Recursion is a tree, with branches and leaves, called parents and children respectively. When you use a recursion algorithm, you more or less consciously are building a tree from the data.
0 Recursion and iteration are different ways to think about a solution. It would be dificult to explain in depth the difference in full scope. In your sample code, you aleady showed the difference. Recursive function is the one that calls itself, while iterative is the one that loops through some block of code.
Recursion is good for proto-typing a function and/or writing a base, but after you know the code works and you go back to it during the optimization phase, try to replace it with a loop.
Tail Call Recursion Once you understand how the above recursion works, you can try to make it a little bit better. Now, to find the actual result, we are depending on the value of the previous function also. The return statement cannot immediately return the value till the recursive call returns a result.
19 Recursion is more costly in memory, as each recursive call generally requires a memory address to be pushed to the stack - so that later the program could return to that point. Still, there are many cases in which recursion is a lot more natural and readable than loops - like when working with trees.
Recursion is usually much slower because all function calls must be stored in a stack to allow the return back to the caller functions. In many cases, memory has to be allocated and copied to implement scope isolation. Some optimizations, like tail call optimization, make recursions faster but aren't always possible, and aren't implemented in all languages. The main reasons to use recursion ...
Recursion started making sense to me when I stopped reading what others say about it or seeing it as something I can avoid and just wrote code. I found a problem with a solution and tried to duplicate the solution without looking.
Tail recursion optimization is to remove call stack for the tail recursion call, and instead do a jump, like in a while loop. But if you do use the return value of a recursive call before return it, it is a ordinary recursion and can't be optimized.
Why? Because recursion is typically well founded over some data structure, inducing an Initial F-algebra and allowing you to prove some properties about termination along with inductive arguments about the structure of the (recursive) computation. The process by which recursion is compiled to loops is tail call optimization.
