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最长公共子序列

2024-11-06 02:51:02   203人阅读

                                         Common Subsequence

                                                Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
                                                                         Total Submission(s): 9595    Accepted Submission(s): 3923


Problem Description
A subsequence of a given sequence is the given sequence with some elements (possible none) left out. Given a sequence X = <x1, x2, ..., xm> another sequence Z = <z1, z2, ..., zk> is a subsequence of X if there exists a strictly increasing sequence <i1, i2, ..., ik> of indices of X such that for all j = 1,2,...,k, xij = zj. For example, Z = <a, b, f, c> is a subsequence of X = <a, b, c, f, b, c> with index sequence <1, 2, 4, 6>. Given two sequences X and Y the problem is to find the length of the maximum-length common subsequence of X and Y. 
The program input is from a text file. Each data set in the file contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct. For each set of data the program prints on the standard output the length of the maximum-length common subsequence from the beginning of a separate line. 
 

 

Sample Input
abcfbc abfcab
programming contest
abcd mnp
 

 

Sample Output
4
2
0
http://acm.hdu.edu.cn/showproblem.php?pid=1159
 
 
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一个简单的动态规划的应用
直接给代码
 1 #include <iostream>
 2 //#include <cstdio>
 3 #include <cstring>
 4 #define N 1005
 5 using namespace std;
 6 int dp[N][N];
 7 string s,ss;
 8 int main(){
 9     while(cin>>s>>ss){
10         int n=s.length();
11         int m=ss.length();
12         memset(dp,0, sizeof(dp));
13         for(int i=1;i<=n;i++){
14             for(int j=1;j<=m;j++){
15                 if(s[i-1]==ss[j-1])
16                     dp[i][j]=dp[i-1][j-1]+1;
17                 else{
18                     dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
19                 }
20             }
21         }
22         cout<<dp[n][m]<<endl;
23     }
24     return 0;
25 }

 

 

最长公共子序列


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