maksyuki 发表于 oj 分类,标签:

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, 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 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.


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





Southeastern Europe 2003



算法分析:求最大公共子串的长度,f[i][j]定义为有前i和j个字符的字符串val_a和val_b的最长公共子串的长度。转移方程为:如果字符串val_a[i] == val_b[j],则有f[i][j] = f[i-1][j-1] + 1;反之则f[i][j] = max (f[i-1][j], f[i][j-1]); 1 <= i, j