115. 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.

动态规划，二维数组，建一个计数的数组。

求能到到末尾的路径数。

到达[i][j]点有两种情况，一种是i,j两点字符相同，此时可以由[i-1][j-1]因为字符相同过来，也可以忽略它由它的前一位[i][j-1]过来。如果i,j两点字符不同那么只有一种情况就是

忽略它从[i][j-1]过来

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

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