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.
Recursion is used to express an algorithm that is naturally recursive in a form that is more easily understandable. A "naturally recursive" algorithm is one where the answer is built from the answers to smaller sub-problems which are in turn built from the answers to yet smaller sub-problems, etc.
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.
I have a Computer Science Midterm tomorrow and I need help determining the complexity of these recursive functions. I know how to solve simple cases, but I am still trying to learn how to solve these
Well, in general, recursion can be mimicked as iteration by simply using a storage variable. Note that recursion and iteration are generally equivalent; one can almost always be converted to the other. A tail-recursive function is very easily converted to an iterative one. Just make the accumulator variable a local one, and iterate instead of ...
1 By using an internal ConcurrentHashMap which theoretically might allow this recursive implementation to properly operate in a multithreaded environment, I have implemented a fib function that uses both BigInteger and Recursion. Takes about 53ms to calculate the first 100 fib numbers.
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.
