1. Distinct Subsequences

Given a stringSand a stringT, count the number of distinct subsequences ofTinS.

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"

Return3.

不好理解， 通过画dp表解题！

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] + dp[i-1][j-1];
                else
                    dp[i][j] = dp[i-1][j];
            }
        }

        return dp[m][n];
    }
}