Question

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

Solution

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++){
                nums[i] += (nums[i-j-1]*nums[j]) ;
            }
        }    
        return nums[n];    
    }
}