[LC] 96. Unique Binary Search Trees

Posted 2021-03-17 xuanlu

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];
    }
}