Headline

The product 1 * ... * n for a given natural number n

Illustration

We face an algorithmic problem because the factorial can be computed by a (simple) algorithm. Assume that n is a natural number. Then, the following steps compute the factorial of n:

  • Initialize a variable r with 1.
  • Repeat the following step until n equals 0:
    • Assign n*r to r.
    • Decrement n.
  • Return r.
Here is also an implementation in Language:Java:

  // An imperative definition of the factorial function
  public static int factorial(int n) {
    int result = 1;
    for (int i=n; i>1; i--) 
      result = result * i;
    return result;
  }

Here is also an implementation in Language:Haskell:

-- A recursive definition of the factorial function
factorial n =
  if n==0
    then 1
    else n * factorial (n-1)

See also the following collection of implementations:

http://www.willamette.edu/~fruehr/haskell/evolution.html

Citation

(http://en.wikipedia.org/wiki/Factorial, 21 April 2013)

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

5! = 5 * 4 * 3 * 2 * 1 = 120

The value of 0! is 1, according to the convention for an empty product.

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