LeetCode Distinct Subsequences

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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()];    }}

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