LeetCode 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

.
题意：求将S变成T有多少种方法，就只能删的情况下。
思路：DP的一道题，dp[i][j]表示S的前i个和T的前j个的匹配情况，首先dp[i][j]=dp[i-1][j]，然后再讨论S[i-1]和T[j-1]的情况。

public class Solution {
    public int numDistinct(String S, String T) {  
		if (S == null || T == null) return 0;
		if (S.length() < T.length()) return 0;
		
		int dp[][] = new int[S.length()+1][T.length()+1];
		dp[0][0] = 1;
		for (int i = 1; i <= S.length(); i++)
			dp[i][0] = 1;
		
		for (int i = 1; i <= S.length(); i++)
			for (int j = 1; j <= T.length(); j++) {
				dp[i][j] = dp[i-1][j]; 
				if (S.charAt(i-1) == T.charAt(j-1))
					dp[i][j] += dp[i-1][j-1];
			}
		
		return dp[S.length()][T.length()];
    }
}