[LC] 96. Unique Binary Search Trees

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

Example:

Input: 3

Output: 5

Explanation:

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

class Solution {

    public int numTrees(int n) {

        int[] nums = new int[n + 1];

        nums[0] = 1;

        nums[1] = 1;

        for (int i = 2; i <= n; i++) {

            for (int j = 0; j < i; j++) {

                // use j - 1 b/c root count 1, left + right + cur_root = total number

                nums[i] += nums[i - j - 1] * nums[j];

            }

        }

        return nums[n];

    }

}