factorial.md

title
Factorial

Definitions

• The factorial of 0 (zero) is defined as being 1 (unity).
• The Factorial Function of a positive integer, n, is defined as the product of the sequence: n, n-1, n-2, ... 1

Example

n	n!	n	n!	n	n!
0	1	10	3628800	20	2432902008176640000
1	1	11	39916800	...
2	2	12	479001600	100	9.332621544 × 10^157
3	6	13	6227020800
4	24	14	87178291200
5	120	15	1307674368000
6	720	16	20922789888000
7	5040	17	355687428096000
8	40320	18	6402373705728000
9	362880	19	121645100408832000

Task

Write a function to return the factorial of a number. Solutions can be recursive or iterative.

Ruby

# Recursive
def factorial(n)
  n == 0 ? 1 : n * factorial(n - 1)
end

# Iterative with Range#each
def factorial(n)
  (2...n).each { |i| n *= i }
  n == 0 ? 1 : n
end

# Functional with Range#reduce
def factorial(n)
  (1..n).reduce(1){ |prod, i| prod * i }
end

(Source: Rosetta Code)

Perl

# Recursive
sub factorial
{
  my $n = shift;
  ($n == 0)? 1 : $n*factorial($n-1);
}

# Iterative using a .. range
sub factorial {
    my $r = 1;
    $r *= $_ for 1..shift;
    $r;
}

# Functional with reduce
use List::Util qw(reduce);
sub factorial
{
  my $n = shift;
  reduce { $a * $b } 1, 1 .. $n
}

(Source: Rosetta Code)

Python

# Recursive
def factorial(n):
    z=1
    if n>1:
        z=n*factorial(n-1)
    return z

# Iterative
def factorial(n):
    result = 1
    for i in range(1, n+1):
        result *= i
    return result

# Functional with reduce
from operator import mul
from functools import reduce

def factorial(n):
    return reduce(mul, range(1,n+1), 1)

(Source: Rosetta Code)

PHP

<?php
// Recursive
function factorial($n) {
  if ($n < 0)  return 0;

  if ($n == 0) return 1;
  else         return $n * factorial($n-1);
}
?>

<?php
// Iterative
function factorial($n) {
  if ($n < 0)  return 0;

  $factorial = 1;
  for ($i = $n; $i >= 1; $i--) {
    $factorial = $factorial * $i;
  }
  return $factorial;
}
?>

(Source: Rosetta Code)

Lua

# Recursive
function fact(n)
  return n > 0 and n * fact(n-1) or 1
end

# Iterative
# ??

(Source: Rosetta Code)

JavaScript

// Recursive
var factorial = n => (n < 2) ? 1 : n * factorial(n - 1);

// Recursive (Classic)
function factorial(n) {
    return n < 2 ? 1 : n * factorial(n - 1);
}

// Iterative
function factorial(n) {
  var sum = 1;
  while (n > 1) {
    sum *= n;
    n--;
  }
  return sum;
}

(Source: Rosetta Code)

Java

// Recursive
public static long factorial(int n) {
    return (n < 2) ? 1 : n * factorial(n - 1);
}

// Iterative
public static long fact(int n) {
    long result = 1;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

(Source: Rosetta Code)

C

/* Recursive */
int factorial(int n) {
    return n == 0 ? 1 : n * factorial(n - 1);
}

/* Iterative */
int factorial(int n) {
    int result = 1;
    for (int i = 1; i <= n; ++i)
        result *= i;
    return result;
}

(Source: Rosetta Code)

Go

// Recursive
func Factorial(n uint64)(result uint64) {
	if(n > 0) {
		result = n * Factorial(n-1)
		return result
	}
	return 1
}

// Iterative
// ??

Rust

// Recursive
fn factorial(n: u64) -> u64 {
    match n {
        0 => 1,
        _ => n * factorial(n-1)
    }
}

// Iterative
fn factorial(n: u64) -> u64 {
    (1..n+1).fold(1, |p, n| p*n)
}

(Source: Rosetta Code)

Erlang

%% Recursive
factorial(1) -> 1;
factorial(N) -> N * factorial(N-1).

%% Functional with a fold
lists:foldl(fun(X,Y) -> X*Y end, 1, lists:seq(1,N)).

(Source: Rosetta Code)

Elixir (on Erlang)

# Recursive
def factorial(0), do: 1
def factorial(n) when n > 0, do: n * factorial(n - 1)

# Functional with reduce
def factorial(0), do: 1
def factorial(n) when n > 0, do: Enum.reduce(1..n, 1, &*/2)  

(Source: Rosetta Code)

Crystal

# Recursive
def factorial(n)
  n == 0 ? 1 : n * factorial(n - 1)
end

# Iterative with Range#each
def factorial(n)
  (2...n).each { |i| n *= i }
  n == 0 ? 1 : n
end

# Functional with Range#reduce
def factorial(n)
  (1..n).reduce(1){ |prod, i| prod * i }
end

References

• Factorial @ Rosetta Code
• Factorial @ Wikipedia