Note: Please show all work and explanations to receive any credit! Thank you.

IV. [50 points] Design (or give) an algorithm. Based on your obtained algorithm, give (i) a natural size metric for its inputs; (ii) its basic operation; (ii) whether the basic operation count can be different for inputs of the same size; and (iv) What is the efficiency class of these algorithm: Cutting a stick: Outline an algorithm that performs this task with the minimum number of cuts if several pieces of the stick can be cut at the same time. Also give a formula for the minimum number of cuts. a. A sticks n inches long needs to be cut into n 1-inch pieces. b. Lighter or heavier? You have n> 2 identical-looking coins and a two-pan balance scale with no weights. One of the coins is a fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same. Design a 0(1) algorithm to determine whether the fake coin is lighter or heavier than the others