Java How to Program, Early Objects, 11th Edition

18.3 Example Using Recursion: Factorials

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

$$n\cdot (n-1)\cdot (n-2)\cdot \dots \cdot 1$$

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

The factorial of integer number (where number $\ge 0$) can be calculated iteratively (non-recursively) using a for statement as follows:

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

A recursive declaration of the factorial calculation for integers greater than 1 is arrived at by observing the following relationship:

$$n!=n\cdot (n-1)!$$

For example, 5! is clearly ...