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pset5 - Introduction to Algorithms Massachusetts Institute...

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Introduction to Algorithms October 23, 2003 Massachusetts Institute of Technology 6.046J/18.410J Professors Shafi Goldwasser and Silvio Micali Handout 17 Problem Set 5 This problem set is due in recitation on Friday, October 31. Reading: Chapters 15.1-15.5, 16.1-16.3. There are four problems. Each problem is to be done on a separate sheet (or sheets) of three- hole punched paper. Mark the top of each sheet with your name, the course number, the problem number, your recitation section, the date, and the names of any students with whom you collabo- rated. Problem 2-1. Spam and Customer Service. You run a meat-processing plant in Cambridgeport. Unfortunately, due to a mixup with your sup- pliers in Peoria, you have accidentally produced a batch of spoiled sausages. When your customer service desk opens at 8am, there are customers waiting in the lobby to return the rotten sausages. Say that customer has sausages, and that all the ’s are distinct. Your underpaid customer service operator requires minutes to handle customer ’s complaint, for some constant . You cannot “partially process” a complaint—all of customer ’s sausage returns must be handled together—and only one customer can be handled at a time. Because you want to maintain the golden reputation of your company, you have decided to pay one dollar to each customer for every minute before ’s complaint is completely handled. For example, if customer 3 is handled first and customer 5 is handled second, you pay dollars to customer 3 and dollars to customer 5. Give an efficient algorithm to find the order
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