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

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

1

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