[prog] functions

[cristofd at hevanet.com]

> What is the 
> difference between recursion and iteration
> and why would you chose to use one over the other?

Iteration involves an explicit command to perform some set of actions 
repeatedly until some condition holds; in C++ this is typically done 
with a while loop or a for loop.
Recursion involves a function which performs some set of actions and 
also calls itself (directly or indirectly) unless some condition holds; 
in C++ the self-call is put directly into the function definition.

Quick example: find factorial of n (that is, 1*2*3*4*...*n)
With iteration:
fac = 1;
for (i=1;i<=n;i++){
    fac = fac * i;
}
With recursion:
int fac(int n){
    if (n==0){
        return 1;
    }else{
        return n*fac(n-1); /*here fac calls itself but with a different 
argument*/
    }
}

Anything that can be done with iteration can be done with recursion, and 
vice versa. In fact, some whole languages only allow using one or the 
other. In C++, where both are possible, the reasons to choose iteration 
are A. that it will sometimes lead to clearer and more concise code, and 
B. that that code may end up running faster and/or using less memory 
once it's compiled. The reason to choose recursion is that IT will 
sometimes lead to clearer and more concise code. Which is better really 
depends on
conte