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

The factorial function can be defined in a manner that suggests a recursive
formulation. To see this, observe that
factorial(5) = 5 · (4 · 3 · 2 · 1) = 5 · factorial(4).
Thus, we can define factorial(5) in terms of factorial(4). In general, for a
positive integer n, we can define factorial(n) to be n·factorial(n − 1). This
leads to the following recursive definition.
This definition is typical of many recursive definitions. First, it contains one or
more base cases, which are defined nonrecursively in terms of fixed quantities. In
this case, n = 0 is the base case. It also contains one or more recursive cases, which
are defined by appealing to the definition of the function being defined. Observe
that there is no circularity in this definition, because each time the function is
invoked, its argument is smaller by one.
A Recursive Implementation of the Factorial Function
Let us consider a Java implementation of the factorial function shown in Code
Fragment 3.29 under the name recursiveFactorial(). Notice that no
looping was needed here. The repeated recursive invocations of the function takes
the place of looping.
Code Fragment 3.29:
the factorial function.
A recursive implementation of
We can illustrate the execution of a recursive function definition by means of a
recursion trace. Each entry of the trace corresponds to a recursive call. Each new
recursive function call is indicated by an arrow to the newly called function. When
the function returns, an arrow showing this return is drawn and the return value may
be indicated with this arrow. An example of a trace is shown in Figure 3.21.
What is the advantage of using recursion? Although the recursive implementation
of the factorial function is somewhat simpler than the iterative version, in this case
there is no compelling reason for preferring recursion over iteration. For some
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