Written by    17:39 February 1, 2016 
Common Subsequence
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 44778 Accepted: 18346


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

Sample Output





if S1[i] == S2[j]

MAXLEN[i][j] = MAXLEN[i-1][j-1] + 1;


MAXLEN[i][j] = max( MAXLEN[i][j-1], MAXLEN[i-1][j]);

题目所求的就是MAXLEN[ S1.length() ][ S2.length() ], 这样就可以在O(m*n)的复杂度下解决了。




Category : acmstudy

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