Consider the following problem. The input consists of n skiers with heights p1, ··· , pn , and n skies with heights s1, ··· , sn. The problem is to assign each skier a ski to to minimize the average difference between the height of a skier and his/her assigned ski. That is, if the ith skier is given the Alpha(i)th ski, then you want to minimize: 1/ffln ∑i=1 to n |pi- s↵(i)| (a) Consider the following greedy algorithm. Find the skier and ski whose height di↵erence is minimized. Assign this skier this ski. Repeat the process until every skier has a ski. Prove of disprove that this algorithm is correct. (b) Consider the following greedy algorithm. Give the shortest skier the shortest ski, give the second shortest skier the second shortest ski, give the third shortest skier the third shortest ski, etc.Prove of disprove that this algorithm is correct. HINT: One of the above greedy algorithms is correct and one is incorrect for the other. The proof of correctness must be done using an exchange argument.

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