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Solution.java
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package DistinctSubsequences;
/**
* User: Danyang
* Date: 1/28/2015
* Time: 18:46
*
* 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.
*/
public class Solution {
/**
* let f[i][j] represents the num of distinct subsequence of b[0..j] in a[0..i]
* f[i][j] = f[i-1][j-1] + f[i-1][j] if a[i]=b[i]
* = f[i-1][j] otherwise
* @param S
* @param T
* @return
*/
public int numDistinct(String S, String T) {
int m = S.length();
int n = T.length();
int[][] f = new int[m+1][n+1];
for(int i=0; i<m+1; i++)
f[i][0] = 1;
for(int i=1; i<m+1; i++) {
for(int j=1; j<n+1; j++) {
if(S.charAt(i-1)==T.charAt(j-1))
f[i][j] = f[i-1][j-1];
f[i][j] += f[i-1][j];
}
}
return f[m][n];
}
}