# Common Subsequence ----最长公共子序列

xiaoxiao2021-02-28  6

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

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or dp【i】【j】=max（dp【i-1】【j】，dp【i】【j-1】）;

dp【i】【j】表示a字符串第i个之前，和b字符串第j个之前的最长公共子序列的长度。

AC代码：

#include<iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;int main(){ // freopen ("in.txt","r",stdin); char a; char b; while (cin>>a>>b) { int n=strlen(a); int m=strlen(b); int dp[n+5][m+5]; for (int i=0;i<=n;i++) for (int j=0;j<=m;j++) { if (i&&j) { if (a[i-1]==b[j-1]) dp[i][j]=dp[i-1][j-1]+1; else dp[i][j]=max(dp[i-1][j],dp[i][j-1]); } else dp[i][j]=0; } /* for (int i=0;i<=n;i++) for (int j=0;j<=m;j++) { cout << dp[i][j] ; if (j==m) cout <<endl; else cout <<" "; }*/ cout << dp[n][m] <<endl; memset (a,0,sizeof(a)); memset (b,0,sizeof(b)); } return 0;}