}
}
class Recursion {
public static void main(String args[]) {
Factorial f = new Factorial();
System.out.println("Factorial of 3 is " + f.fact(3));
System.out.println("Factorial of 4 is " + f.fact(4));
System.out.println("Factorial of 5 is " + f.fact(5));
}
}
The output from this program is shown here:
Factorial of 3 is 6
Factorial of 4 is 24
Factorial of 5 is 120
If you are unfamiliar with recursive methods, then the operation of fact( ) may seem a
bit confusing. Here is how it works. When fact( ) is called with an argument of 1, the function
returns 1; otherwise, it returns the product of fact(n1)*n. To evaluate this expression, fact( )
is called with n1. This process repeats until n equals 1 and the calls to the method begin
returning.
To better understand how the fact( ) method works, let's go through a short example.
When you compute the factorial of 3, the first call to fact( ) will cause a second call to be
made with an argument of 2. This invocation will cause fact( ) to be called a third time with
an argument of 1. This call will return 1, which is then multiplied by 2 (the value of n in the
second invocation). This result (which is 2) is then returned to the original invocation of
fact( ) and multiplied by 3 (the original value of n). This yields the answer, 6. You might
find it interesting to insert println( ) statements into fact( ), which will show at what level
each call is and what the intermediate answers are.
When a method calls itself, new local variables and parameters are allocated storage
on the stack, and the method code is executed with these new variables from the start.
As each recursive call returns, the old local variables and parameters are removed from
the stack, and execution resumes at the point of the call inside the method. Recursive
methods could be said to "telescope" out and back.
Recursive versions of many routines may execute a bit more slowly than the iterative
equivalent because of the added overhead of the additional function calls. Many recursive
calls to a method could cause a stack overrun. Because storage for parameters and local
variables is on the stack and each new call creates a new copy of these variables, it is possible
that the stack could be exhausted. If this occurs, the Java run-time system will cause an
exception. However, you probably will not have to worry about this unless a recursive
routine runs wild.
The main advantage to recursive methods is that they can be used to create clearer and
simpler versions of several algorithms than can their iterative relatives. For example, the
QuickSort sorting algorithm is quite difficult to implement in an iterative way. Also, some types
of AI-related algorithms are most easily implemented using recursive solutions.
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