Leetcode 96. Unique Binary Search Trees

Posted 2022-11-25 zhangwj0101

Question

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

Code

 public int numTrees(int n) 

        if (n < 1) 
            return 1;
        
        int[] nums = new int[n + 1];
        nums[0] = 1;
        nums[1] = 1;
        for (int i = 2; i <= n; i++) 
            for (int k = 1; k <= i; k++) 
                nums[i] += nums[k - 1] * nums[i - k];
            
        
        return nums[n];