[POJ] 1458 Common Subsequence

Common Subsequence
Time Limit: 1000MS      Memory Limit: 10000K
Total Submissions: 56614        Accepted: 23609
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.
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
Source

Southeastern Europe 2003

LCS问题
f[i][j]表示S长度为i的前缀和T长度为j的前缀的LCS
f[i][j]=f[i-1][j-1]+1 (s[i]==t[j])
f[i][j]=max( f[i-1][j] , f[i][j-1] ) (else)

//Writer:GhostCai && His Yellow Duck

#include<iostream>
#include<cstring>
#define MAXN 500
using namespace std;

char s[MAXN],t[MAXN]; 
int lens,lent;
int f[MAXN][MAXN];

int main(){
    while(cin>>s+1>>t+1){
        memset(f,0,sizeof(f));
        lens=strlen(s+1);
        lent=strlen(t+1);
        for(int i=1;i<=lens;i++){
            for(int j=1;j<=lent;j++){
                if(s[i]==t[j]){
                    f[i][j]=f[i-1][j-1]+1;
                }else{
                    f[i][j]=max(f[i-1][j],f[i][j-1]);
                }
            }
        }
        cout<<f[lens][lent]<<endl;
    }
    return 0;
}