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

In Section 7.3.6 we described how to evaluate an arithmetic expression using a
postorder traversal, which is exactly the algorithm the JVM uses. We described
that algorithm in a recursive way, however, not in a way that explicitly uses an
operand stack. Nevertheless, this recursive description is equivalent to a
nonrecursive version based on using an operand stack.
Implementing Recursion
One of the benefits of using a stack to implement method invocation is that it
allows programs to use recursion. That is, it allows a method to call itself, as
discussed in Section 3.5. Interestingly, early programming languages, such as
Cobol and Fortran, did not originally use run-time stacks to implement method
and procedure calls. But because of the elegance and efficiency that recursion
allows, all modern programming languages, including the modern versions of
classic languages like Cobol and Fortran, utilize a run-time stack for method and
procedure calls.
In the execution of a recursive method, each box of the recursion trace
corresponds to a frame of the Java method stack. Also, the content of the Java
method stack corresponds to the chain of boxes from the initial method invocation
to the current one.
To better illustrate how a run-time stack allows for recursive methods, let us
consider a Java implementation of the classic recursive definition of the factorial
function,
n! = n(n − 1)(n − 2)1,
as shown in Code Fragment 14.1.
Code Fragment 14.1: Recursive method
factorial.
The first time we call method factorial, its stack frame includes a local
variable storing the value n. Method factorial() recursively calls itself to
compute (n − 1)!, which pushes a new frame on the Java run-time stack. In turn,
this recursive invocation calls itself to compute (n − 2)!, etc. The chain of
889