Common Subsequence

题目链接

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_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

 

Source

Southeastern Europe 2003

 

AC代码:

 

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
char s1[1005],s2[1005];
int l1,l2,dp[1005][1005];
int main(){
    while(~scanf("%s%s",s1 + 1,s2 + 1)){//下标从1开始
        l1 = strlen(s1 + 1);
        l2 = strlen(s2 + 1);
        for(int i = 0;i <= l2;i++)//填充第一行
            dp[0][i] = 0;
        for(int i = 0;i <= l1;i++)//填充第一列
            dp[i][0] = 0;
        for(int i = 1;i <= l1;i++)
            for(int j = 1;j <= l2;j++){
                if(s1[i] == s2[j])//不理解的强烈建议画图看看就明白了
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                else
                    dp[i][j] = max(dp[i - 1][j],dp[i][j - 1]);
            }
        printf("%d\n",dp[l1][l2]);
    }
    return 0;
}