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

Last Updated : 09 Aug, 2022

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 : 3         ()       /    \      ()     ()     /  \    /  \   ()    () ()   ()  / \ ()  ()

Let the size of the heap be N and the height be h. If we take a few examples, we can notice that the value of h in a complete binary tree is floor(log₂N).

Examples:

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

Implementation:

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 floor(log2(N));
}
 
// driver node
int main()
{
    int N = 2;
    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

Time Complexity: O(1), Since performing constant operations.
Auxiliary Space: O(1), Since constant extra space is used.

Heap Sort for decreasing order using min heap

Shashank_Pathak

Improve

Article Tags :

Practice Tags :

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

C++

Java

Python 3

C#

PHP

Javascript

Similar Reads

Some other type of Heap

Easy problems on Heap