HDU 1081 To The Max
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To The Max
Problem 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.
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 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.
Sample Input
40 -2 -7 0 9 2 -6 2-4 1 -4 1 -18 0 -2
Sample Output
15
题意:给出一个二维的矩阵,求和最大的子矩阵的大小。
可以用区间DP的思想来做,注意,如果全是负值,就可以认为取0X0是最大的矩阵,和为0.这样其实就简便了一些,如果一个子矩阵的和为负的,直接就不取了。
一直分区间,把每个区间内的和都求出来与MAX比较。
#include<stdio.h>#include<string.h>int a[101][101],b[101];int n;int dp(){ int i; int max=0,sum=0; for(i=1;i<=n;i++) { sum+=b[i]; if(sum<0) sum=0; if(sum>max) max=sum; } return max;}int main(){ int i,j,k; while(~scanf("%d",&n)) { memset(a,0,sizeof(a)); for(i=1; i<=n; i++) for(j=1; j<=n; j++) scanf("%d",&a[i][j]); int sum=0,max=0; for(i=1; i<=n; i++) { memset(b,0,sizeof(b)); for(j=i;j<=n;j++) { for(k=1;k<=n;k++) { b[k]+=a[j][k]; } sum=dp(); if(sum>max) max=sum; } } printf("%d\n",max); } return 0;}
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