Design a greedy algorithm which takes as input the number of turkeys n, and the n lists of intervals [a_i, b_i ], and outputs the maximum number of turkeys m that you can talk to. You are expected to write the pseudocode of your algorithm.

Find a closest pair (p, q) of points from the input set. Points p and q (in any

order) form the first two points in your sequence. Now repeatedly pick from

among the “not yet picked” points, a point that is closest to the last point in

the sequence (with ties broken arbitrarily). Append the newly picked point to

the sequence. Do this until all points are picked.

(a) The intuition for this algorithm is that it tries to get to the next city by traveling

as short a distance as possible. However, this greedy algorithm does not always

produce an optimal traveling salesperson’s tour. Demonstrate this by constructing

a counterexample, i.e., an input set of points for which there exists a tour that is

shorter in length than the tour constructed by the above greedy algorithm. For your

counterexample, clearly show what the greedy algorithm produces and also identify

a shorter tour.

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