You probably already see one problem with recursion. Where does it all end? In fact when you write recursive methods you have to be careful to include stopping conditions. Although Java doesn't put any particular limits on the depth to which you can expand a recursion, it is very possible to have a run-away recursion eat up all the memory in your computer.

Let's look at an example. n! (pronounced "En-factorial) is defined as n times n-1 times n-2 times n-3 ... times 2 times 1 where n is a positive integer. 0! is defined as 1. As you see n! = n time (n-1)!. This lends itself to recursive calculation, as in the following method:

public static long factorial (int n) { if (n == 0) { return 1; } else { return n*factorial(n-1); } } Something to think about: What happens if a negative integer is passed into the factorial method? For example suppose you ask for factorial(-1). Then you get the following chain of calls: -1 * -2 * -3 * -4 * .... If you're lucky your program may unexpectedly pop into the positive numbers and count down to zero. If you're not, your program will crash with a StackOutOfMemoryError. Stopping conditions are very important. In this case you should check to see if you've been passed a negative integer; and, if you have been, return infinity. ( The factorial is a special case of the gamma function for non-negative integers. Although the factorial function is only defined for non-negative integers, the gamma function is defined for all real numbers. It is possible to show that the gamma function is infinite for negative integers. ) Java doesn't support infinite values for longs, though, so return the warning value -1 instead. (Java does support infinite values for floats and doubles.) Here's a better recursive factorial method:

public static long factorial (int n) { if (n < 0) { return -1; } else if (n == 0) { return 1; } else { return n*factorial(n-1); } }