最长子序列问题
定义二维 int 数组a[i][j]，列数为len(s1)+1,行数为len(s2)+1,首行，首列都赋值0,然后对[i][j]逐行扫描，分两种情况
第一种：s1[i]==s2[j],a[i][j]=a[i-1][j-1]+1,
第二种：s1[i]!=s2[j],a[i][j]=max(a[i-1][j],a[i][j-1]),
直到扫描结束，最后的数a[i][j]就是最长子序列的长度。
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例如，http://202.196.6.170/JudgeOnline/ （郑州轻工业学院OJ） 上的 1207 Common Subsequence
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
当然，此题只是涉及了最长子序列长度的求解，并未要求输出最长子序列，所以以上方法能够实现