leetcode: Distinct Subsequences

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.

利用动态规划：

A[i][j]表示字符串S(0,i)中，关于T(0,j)的number ofdistinct subsequences。

if(S[i-1]==T[j-1])A[i][j] = A[i-1][j-1]+A[i-1][j];

else A[i][j] = A[i-1][j];

A[i][0] = 1;

A[0][j] = 0;