Common Subsequence

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 53443    Accepted Submission(s): 24607

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

【题意】

　　一个给定序列的子序列是一个给定序列，其中有些元素(可能没有)被省略。给定一个序列 X = <x1, x2, ..., xm> 另一个序列 Z = <z1, z2, ..., zk> 是X的子序列，如果存在严格递增序列， <i1, i2, ..., ik> 对所有 j = 1,2，…，k, xij = zj。例如，Z = <a, b, f, c> 是 X = <a, b, c, f, b, c>  的子序列，索引序列< 1,2,4,6 >。给定两个序列X和Y，问题是求X和Y的最大长度公共子序列的长度。

　　序列由任意数量的空格分隔。输入数据是正确的。对于每组数据，程序在标准输出上打印从单独行开始的最大长度公共子序列的长度。

　　注意：最长公共子序列 ，可以不连续。

【代码】

#include<bits/stdc++.h>
#define MAX 5005
using namespace std;
int f[MAX][MAX];
string s,t;
int main(){
    while(cin>>s>>t){
        for(int i=1;i<=s.length();i++)
            for(int j=1;j<=t.length();j++){
                f[i][j]=max(f[i-1][j],f[i][j-1]);
                if(s[i-1]==t[j-1])
                f[i][j]=max(f[i][j],f[i-1][j-1]+1);
       }
       cout<<f[s.length()][t.length()]<<endl;
    }
    return 0;
}

原文地址：https://www.cnblogs.com/fangxiaoqi/p/10915451.html