Consider the following algorithm to make change. The algorithm takes as input:…

Consider the following algorithm to make change. The algorithm takes as input:

• tr, the amount of change to make. • p, the base of the denomination set (the “coins” are powers of p).

IN: n, p E N = 1, 2, … p > 1 1: D ; 2: C 3: r 4—n 4: while r > 0 do 5: x 4— max(x E Dix

(a) Which of the following best describes the algorithm above (circle one): divide-and-conquer dynamic greedy

(b) Prove that the algorithm is fully correct. You should start by finding a suitable loop invariant for partial correctness. Note that for any p > I:

pn = 1 + E (ps(p— I)) ce

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