Do iterative and recursive versions of an algorithm have the same time complexity?

Question

Say, for example, the iterative and recursive versions of the Fibonacci series. Do they have the same time complexity?

Answer 1

Yes, if you use exactly the same ideas underlying the algorithm, it does not matter. However, recursion is often easy to use with regard to iteration. For instance, writing a recursive version of the towers of Hanoi is quite easy. Transforming the recursive version into a corresponding iterative version is difficult and error prone even though it can be done. Actually there is theorem that states that every recursive algorithm can be transformed into an equivalent iterative one (doing this requires mimicking the recursion iteratively using one or more stack data structures to hold parameters passed to recursive invocations).