# 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 :
()
/    \
()     ()
/  \    /  \
()    () ()   ()
/ \
()  ()```

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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

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## Javascript

 ``
Output :
`2`

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