Problem
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.
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.
Example
Input
4
0 -2 -7 0 9 2 -6 2
-4 1 -4 1 -1
8 0 -2
Output
15
Source: Greater New York 2001
源碼：
解題報告：
題目大意：給出一個矩陣，求出子矩陣和最大值
算法思想：通過模擬，枚舉顯然耗時，可以枚舉行，對列用動態規劃
先將二維的轉換到一維上面：可以用兩個循環語句i，j，表示從i到j行的矩陣。
對列求和便轉爲一維
一維求解:
直接模擬求解：
簡單的枚舉所有的可能子矩陣