115. 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.

设状态为 f[i][j]，S 的子串 S(0-i)含有 T 的子串 T(0-j)的不同子串个数，状态
方程：

f[i][j] = f(i-1,j-1) + f(i-1,j) if t[i] = s[j]
          f(i-1,j) if t[i] != s[j]

	r	a	b	i	t
r	1
a	1	1
b	1	1	1
b	1	1	2	0
b	1	1	3	0	0
i	1	1	3	3	0
t	1	1	3	3	3

使用滚动数组+临时变量存储 f(i-1,j-1)，可以优化空间复杂度到 O(n)

public class Solution {
    public int numDistinct(String S, String T) {
        int lenS = S.length();
        int lenT = T.length();
        if(lenT == 0 || lenS == 0 || lenS=0; j--){
                f[j+1] += (S.charAt(i) == T.charAt(j)? f[j]:0);
            }
        }
        
        return f[lenT];
    }
}