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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 3.1 - Problem 59e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 3.1 - Problem 59e

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# a) Devise a greedy algorithm that determines the fewest

ISBN: 9780073383095 37

## Solution for problem 59E Chapter 3.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 59E

a) Devise a greedy algorithm that determines the fewest lecture halls needed to accommodate n talks given the starting and ending time for each talk.

b) Prove that your algorithm is optimal.

Suppose we have s men m1, m2, …, ms and s women w1, w2, …, ws. We wish to match each person with a member of the opposite gender. Furthermore, suppose that each person ranks, in order of preference, with no ties, the people of the opposite gender. We say that a matching of people of opposite genders to form couples is stable if we cannot find a man m and a woman w who are not assigned to each other such that m prefers w over his assigned partner and w prefers m to her assigned partner.

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