Question

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

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).

Example 1:

Input: S = "rabbbit", T = "rabbit"Output: 3Explanation:As shown below, there are 3 ways you can generate "rabbit" from S.(The caret symbol ^ means the chosen letters)rabbbit^^^^ ^^rabbbit^^ ^^^^rabbbit^^^ ^^^

Example 2:

Input: S = "babgbag", T = "bag"Output: 5Explanation:As shown below, there are 5 ways you can generate "bag" from S.(The caret symbol ^ means the chosen letters)babgbag^^ ^babgbag^^    ^babgbag^    ^^babgbag  ^  ^^babgbag    ^^^

Answer

class Solution {public:    int numDistinct(string s, string t) {         vector
     
      
       > dp(t.size(), vector
       
        (s.size()));        int dis = 0;        for (int i = 0; i < t.size(); i++) {             dis = 0;            for (int j = 0; j < s.size(); j++) {                dp[i][j] = dis;                if (t[i] == s[j]) {                    if (i == 0) dis++;                    else if (j != 0)                        dis = dp[i - 1][j] + dp[i][j];                }            }        }        return dis;    }};
       
      
     

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