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Homework 2 - W08/CS5592 Suggested Solutions to Homework Two...

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W08/CS5592 Suggested Solutions to Homework Two Design and Analysis of Algorithms Due: Monday, Feb. 18, 2008, in class There are four problems 1 The number of cars produced by Toyota company in the past n years are stored in an array A[1], A[2], …, A[ n ]. We wish to find if there is a period of consecutive years such that the total number of cars produced in this period is exactly equal to M. That is, we wish to find if there exist i and j , 1 i j n , such that = j i k k A ] [ = M. Please design an O( n ) time greedy algorithm to solve this problem. You need to give a pseudo code. 2 There are n activities, a 1 , a 2 , …, a n , that need to use a common resource. Activity i (1 i n ) needs occupy the resource for non-interrupted t i time. There is no deadline for each activity, but there is a penalty p i associated with the starting time of a i . Suppose activity a i starts to use the resource at time s i , its penalty is proportional to s i . Please design an efficient algorithm that schedules these activities starting from
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