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# Double factorial

• Difficulty Level : Easy
• Last Updated : 29 Apr, 2021

Double factorial of a non-negative integer n, is the product of all the integers from 1 to n that have the same parity (odd or even) as n. It is also called as semifactorial of a number and is denoted by !!. For example, double factorial of 9 is 9*7*5*3*1 which is 945. Note that, a consequence of this definition is 0!! = 1.
Examples:

```Input: 6
Output: 48
Note that 6*4*2 = 48

Input: 7
Output: 105
Note that 7*5*3 = 105```

For even n, the double factorial is: For odd n, the double factorial is: Recursive Solution:
Double factorial can be calculated using following recursive formula.

```  n!! = n * (n-2)!!
n!! = 1 if n = 0 or n = 1 ```

Following is the implementation of double factorial.

## C++

 `#include`` ` `// function to find double factorial of given number``unsigned ``int` `doublefactorial(unsigned ``int` `n)``{``    ``if` `(n == 0 || n==1)``      ``return` `1;``    ``return` `n*doublefactorial(n-2);``}`` ` `int` `main()``{``    ``printf``(``"Double factorial is %d"``, doublefactorial(5));``    ``return` `0;``}`

## Java

 `import` `java.io.*;` `class` `GFG {` `    ``// function to find double factorial``    ``// of given number``    ``static` `long` `doublefactorial(``long` `n)``    ``{``        ``if` `(n == ``0` `|| n==``1``)``            ``return` `1``;``            ` `        ``return` `n * doublefactorial(n - ``2``);``    ``}` `    ``// Driver code``    ``static` `public` `void` `main (String[] args)``    ``{``        ``System.out.println(``"Double factorial"``            ``+ ``" is "` `+ doublefactorial(``5``));``    ``}``}` `// This code is contributed by anuj_67.`

## Python3

 `# function to find double``# factorial of given number``def` `doublefactorial(n):` `    ``if` `(n ``=``=` `0` `or` `n ``=``=` `1``):``        ``return` `1``;``    ``return` `n ``*` `doublefactorial(n ``-` `2``);` `# Driver Code``print``(``"Double factorial is"``,``       ``doublefactorial(``5``));` `# This code is contributed``# by Smitha`

## C#

 `using` `System;` `class` `GFG {` `    ``// function to find double factorial``    ``// of given number``    ``static` `uint` `doublefactorial(``uint` `n)``    ``{``        ``if` `(n == 0 || n==1)``            ``return` `1;``            ` `        ``return` `n * doublefactorial(n - 2);``    ``}` `    ``// Driver code``    ``static` `public` `void` `Main ()``    ``{``        ``Console.WriteLine(``"Double factorial"``             ``+ ``" is "` `+ doublefactorial(5));``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output:

`Double factorial is 15`

Iterative Solution:
Double factorial can also be calculated iteratively as recursion can be costly for large numbers.

## C++

 `#include`` ` `// function to find double factorial of given number``unsigned ``int` `doublefactorial(unsigned ``int` `n)``{``    ``int` `res = 1;``    ``for` `(``int` `i=n; i>=0; i=i-2)``    ``{``        ``if` `(i==0 || i==1)``            ``return` `res;``        ``else``            ``res *= i;``    ``}``}`` ` `int` `main()``{``    ``printf``(``"Double factorial is %d"``, doublefactorial(5));``    ``return` `0;``}`

## Java

 `// Java Program to find double factorial``// of given number``import` `java .io.*;` `class` `GFG {``    ` `    ``// function to find double factorial``    ``// of given number``    ``static` `int` `doublefactorial(``int` `n)``    ``{``        ``int` `res = ``1``;``        ``for` `(``int` `i = n; i >= ``0``; i = i-``2``)``        ``{``            ``if` `(i == ``0` `|| i == ``1``)``                ``return` `res;``            ``else``                ``res *= i;``        ``}``        ` `        ``return` `res;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``System.out.println(``"Double factorial"``             ``+ ``" is "` `+ doublefactorial(``5``));``    ``}``}` `// This code is Contributed by Anuj_67`

## Python3

 `# Python3 Program to find double``# factorial of given number` `# Function to find double``# factorial of given number``def` `doublefactorial(n):``    ``res ``=` `1``;``    ``for` `i ``in` `range``(n, ``-``1``, ``-``2``):``        ``if``(i ``=``=` `0` `or` `i ``=``=` `1``):``            ``return` `res;``        ``else``:``            ``res ``*``=` `i;``    ` `# Driver Code``print``(``"Double factorial is"``,``        ``doublefactorial(``5``));` `# This code is contributed by mits`

## C#

 `// C# Program to find double factorial``// of given number``using` `System;` `class` `GFG {``    ` `    ``// function to find double factorial``    ``// of given number``    ``static` `int` `doublefactorial(``int` `n)``    ``{``        ``int` `res = 1;``        ``for` `(``int` `i = n; i >= 0; i = i-2)``        ``{``            ``if` `(i == 0 || i == 1)``                ``return` `res;``            ``else``                ``res *= i;``        ``}``        ` `        ``return` `res;``    ``}` `    ``// Driver code   ``    ``static` `void` `Main()``    ``{``        ``Console.Write(``"Double factorial"``          ``+ ``" is "` `+ doublefactorial(5));``    ``}``}` `// This code is Contributed by Anuj_67`

## PHP

 `= 0; ``\$i` `= ``\$i` `- 2)``    ``{``        ``if` `(``\$i` `== 0 ``or` `\$i` `== 1)``            ``return` `\$res``;``        ``else``            ``\$res` `*= ``\$i``;``    ``}``}  ``    ` `    ``// Driver Code``    ``echo` `"Double factorial is "``, doublefactorial(5);` `// This code is contributed by anuj_67.``?>`

## Javascript

 ``

Output:

`Double factorial is 15`

Time complexity of the above solutions is O(n).
Important Points :

1. Double factorial and factorial are related using below formula.

```Note : n!! means double factorial.
If n is even, i.e., n = 2k
n!! = 2kk!
Else (n = 2k + 1)
n!! = (2k)! / 2kk!
```

2.Double factorial is frequently used in combinatorics. Refer wiki for list of applications. An example application is count of perfect matchings of a complete graph Kn+1 for odd n.

References:
https://en.wikipedia.org/wiki/Double_factorial
This article is contributed by Rahul Agrawal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.