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create a web site create a web site 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.

create a web site 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); }}It can be proven mathematically that all recursive algorithms have non-recursive counterparts.

create a web site 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. Here's an example of a recursive program for which I have not been able to find a simple, non-recursive equivalent method. The goal is to find all possible RAM configurations for a PC, given the size of the memory chips it will accept and the number of slots it has available.

create a web site We are not concerned with how the RAM is arranged inside the PC, only with the total quantity of installed RAM. For some computers this can easily be calculated by hand. For instance Apple's PowerBook 5300 series comes with 8 megabytes of RAM soldered onto the logic board and one empty slot that can hold chips of 8, 16, 32 or 56 MB capacity. Therefore the possible Ram configurations are 8, 16, 24, 40 and 64 MB. However as the number of available slots and the number of available chip sizes increases this becomes a much more difficult problem.

create a web site

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