Java™ How to Program, Seventh Edition

15.3. Example Using Recursion: Factorials

Let us write a recursive program to perform a popular mathematical calculation. Consider the factorial of a positive integer n, written n! (and pronounced “n factorial”), which is the product

n · (n – 1) · (n – 2) · ... · 1

with 1! equal to 1 and 0! defined to be 1. For example, 5! is the product 5 · 4 · 3 · 2 · 1, which is equal to 120.

The factorial of integer number (where number ≥ 0) can be calculated iteratively (nonrecursively) using a for statement as follows:

factorial = 1;

for ( int counter = number; counter >= 1; counter-- )
   factorial *= counter;

A recursive declaration of the factorial method is arrived at by observing the following relationship:

n! = n · (n – 1)!

For example, 5! is clearly ...