Height of a complete binary tree (or Heap) with N nodes

Difficulty Level : Easy
Last Updated : 04 May, 2021

Consider a Binary Heap of size N. We need to find the height of it.
Examples :

Input : N = 6
Output : 2
        ()
      /    \
     ()     ()
    /  \    /
  ()    () ()

Input : N = 9
Output :
        ()
      /    \
     ()     ()
    /  \    /  \
  ()    () ()   ()
 / \
()  ()

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Let the size of heap be N and height be h
If we take few examples, we can notice that the value of h in a complete binary tree is ceil(log₂(N+1)) – 1.
Examples :

 N    h
---------
 1    0
 2    1
 3    1
 4    2
 5    2
 .....
 .....

C++

// CPP program to find height of complete
// binary tree from total nodes.
#include <bits/stdc++.h>
using namespace std;
 
int height(int N)
{
    return ceil(log2(N + 1)) - 1;
}
 
// driver node
int main()
{
    int N = 6;
    cout << height(N);
    return 0;
}

Java

// Java program to find height
// of complete binary tree
// from total nodes.
import java.lang.*;
 
class GFG {
     
    // Function to calculate height
    static int height(int N)
    {
        return (int)Math.ceil(Math.log(N +
                    1) / Math.log(2)) - 1;
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 6;
        System.out.println(height(N));
    }
}
 
// This code is contributed by
// Smitha Dinesh Semwal

Python 3

# Python 3 program to find
# height of complete binary
# tree from total nodes.
import math
def height(N):
    return math.ceil(math.log2(N + 1)) - 1
 
# driver node
N = 6
print(height(N))
 
# This code is contributed by
# Smitha Dinesh Semwal

C#

// C# program to find height
// of complete binary tree
// from total nodes.
using System;
 
class GFG {
    static int height(int N)
    {
        return (int)Math.Ceiling(Math.Log(N
                   + 1) / Math.Log(2)) - 1;
    }
 
    // Driver node
    public static void Main()
    {
        int N = 6;
        Console.Write(height(N));
    }
}
 
// This code is contributed by
// Smitha Dinesh Semwal

PHP

<?php
// PHP program to find height
// of complete binary tree
// from total nodes.
 
function height($N)
{
    return ceil(log($N + 1, 2)) - 1;
}
 
// Driver Code
$N = 6;
echo height($N);
 
// This code is contributed by aj_36
?>

Javascript

<script>
 
    // Javascript program to find height
    // of complete binary tree
    // from total nodes.
     
    function height(N)
    {
        return Math.ceil(Math.log(N + 1) / Math.log(2)) - 1;
    }
     
      let N = 6;
      document.write(height(N));
         
</script>

Output :

My Personal Notes

Related Articles

Table of Contents

Height of a complete binary tree (or Heap) with N nodes

C++

Java

Python 3

C#

PHP

Javascript

Start Your Coding Journey Now!