1. 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.

2. 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].

3. Output

Output the sum of the maximal sub-rectangle.

4. Example

input
4
0 -2 -7 0 9 2 -6 2
-4 1 -4 1 -1
8 0 -2
output
15

5. Code

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import java.util.Arrays;
import java.util.Scanner;

public class Main {
	
	public static void main(String args[])
    {
        Scanner in = new Scanner(System.in);
        
        while(in.hasNextInt())
        {
        	int n = in.nextInt();
            int[][] matrix = new int[n][n];
            
            for(int i = 0; i < n; i++ ){
            	for(int j = 0; j < n; j++ ){
            		matrix[i][j] = in.nextInt();
            	}
            }
            
            int result = Integer.MIN_VALUE;
            int[] dp = new int[n];
            for(int i = 0; i< n; i++){
            	Arrays.fill(dp, 0);
            	for(int j = i; j< n; j++){
            		for(int k = 0; k< n; k++){
            			dp[k] +=matrix[j][k];
            		}
            		result = Math.max(result, maxSubArraySum(dp));
            	}
            }
            System.out.println(result);
        }
    }
	
	private static int maxSubArraySum(int[] array){
		int pre = 0;
		int sum = Integer.MIN_VALUE;
		for(int i = 0; i < array.length; i++ ){
			if(pre < 0){
				pre = array[i];
			}else{
				pre += array[i];
			}
			if(sum < pre){
				sum = pre;
			}
		}
		return sum;
	}
}

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