/** 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 m = S.length(); int n = T.length(); if (m > dp(m+1, vector(n+1, 0)); for (int i = 0; i <= m; ++i) dp[i][0] = 1; for (int i =1; i <=m; ++i) { for (int j =1; j <=n; ++j) { if (S[i-1] == T[j-1]) { dp[i][j] = dp[i-1][j] + dp[i-1][j-1]; } else { dp[i][j] = dp[i-1][j]; } } } return dp[m][n]; //note here we return m,n } };