Example: Factorials

The most popular example of using recursion is calculating the factorial of a positive integer $N$. The factorial of a positive integer $N$ is just the product of all the integers from $1$ to $N$. For example, the factorial of $5$, written as $5!$, is calculated as $5 * 4 * 3 * 2 * 1 = 120$. The definition of the factorial function itself is recursive.

$$ \text{fact}(N) = N * \text{fact}(N - 1) $$

The corresponding pseudocode is shown below.

function FACT(N)
    if N == 1
        return 1
        return N * FACT(N-1)
    end if
end function

The recursive version of the factorial is slower than the iterative version, especially for high values of $N$. However, the recursive version is simpler to program and more elegant, which typically results in programs that are easier to maintain over their lifetimes.