POJ1458————Common Subsequence

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本文介绍了一种解决最长公共子序列问题的有效算法。通过动态规划方法，在两个字符串中找到最长的共有子序列长度。输入为两个字符串，输出则是该最长子序列的长度。

Common Subsequence

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 52488		Accepted: 21709

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, x_{i_j} = 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

最长公共子序列= =

#include <cstdio>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <string>
#include <cstring>
using namespace std;
const int MAXN=1010;
const int INF=0xfffffff;
int dp[MAXN][MAXN];
int main(){
    ios::sync_with_stdio(false);
    string a,b;
    while(cin>>a>>b){
        int n=a.length();
        int m=b.length();
        memset(dp,0,sizeof(dp));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(a[i]==b[j]){
                    dp[i+1][j+1]=dp[i][j]+1;
                }else{
                    dp[i+1][j+1]=max(dp[i][j+1],dp[i+1][j]);
                }
            }
        }
        cout<<dp[n][m]<<endl;
    }
}