96. Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

 1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

一刷
题解：与95. Unique Binary Search Trees II的不同之处在于，求出所有的排列组合数目而不是真正的排列组合。

根据表达式dp[n+1] = sum_{i=0}^n(dp[n-i]*dp[i]),可以得到下题的解：
Time complexity - O(n), space complexity - O(n)

public class Solution {
    public int numTrees(int n) {
       if(n<0) return 0;
       int[] dp = new int[n+1];
       dp[0] = 1;//null
       
       for(int i=1; i<=n; i++){//n+1, n = i-1
           for(int j=0; j<i; j++){
               dp[i] += dp[i-1-j]*dp[j];
           }
       }
       
       return dp[n];
    }
}