Unique Binary Search Trees II

Given an integer A, how many structurally unique BST’s (binary search trees) exist that can store values 1…A?

The first and the only argument of input contains the integer, A.

Return an integer, representing the answer asked in problem statement.

1 <= A <= 18

Input 1:
    A = 3

Output 1:
    5

Explanation 1:

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

Method:

From 1 to A, if we pick a number j, then there is j - 1 ways to order the left subtree, and A - j number of ways to order the right subtree

Solution:

Time: O(n^2)
Space: O(n)

public class Solution {
    public int numTrees(int A) {
        int[] dp = new int[A + 1];
        dp[0] = 1;
        dp[1] = 1;
        for (int i = 2; i <= A; i ++) {
            for (int j = 1; j <= i; j ++) {
                dp[i] += (dp[j - 1] * dp[i - j]);
            }
        }
        return dp[A];
    }
}