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POJ - 1458 Common Subsequence

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      

題目大意:給出兩個字元串,求出他們的最長公共子序列

解題思路:LCS

AC代碼:

#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=1e3;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int main()
{
	while(scanf("%s%s",a+1,b+1)!=EOF)
	{
		memset(dp,0,sizeof(dp));
		int alen=strlen(a+1),blen=strlen(b+1);
		for(int i=0;i<=alen;i++)
		{
			for(int j=0;j<=blen;j++)
			{
				if(i==0||j==0)
					dp[i][j]=0;
				else if(a[i]==b[j])
					dp[i][j]=dp[i-1][j-1]+1;
				else
					dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
			}
		}
		cout<<dp[alen][blen]<<endl;
	}
	return 0;
}