Count Balanced Binary Trees of Height h in C++

We are given with the height H of a binary tree. The goal is to find the number/count of balanced Binary Trees of given height.

A binary tree − is a tree data structure in which each node has at most two children, which are the left child and the right child.

Height-balanced binary tree − is defined as a binary tree in which the depth of the two subtrees of every node differ by 1 or 0 only. That is the height of the left subtree and the right subtree at every node has a maximum difference of 1.

Following figure contains the possible height balanced binary trees for height h=3.


Height H=2


Count of Balanced Binary Trees of Height H is : 3

Explanation − Given figure contains possible balanced trees for height H=2


Height H=3


Count of Balanced Binary Trees of Height H is : 15

Approach used in the below program is as follows

  • The integer H is used to represent the height of Binary trees.

  • The function countBTheight(int h) takes the height of the tree as input and returns the number of possible Balanced Binary trees with height h.

  • We are using the recursive approach.

  • If the tree has height 1, i.e it has only one node then only one tree with a single node is present and that is balanced. ( if(h==1), return 1)

  • Otherwise the height is the sum of left and right subtrees with height one or two less than the root. (Balanced trees have a difference between the heights as 1).

  • The function returns the count as result.


 Live Demo

#include <iostream>
int countBTheight(int h){
   // One tree is possible with height 0 or 1
   if (h == 0 || h == 1)
      return 1;
   return countBTheight(h-1) * (2 *countBTheight(h-2) + countBTheight(h-1));
int main(){
   int H = 4;
   std::cout << "Count of balanced binary trees of height H is: "<<countBTheight(H);


Count of balanced binary trees of height H is: 315

Updated on: 28-Jul-2020


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