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perl scripting perl scripting 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 * ..

perl scripting .. 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.

perl scripting 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.

perl scripting (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); }}It can be proven mathematically that all recursive algorithms have non-recursive counterparts. For instance the factorial method could have been written non-recursively like this:public static long factorial (int n) { long result = 1; for (int i = 1; i <= n; i++) { result *= i; } return result;}The non-recursive equivalent in this problem is straight-forward, but sometimes the non-recursive counterpart to a recursive algorithm isn't at all obvious. To see that one always exists, note that at the machine level of the computer, there's no such thing as recursion and that everything consists of values on a stack. Therefore even if you can't find a simpler way to rewrite the algorithm without recursion, you can always use your own stack instead of the Java stack.

perl scripting

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