To the Max - POJ 1050 dp
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To the Max
Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 39758 Accepted: 21010
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.
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
题意:找到和最大的矩阵并输出最大的和。
思路:我们先看一下如果是一维的怎么办,sum[i]= sum[i-1]<=0 ? num[i] :sum[i-1]+num[i]。
这道题只要把当做是n*(n-1)/2个一维的数,然后去算就可以了,复杂度应该是小于o(n^3),但是最后时间出来是16ms,看来数据比较水。
AC代码如下:
#include<cstdio>#include<cstring>using namespace std;int num[110];int res1[110][110];int res2[110][110];int main(){ int n,i,j,k,ans=-100000000; scanf("%d",&n); for(k=1;k<=n;k++) { for(i=1;i<=n;i++) scanf("%d",&num[i]); for(i=1;i<=n;i++) for(j=i;j<=n;j++) { res1[i][j]=res1[i][j-1]+num[j]; if(res2[i][j]<=0) res2[i][j]=res1[i][j]; else res2[i][j]=res2[i][j]+res1[i][j]; if(res2[i][j]>ans) ans=res2[i][j]; } } printf("%d\n",ans);}
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