TO THE MAX

http://acm.sdibt.edu.cn/JudgeOnline/problem.php?id=1207

Time Limit: 1 Sec  Memory Limit: 64 MBSubmit: 6  Solved: 6[Submit][STATUS][DISCUSS]

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

題目大意：

從一個輸入的矩陣中找出一個子矩陣，這個子矩陣的和是該矩陣的所有子矩陣中最大的

解題思路：

1.最大子矩陣問題，可以轉(zhuǎn)換為最大子段和問題

2.設(shè)置一個大小為N的一維數(shù)組，然后將矩陣中同一列的若干數(shù)合并到該一維數(shù)組的對應(yīng)項(xiàng)中

  問題就轉(zhuǎn)換成求該一維數(shù)組的最大子段和問題

3.最大子段和問題核心代碼：

for(k=1;k<=n;k++)
{
    if(sum+dp[k]<0)
        sum=0;
    else
    {
        sum+=dp[k];
        if(max<sum)
            max=sum;
    }
}