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.

https://oj.leetcode.com/problems/distinct-subsequences/

思路：DP。dp[i][j]代表从s[0..i]中删除几个字符得到t[0..j]的不同删除方法数。

• 初始化：如果t为空，任意的s删除到t都是1种。
• 如果S[i] = T[j], dp[i][j] = dp[i-1][j-1]+dp[i-1][j]
• 如果S[i] 不等于 T[j], dp[i][j] = dp[i-1][j]

public class Solution {    public int numDistinct(String S, String T) {        int m = S.length();        int n = T.length();        int[][] dp = new int[m + 1][n + 1];        for (int i = 0; i <= m; i++)            dp[i][0] = 1;        for (int i = 1; i <= m; i++) {            for (int j = 1; j <= n; j++) {                if (S.charAt(i - 1) == T.charAt(j - 1))                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];                else                    dp[i][j] = dp[i - 1][j];            }        }        return dp[m][n];    }    public static void main(String[] args) {        String S = "rabbbit";        String T = "rabbit";        System.out.println(new Solution().numDistinct(S, T));    }}

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参考：

http://www.programcreek.com/2013/01/leetcode-distinct-subsequences-total-java

http://www.cnblogs.com/TenosDoIt/p/3440022.html