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

Shashank_Pathak

Maths is the language of nature

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Improved By : Smitha Dinesh Semwal, jit_t

Practice Tags :

Tree

Heap