A Closer Look at Methods and Classes - Recursion
(Page 6 of 12 )
Java supports recursion. Recursion is the process of defining something in terms of itself. As it relates to Java programming, recursion is the attribute that allows a method to call itself. A method that calls itself is said to be recursive.
The classic example of recursion is the computation of the factorial of a number. The factorial of a number N is the product of all the whole numbers between 1 and N. For example, 3 factorial is 1 × 2 × 3, or 6. Here is how a factorial can be computed by use of a recursive method:
// A simple example of recursion.
class Factorial {
// this is a recursive function
int fact(int n) {
int result;
if(n==1) return 1;
result = fact(n-1) * n;
return result;
}
}
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(n–1)*n. To evaluate this expression, fact( ) is called with n–1. 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. A recursive call does not make a new copy of the method. Only the arguments are new. 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. Some problems, especially AI-related ones, seem to lend themselves to recursive solutions. Finally, some people seem to think recursively more easily than iteratively.
When writing recursive methods, you must have an if statement somewhere to force the method to return without the recursive call being executed. If you don’t do this, once you call the method, it will never return. This is a very common error in working with recursion. Use println( ) statements liberally during development so that you can watch what is going on and abort execution if you see that you have made a mistake.
Here is one more example of recursion. The recursive method printArray( ) prints the first i elements in the array values.
// Another example that uses recursion.
class RecTest {
int values[];
RecTest(int i) {
values = new int[i];
}
// display array -- recursively
void printArray(int i) {
if(i==0) return;
else printArray(i-1);
System.out.println("[" + (i-1) + "] " + values[i-1]);
}
}
class Recursion2 {
public static void main(String args[]) {
RecTest ob = new RecTest(10);
int i;
for(i=0; i<10;; i++) ob.values[i] = i;
ob.printArray(10);
}
}
This program generates the following output:
[0] 0
[1] 1
[2] 2
[3] 3
[4] 4
[5] 5
[6] 6
[7] 7
[8] 8
[9] 9
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 This article is excerpted from chapter 7 of Java: the Complete Reference, J2SE 5 Edition, written by Herbert Schildt (McGraw-Hill/Osborne, 2004; ISBN: 0072230738). Check it out at your favorite bookstore. Buy this book now.
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