zoj 1074 To the Max 最大子矩阵之和

//这题开始方法想错了，调了半天，才发现动规方程列不正确
//这题可以看做一维数组的连续子串最大和的扩展
//方法是把二维转换成一维，再用一维的动规方程求
//把多行合并成一行求
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

const int N = 105;
const int INF = 1000000000;

int num[N][N];
int sum[N];
int dp[N];

int n, ans;

void maxsubsum()
{
	dp[0] = sum[0];
	for (int i = 1; i < n; i++)
	{
		dp[i] = max(dp[i-1]+sum[i], sum[i]);
		ans = max(ans, dp[i]);
	}
}

int main()
{
	while (scanf("%d", &n) != EOF)
	{
		ans = -INF;
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				scanf("%d", &num[i][j]);

		for (int i = 0; i < n ; i++)
		{
			for (int j = i; j < n; j++)
			{
				memset(sum, 0, sizeof(sum));
				//把第i行到第j行压缩成一行
				for (int s = 0; s < n; s++)
				for (int k = i; k <= j; k++)
					sum[s] += num[k][s];

				//求一维数组连续子串和的最大值
				maxsubsum();
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}