Problem distinct subsequence

Problem desciption: Given a stringSAnd a stringT, Count the number of distinct subsequencesTInS.

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"ABCDE"While"AEC"Is not ).

Here is an example:
S="Rabbbit",T="Rabbit"

Return3.

Solution: Uses the idea of dynamic programming. Mat [I] [J] indicates the results of subproblem S = S. substring (0, I-1), t = T. substring (0, J-1)

 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 }