To The Max(dp思想)
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http://acm.hdu.edu.cn/showproblem.php?pid=1081
To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 10135 Accepted Submission(s): 4885
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
思路还是不够
//dp有一个特点就是要求出结果必须枚举所有情况,这根搜索有很大的区别#include <cstdio>int dp[110][110];const int maxn=1<<30;int main(){ int n; while(scanf("%d",&n)!=EOF){ for(int i=1;i<=n;i++) for(int j=1;j<=n;j++){ int a; scanf("%d",&a); dp[i][j]=dp[i][j-1]+a;//dp思想,再次想到了记忆化搜索 } int ans=-maxn; for(int i=1;i<=n;i++) for(int j=i;j<=n;j++){//ij分别表示子矩阵的某一行开头和结尾,这里少掉一维的话就不好表示了 int sum=0; for(int k=1;k<=n;k++){//这里是一维求最大连续和的思想 if(sum<0)sum=0; sum+=dp[k][j]-dp[k][i-1]; if(sum>ans)ans=sum; } }//枚举了所有的情况 printf("%d\n",ans); } return 0;}
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