Recursion - Absolute Java - page 662

General Form for a Recursive Method That Returns a Value
The recursive methods you have seen thus far are all void methods, but recursion is
not limited to these methods. A recursive method can return a value of any type. The
technique for designing recursive methods that return a value is basically the same
as what you learned for void methods. An outline for a successful recursive method
definition that returns a value is as follows:
• One or more cases in which the value returned is computed in terms of calls to the
same method (that is, using recursive calls). As is the case with void methods, the
arguments for the recursive calls should intuitively be “smaller.”
• One or more cases in which the value returned is computed without the use of any
recursive calls. These cases without any recursive calls are called base cases or stopping
cases (just as they were with void methods).
This technique is illustrated in the next Programming Example.
EXAMPLE: Another Powers Method
In Chapter 5 , we introduced the static method pow of the class Math , that computes
powers. For example, Math.pow(2.0,3.0) returns 2.0 3.0 , so the following sets the
variable result equal to 8.0 :
double result = Math.pow(2.0, 3.0);
The method pow takes two arguments of type double and returns a value of type
double . Display 11.3 contains a recursive definition for a static method that is
similar to pow , but that works with the type int rather than double . This new
method is called power . For example, the following will set the value of result2
equal to 8 , because 2 3 is 8 :
int result2 = power(2, 3);
Outside the defining class, this would be written as
int result2 = RecursionDemo2.power(2, 3);
Our main reason for defining the method power is to have a simple example of a
recursive method, but there are situations in which the method power would be
preferable to the method pow . The method pow returns a value of type double ,
which is only an approximate quantity. The method power returns a value of type
int , which is an exact quantity. In some situations, you might need the additional
accuracy provided by the method power .
The definition of the method power is based on the following formula:
x n is equal to x n−1 * x