# 题目

## 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

15

# 题解

`dp[i] = max(dp[i-1]+a[i] , a[i])`

# 代码

```/*
By:OhYee
Github:OhYee
Blog:http://www.oyohyee.com/
Email:oyohyee@oyohyee.com

かしこいかわいい？
エリーチカ！

*/
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <string>
#include <iostream>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <functional>
using namespace std;
const int INF = 0x7FFFFFFF;
const int maxn = 105;
const int delta[] = {1,-1,0,0};

int Map[maxn][maxn];
int dp[maxn];
int sum[maxn][maxn];

int n;

int DP(int s,int v) {
int Max = -INF;
for(int i = 1;i <= n;i++) {
int t = sum[v][i] - sum[s][i];
dp[i] = max(dp[i - 1] + t,t);
Max = max(Max,dp[i]);
}
return Max;
}

bool Do() {
if(scanf("%d",&n) == EOF)
return false;

for(int i = 1;i <= n;i++)
for(int j = 1;j <= n;j++) {
scanf("%d",&Map[i][j]);
sum[i][j] = sum[i - 1][j] + Map[i][j];
}
int Max = -INF;
for(int i = 1;i <= n;i++)
for(int j = 0;j < i;j++) {
Max = max(Max,DP(j,i));
}

printf("%d\n",Max);

return true;
}

int main() {
while(Do());
return 0;
}
```