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

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

Examples :

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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 
?> 

Output :

My Personal Notes

Recommended Posts:

Shashank_Pathak

Maths is the language of nature

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : Smitha Dinesh Semwal, jit_t

Writing code in comment? Please use ide.geeksforgeeks.org, generate link and share the link here.