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Prashant Mishra

Posted on • Originally published at leetcode.com

# Distinct Subsequence Leetcode

Given two strings s and t, return the number of distinct subsequences of s which equals t.

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

The test cases are generated so that the answer fits on a 32-bit signed integer.

Example 1:

``````Input: s = "rabbbit", t = "rabbit"
Output: 3
``````

Explanation:

``````As shown below, there are 3 ways you can generate "rabbit" from S.
rabbbit
rabbbit
rabbbit
``````
``````class Solution {
public int numDistinct(String s, String t) {
// we will use little bit of backtracking here
int dp[][] = new int[s.length()][t.length()];
for(int row[] : dp) Arrays.fill(row, -1);
return distinctCount(s,t,s.length()-1,t.length()-1,dp);
}
public int distinctCount(String s, String t, int i,int j,int dp[][]){
//base case
if(i=0 && j=0 && s.charAt(i)==t.charAt(j)) return 1;
if(j<0) return 1;
if(i<0) return 0;
if(dp[i][j]!=-1) return dp[i][j];
if(s.charAt(i)==t.charAt(j)){
// so basically if its a, match , we will either reduce s and t index both or we will just reduce the index of  s only.
// in both the case we will return the sum of values that we get.
return dp[i][j]= distinctCount(s,t,i-1,j-1,dp) + distinctCount(s,t,i-1,j,dp);
}
else{
// else if its not a match we will have to reduce the s string index so
//as to reach to an index of s where s.charAt(i) == t.charAt(j);
return dp[i][j] = distinctCount(s,t,i-1,j,dp);
}
}
}
``````