Smallest Hitting Set: Design and analyze an efficient greedy algorithm for the following problem:

Input: A set P = { p1, p2, … , pn} of points, and a set I = { I1, I2, … , Im} of intervals, all on the real line. These intervals and points are given in no particular order. Each interval is given by its starting and finishing times.

Output: (i) A minimum cardinality subset H of P such that every interval in I is hit by (i.e., contains) at least one point in H, or

(ii) an interval Ik I that is not hit by any point in P.

Input: A set P = { p1, p2, … , pn} of points, and a set I = { I1, I2, … , Im} of intervals, all on the real line. These intervals and points are given in no particular order. Each interval is given by its starting and finishing times.

Output: (i) A minimum cardinality subset H of P such that every interval in I is hit by (i.e., contains) at least one point in H, or

(ii) an interval Ik I that is not hit by any point in P.

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