POJ 1050 To the Max(DP_最大字段和)

题目链接

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

40 -2 -7 0 9 2 -6 2-4 1 -4  1 -18  0 -2

Sample Output

15

        求最大子矩阵和
解题思路：
          a11  a12  a13
        a21  a22  a23
        a31  a32  a33   
        可以先求出a11, a12, a13的最大子段和，然后再求出a11+a21, a12+a22, a13+a23的最大子段和，接着求a11+a21+a31, a12+a22+a32, a13+a23+a33的最大子段和，求完以第一行开头的，再接着求以第二行开头的，以此类推求出所有的最大子段和，求出他们中最大的就是解。

代码如下：

/*                                    _ooOoo_                                   o8888888o                                   88" . "88                                   (| -_- |)                                    O\ = /O                                ____/`---'\____                              .   ' \\| |// `.                               / \\||| : |||// \                             / _||||| -:- |||||- \                               | | \\\ - /// | |                             | \_| ''\---/'' | |                              \ .-\__ `-` ___/-. /                           ___`. .' /--.--\ `. . __                        ."" '< `.___\_<|>_/___.' >'"".                       | | : `- \`.;`\ _ /`;.`/ - ` : | |                         \ \ `-. \_ __\ /__ _/ .-` / /                 ======`-.____`-.___\_____/___.-`____.-'======                                    `=---='                 .............................................*/#include <map>#include <queue>#include <cmath>#include <cstdio>#include <string>#include <cstring>#include <cstdlib>#include <iostream>#include <algorithm>#define pi 3.1415926#define INF 123456789using namespace std;int main(){    int n, i, j, a[105][105], b[105], q, t, Max;    while(~scanf("%d", &n)){        for(i = 0; i < n; i ++){            for(j = 0; j < n; j ++)                scanf("%d", &a[i][j]);        }        for(i = 0, Max = -INF; i < n; i ++){            memset(b, 0, sizeof(b));            for(j = i; j < n; j ++){                for(q = 0; q < n; q ++)                    b[q] += a[j][q];                for(q = 0, t = 0; q < n; q ++){                    t += b[q];                    if(t > Max) Max = t;                    if(t < 0) t = 0;                }            }        }        printf("%d\n", Max);    }    return 0;}