动态规划—杭电1159 Common Subsequence

http://acm.hdu.edu.cn/showproblem.php?pid=1159

Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9101 Accepted Submission(s): 3681


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

辅助空间变化示意图

	a	b	c	f	b	c
a	1	1	1	1	1	1
b	1	2	2	2	2	2
f	1	2	2	3	3	3
c	1	2	3	3	3	4
a	1	2	3	3	3	4
b	1	2	3	3	4	4

#include <iostream>
#include <string.h>
#define max(a,b) a>b?a:b
using namespace std;
char a[1001],b[1001];
int dp[1001][1001];
int main()
{
	while(cin>>a>>b)
	{
		memset(dp,0,sizeof(dp));
		int lena,lenb;
		lena=strlen(a);
		lenb=strlen(b);
		int i,j;
		for(i=0;i<lena;i++)
			for(j=0;j<lenb;j++)
			{
				if(a[i]==b[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]);
			}
			cout<<dp[lena][lenb]<<endl;				
	}
	return 0;
}