Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

3.5 Recursion
We have seen that repetition can be achieved by writing loops, such as for loops and
while loops. Another way to achieve repetition is through recursion, which occurs
when a function calls itself. We have seen examples of methods calling other
methods, so it should come as no surprise that most modern programming languages,
including Java, allow a method to call itself. In this section, we will see why this
capability provides an elegant and powerful alternative for performing repetitive
tasks.
The Factorial function
To illustrate recursion, let us begin with a simple example of computing the value
of the factorial function. The factorial of a positive integer n, denoted n!, is defined
as the product of the integers from 1 to n. If n = 0, then n! is defined as 1 by
convention. More formally, for any integer n ≥ 0,
For example, 5! = 5·4·3·2·1 = 120. To make the connection with methods clearer,
we use the notation factorial(n) to denote n!.
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