Suppose that each person in a group of n people votes for exactly two people from a slate of candidates to fill two positions on a committee. The top two finishers both win positions as long as each receives more than n /2 votes. a) Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n /2 votes and, if so, determine who these two candidates are. b) Use the Master Theorem to estimate the number of comparisons needed by the algorithm you devised in part (a)

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.