Write a dynamic programming algorithm to calculate the following recursive function (5"). |4- еxp n-1)+12-еxp (n- 2), п>1 exp(n)= 6, n=1 1, n=0

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Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic programming-based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Draw the recursion tree for the algorithm where N = 7. Derive the complexity bound of the algorithm. Do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.

A recursive algorithm has been developed as shown below: Input: List A = (a₁,..., an) such that N > 1 Output: value x foo(A) if length(A) == 1 return a₁ A' = (a₁,..., aN-1) q = foo(A') if (q> an) else return q return an State what problem this algorithm solves and write down the two recurrence equations that characterise this recursive algorithm.