As president of the Northeastern chapter of the Big Ballers Club, you need to staff a...
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As president of the Northeastern chapter of the Big Ballers Club, you need to staff a booth at this year's open house. The open house runs for the interval [s, t]. There are n volunteers, each of which is able to cover the booth for the interval [si, ti] (i € {1,...,n)). You need to select a set of volunteers SC (1,...,n} to cover the entire open house, meaning that Uies [si, ti] 2 [s, t]. Equivalently, for every time z € [s, t], there is some volunteer i ES such that z € [s,, ti]. Each member will be paid for their services, but ironically the Big Ballers Club has very limited funds, so you need to ensure IS] is as small as possible. In this problem you will design an efficient greedy algorithm that takes as input the numbers s, t,s₁,₁,Sn, and outputs a set S that covers the open house and uses the minimum number of staffers. The running time of your algorithm should be at most O(n²). You may assume that a solution exists. The following is an example input with 9 volunteers. One optimal solution is S = {1,3,9). [$4,4] [$₁,₁] [Sg, tg] [$6.t6] [$2,t₂] [$5.ts] [S7, t7] [58, ta] (b) Analyze the running time of your algorithm. Solution: [$3,13] (a) Describe your algorithm in pseudocode. Provide a few sentences describing your algorithm. Solution: (c) Prove that your algorithm finds a set of volunteers 5 of minimum size to cover the open house. Solution: As president of the Northeastern chapter of the Big Ballers Club, you need to staff a booth at this year's open house. The open house runs for the interval [s, t]. There are n volunteers, each of which is able to cover the booth for the interval [si, ti] (i € {1,...,n)). You need to select a set of volunteers SC (1,...,n} to cover the entire open house, meaning that Uies [si, ti] 2 [s, t]. Equivalently, for every time z € [s, t], there is some volunteer i ES such that z € [s,, ti]. Each member will be paid for their services, but ironically the Big Ballers Club has very limited funds, so you need to ensure IS] is as small as possible. In this problem you will design an efficient greedy algorithm that takes as input the numbers s, t,s₁,₁,Sn, and outputs a set S that covers the open house and uses the minimum number of staffers. The running time of your algorithm should be at most O(n²). You may assume that a solution exists. The following is an example input with 9 volunteers. One optimal solution is S = {1,3,9). [$4,4] [$₁,₁] [Sg, tg] [$6.t6] [$2,t₂] [$5.ts] [S7, t7] [58, ta] (b) Analyze the running time of your algorithm. Solution: [$3,13] (a) Describe your algorithm in pseudocode. Provide a few sentences describing your algorithm. Solution: (c) Prove that your algorithm finds a set of volunteers 5 of minimum size to cover the open house. Solution:
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Related Book For
Income Tax Fundamentals 2015
ISBN: 9781305177772
33rd Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven Gill
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