# t3 - n State and prove time complexity of your algorithm 1...

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COT 5405, Test 3 Duration - 90 mins, 2 Problems (10 pts each) 1. (10 points) Supposethatyouhaveonemachineandasetof n jobs a 1 ,...,a n toprocess on that machine. Each job a j has a processing time t j and a proFt p j , and a deadline d j . The machine can process only one job at a time, and a job a j must run uninterruptedly for t j consecutive time units. If job a j is completed by its deadline d j , you receive a proFt p j , but if it is completed after its deadline, you receive a proFt of 0. Give an eﬃcient algorithm to Fnd the schedule that obtains the maximum amount of proFt, assuming that all processing times are integers between 1 and

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Unformatted text preview: n . State and prove time complexity of your algorithm. 1 2. (10 points) Let A = { A 1 , . . ., A n } be a set of distinct coin types, where A 1 < A 2 < . . . < A n . The coin-changing problem is deFned as follows. Given an integer C , Fnd the smallest number of coins from A , that add up to C , given that unlimited number of coins of each type is available. Design an eﬃcientdynamicprogrammingalgorithmthatoninputs A and C , outputs the minimum number of coins needed to solve the coin-changing problem. State and prove time complexity of your algorithm. 2...
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t3 - n State and prove time complexity of your algorithm 1...

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