Common Subsequence POJ

Common Subsequence

POJ - 1458

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         abfcabprogramming    contest abcd           mnp

Sample Output

420

题意：求最长公共子序列

分析：dp两种思路，找每个字符作为结束的最大长度和作为开始的最大长度 。

收获：刚开始学习dp

 

#include <cstdio>#include <iostream>#include <string.h>#include <algorithm>using namespace std;char s1[5000],s2[5000];int dp[500][500];int main (){    int maxn=0;    while(scanf("%s%s",s1,s2)!=EOF)    {        memset(dp,0,sizeof(dp));        int n=strlen(s1);        int m = strlen (s2);        for(int i=0;i<n;i++)        {            for(int j=0;j<m;j++)            {                if(s1[i]==s2[j])                {                    dp[i+1][j+1]=dp[i][j]+1;                }                else                {                    dp[i+1][j+1]=max(dp[i+1][j],dp[i][j+1]);                }            }        }        printf("%d\n",dp[n][m]);    }    return 0;}