Common Subsequence ————LCS

亦凉 2022-05-17 10:10 161阅读 0赞

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, x ij = 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.  
**Input**  
The program input is from the std input. Each data set in the input contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct.  
**Output**  
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

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LCS的模板题，纯模板，不添加任何杂质

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//#include<bits/stdc++.h>
    #include<cstdio>
    #include<iostream>
    #include<cstring>
    using namespace std;
    const int MAXN=1000;
    int dp[MAXN][MAXN];
    char s1[MAXN],s2[MAXN];
    
    
    int main()
    {
        while(~scanf("%s %s",s1,s2))
        {
            int len1=strlen(s1);
            int len2=strlen(s2);
            memset(dp,0,sizeof(dp));
            for(int i=0;i<len1;i++)
                for(int j=0;j<len2;j++)
                    if(s1[i]==s2[j])
                        dp[i+1][j+1]=dp[i][j]+1;
                    else
                        dp[i+1][j+1]=max(dp[i+1][j],dp[i][j+1]);
            printf("%d\n",dp[len1][len2]);
        }
        return 0;
    }