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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | class Factorial { 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 3 is “ + f.fact(4)); System.out.println(“Factorial of 3 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 2. This call will return 1, which is then be called a third time with an argument of 1. This call will return1, 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 multiply 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, 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.

## No comments:

## Post a Comment