Problem: Binomial coefficient can be computed recursively as follows:
if k=0 or k=n, then C(n,k)=1
if k>y>0, then C(n,k) = C(n-1,k-1) + C(n-1,k)
(a) Write a recursive procedure that computes the binomial coefficient. Prove that the time complexity of your procedure is: T(n,k) = 2^(n-1).
(b) Give a dynamic programming solution to the binomial coefficient algorithm. The time complexity of your solution should be O(n^2).