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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.

class Solution {public:    int numDistinct(string s, string t) {        int l1 = s.length();        int l2 = t.length();                int dp[l1+1][l2+1];        for(int i=0;i<l1+1;i++){            for(int j=0;j<l2+1;j++){                if(i==0 && j==0){                    dp[i][j] = 1;                }else if (i==0){                    dp[i][j] = 0;                }else if(j==0){                    dp[i][j] = 1;                }else {                    if(s[i-1] == t[j-1]){                        dp[i][j] = dp[i-1][j-1] + dp[i-1][j];                    }else {                        dp[i][j] = dp[i-1][j];                    }                }            }        }        return dp[l1][l2];    }};

 

Distinct Subsequences