Unique Binary Search Trees

Problem

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

Solution

public class Solution {
    public int numTrees(int n) {
        if (n <= 1) return 1;
        int[] G = new int[n+1];
        G[0] = G[1] = 1; //This is valid statement in java 
        for (int i = 2; i <= n; i++) {
            for (int j = 1; j <= i; j++) {
                G[i] += G[j - 1] * G[i - j]; 
            }
        }
        return G[n];
    }
}

Analysis

G(n) is the number of BST with length n
It can be constructed with each number as root
G(n) = F(1, n) + F(2, n) + F(3, n) + ... + F(n, n), where F(i, n) is the number of BST with i as root
For each BST with a root i, we can construct it with left subtrees times right subtrees
F(i, n) = G(i-1) * G(n-1)
At the end, we return the G(n) as required