Problem Distinct Subsequence

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Problem Desciption : 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.

Solution : 採用動態編程 (Dynamic Programming)的思路。mat[i][j]表示子問題S = S.substring(0, i-1), T= T.substring(0,j-1)的結果

 1 public int numDistinct(String S, String T) { 2         int slen = S.length(); 3         int tlen = T.length(); 4         if (slen == 0) return 0; 5         if (tlen == 0) return 1; 6         int[][] mat = new int[slen + 1][tlen +1]; 7         for (int i = 0; i <= slen; i++) mat[i][0] = 1; 8         for (int i = 1; i <= slen; i++)  9             for (int j = 1; j <= tlen; j++) {10                 if (S.charAt(i-1) == T.charAt(j-1))11                     mat[i][j] = mat[i-1][j-1] + mat[i-1][j];12                 else 13                     mat[i][j] = mat[i-1][j];14         }15 16         return mat[slen][tlen];17     }