <= row ; n++)
        F[n][0] = 0 ;
    for(m = 0 ; m <= colum ; m++)
        F[0][m] = 0;

    for(n = 1 ; n <= row ; n++)
        for(m = 1 ; m <= colum ; m++)
            F[n][m] = F[n][m-1] + F[n-1][m] + array[n][m] - F[n-1][m-1];
}

int main(){
    //store the number of the two-dimension matrix
    int **array = NULL ; 
    //store the number of the F[i][j] which is the sum of the sub-matrix array[1][1] to the array[i][j]
    int **F = NULL;
    // n is the row of the array ,and m is the colum of the array
    int n , m;
    // for row loop
    int row;
    //for colum loop
    int colum;
    int start = 1 ,end = 1;
    //the max sum of the sub-array
    int maxSum = 0;

    scanf("%d %d",&n,&m);
    
    array = mallocFor2Array(array , n+1 , m+1);
    F = mallocFor2Array(F , n+1 , m+1);

    for(colum = 0 ; colum < n ; colum++)
        for(row = 0 ; row < m ; row++){
            scanf("%d", &array[colum+1][row+1]);
        }

    initFArray(F ,array , n , m);

//list all the situation and get the maxSum
    for(start = 1 ; start <= n ; start++)
        for(end = start ; end <= n; end++){
            int sum = MaxSum(F , start , end , m);
            if(sum > maxSum)
                maxSum = sum;
        }

    printf("%d",maxSum);
    return 0 ;
}

测试数据：
4 4
1 2 3 4
-3 6 -7 9
11 -2 6 8
21 -9 3 -1

输出最大和为52