## Concept:

# Factorial

## 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*.

- Assign
- Return
*r*.

```
// 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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