Skip to content
Related Articles
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 :
()
/    \
()     ()
/  \    /  \
()    () ()   ()
/ \
()  ()```

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 ``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

 ``

## Javascript

 ``
Output :
`2`

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 industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up