Implement the following algorithm (it means create the code in any programming language that you are familiar with):

Let C(n,k) be the number of combinations of n items taken k at a time.

C(n,k) = 1 if n = k or k = 0

else

C(n,k) = C(n - 1,k - 1) + C(n - 1,k)

As in the Fibonacci Numbers study case, implement this algorithm (above) in two ways:

(a) recursive variant

(b) non-recursive variant.

a) What is the order (THETA) of this algorithm worst case if recursion is used?

Prove your answer by formulating and solving the T(n) equation or by recursion tree.

b) What is the order (THETA) of the non-recursive version of this algorithm?

Prove your answer by formulating and solving the T(n) equation or by "recursion tree".