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.

**let f_ij be the number of distinct subsequences of T[0,j] in S[0,i], then**

**f_i+1,j = S[i+1] == T[j] ? f_{i,j-1} + f_{i,j} : f_{i,j}**

public class Solution {

public int numDistinct(String S, String T) {

// Start typing your Java solution below

// DO NOT write main() function

if(S.length() ==0 ) return 0;

assert T.length() >0;

int[] dp = new int[T.length()];

for(int i = 0; i < dp.length; i++) dp[i] = 0;

for(int i =0 ; i < S.length() ; i++){

for(int j = T.length()-1; j>=0; j--){

if(T.charAt(j) == S.charAt(i)){

dp[j] += j>0 ? dp[j-1] : 1;

}

}

}

return dp[T.length()-1];

}

}

## No comments:

## Post a Comment