Given a positive integer H, the task is to find the number of possible Binary Search Trees of height H consisting of the first (H + 1) natural numbers as the node values. Since the count can be very large, print it to modulo 109 + 7.
Input: H = 2
Explanation: All possible BSTs of height 2 consisting of 3 nodes are as follows:
Therefore, the total number of BSTs possible is 4.
Input: H = 6
Approach: The given problem can be solved based on the following observations:
- Only (H + 1) nodes are can be used to form a Binary Tree of height H.
- Except for the root node, every node has two possibilities, i.e. either to be the left child or to be the right child.
- Considering T(H) to be the number of BST of height H, where T(0) = 1 and T(H) = 2 * T(H – 1).
- Solving the above recurrence relation, the value of T(H) is 2H.
Therefore, from the above observations, print the value of 2H as the total number of BSTs of height H consisting of the first (H + 1) natural numbers.
Below is the implementation of the above approach:
Time Complexity: O(log2H)
Auxiliary Space: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.