Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

 1 public class Solution {
 2     public int numDistinct(String S, String T) {
 3         int len1 =S.length();
 4         int len2 = T.length();
 5         int[][] dp = new int [len1+1][len2+1];
 6         for(int i=0;i<=len2;i++){
 7             dp[0][i] = 0;
 8         }
 9         for(int i=0;i<=len1;i++){
10             dp[i][0] = 1;
11         }
12         for(int i=1;i<=len1;i++){
13             for(int j=1;j<=len2;j++){
14                 if(S.charAt(i-1)!=T.charAt(j-1))
15                     dp[i][j] = dp[i-1][j];
16                 else 
17                     dp[i][j] = dp[i-1][j] + dp[i-1][j-1];
18             }
19         }
20         return dp[len1][len2];
21     }
22 }
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posted @ 2014-02-17 02:18  krunning  阅读(127)  评论(0)    收藏  举报