poj1050

To the Max

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 39081		Accepted: 20639

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

/* 
 * File:   main.cpp
 * Author: liaoyu <liaoyu@whu.edu.cn>
 *
 * Created on April 1, 2014, 5:34 PM
 */

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <cmath>
#include <algorithm>
using namespace std;

int a[105][105];

int maxSubArray(int n, int* a)
{
    int max = 0x80000000;
    int b = a[0];
    for (int i = 1; i < n; i++) {
        if (b > 0)b += a[i];
        else b = a[i];
        if (b > max)max = b;
    }
    return max;
}
int b[105];

int main()
{
    int n;
    scanf("%d", &n);
    int max = 0x80000000;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            scanf("%d", &a[i][j]);
    for (int i = 0; i < n; i++)
        for (int j = i; j < n; j++) {
            for (int l = 0; l < n; l++) {
                b[l] = 0;
                for (int k = i; k <= j; k++) {
                    b[l] += a[l][k];
                }
            }
            int tmp = maxSubArray(n, b);
            if (tmp > max)max = tmp;
        }
    printf("%d\n", max);
}