hdu 5791 (DP) Two

最新推荐文章于 2025-09-06 09:33:29 发布

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原文链接：http://www.cnblogs.com/JJCHEHEDA/p/5738830.html

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#java

本文介绍了一个关于寻找两个序列相同公共子序列数量的问题，并提供了一种使用动态规划解决该问题的方法。通过构建二维DP数组来记录不同序列长度下的公共子序列数量，最终输出结果取模1000000007。

hdu 5791

Two

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1421 Accepted Submission(s): 630

Problem Description

Alice gets two sequences A and B. A easy problem comes. How many pair of sequence A' and sequence B' are same. For example, {1,2} and {1,2} are same. {1,2,4} and {1,4,2} are not same. A' is a subsequence of A. B' is a subsequence of B. The subsequnce can be not continuous. For example, {1,1,2} has 7 subsequences {1},{1},{2},{1,1},{1,2},{1,2},{1,1,2}. The answer can be very large. Output the answer mod 1000000007.

Input

The input contains multiple test cases.

For each test case, the first line cantains two integers

Output

For each test case, output the answer mod 1000000007.

Sample Input

3 2 1 2 3 2 1 3 2 1 2 3 1 2

Sample Output

2 3

求两个序列的相同的公共子序列的个数，取模。

DP[i][j]表示到a数组的第 i 个和b数组的第 j 个之间的个数，可以归纳出，当a[i]==b[j]时，dp[i][j]=dp[i-1][j]+dp[i][j-1]+1;

当不等的时候，dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1].(仔细琢磨琢磨，会发现很有道理)因为有减法的运算所以最后答案可能出现

负数，注意处理一下。

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<iostream>
 4 #include<algorithm>
 5 using namespace std;
 6 
 7 typedef long long ll;
 8 const int mod = 1000000007;
 9 ll dp[1010][1010];
10 int a[1010],b[1010];
11 
12 int main()
13 {
14     int n,m;
15     while (~scanf("%d%d",&n,&m)){
16         for (int i=1 ; i<=n ; i++) scanf("%d",&a[i]);
17         for (int i=1 ; i<=m ; i++) scanf("%d",&b[i]);
18         memset(dp,0,sizeof(dp));
19         for (int i=1 ; i<=n ; i++){
20             for (int j=1 ; j<=m ; j++){
21                 if (a[i]==b[j]) dp[i][j]=dp[i-1][j]+dp[i][j-1]+1;
22                 else dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1];
23                 dp[i][j]%=mod;
24             }
25         }
26         printf("%I64d\n",(dp[n][m]+mod)%mod);
27     }
28     return 0;
29 }