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Engineering
Data Structures and Algorithms
(50 MARKS) (Greedy Algorithms.) A group of friends is organizing a bike racing competition. There are n friends and m bikes, but bikes ate not equal, some of them perform better and some of them perform worse. You may think that each bike has a performance factor pi, 1 ≤ i ≤ m in the range (1,100) where 1 is the worst and 100 is the best. Each frieng has a greed factor 9i, 1 ≤ i ≤ n which is the minimum bike performace this firend will be content with. Your goal is to maximize the number of content friends, i.e., friends i assigned a bike j with gi ≤ pj. Give a correct greedy algorithm for this problem (15 marks), prove that it finds the optimal solution (20 marks), and give an efficient implementation (15 marks).

(50 MARKS) (Greedy Algorithms.) A group of friends is organizing a bike racing competition. There are n friends and m bikes, but bikes ate not equal, some of them perform better and some of them perform worse. You may think that each bike has a performance factor pi, 1 ≤ i ≤ m in the range (1,100) where 1 is the worst and 100 is the best. Each frieng has a greed factor 9i, 1 ≤ i ≤ n which is the minimum bike performace this firend will be content with. Your goal is to maximize the number of content friends, i.e., friends i assigned a bike j with gi ≤ pj. Give a correct greedy algorithm for this problem (15 marks), prove that it finds the optimal solution (20 marks), and give an efficient implementation (15 marks).

Question
(50 MARKS) (Greedy Algorithms.) A group of friends is organizing a bike racing competition. There are n friends and m bikes, but bikes ate not equal, some of them perform better and some of them perform worse. You may think that each bike has a performance factor pi, 1 ≤ i ≤ m in the range (1,100) where 1 is the worst and 100 is the best. Each frieng has a greed factor 9i, 1 ≤ i ≤ n which is the minimum bike performace this firend will be content with. Your goal is to maximize the number of content friends, i.e., friends i assigned a bike j with gi ≤ pj. Give a correct greedy algorithm for this problem (15 marks), prove that it finds the optimal solution (20 marks), and give an efficient implementation (15 marks).
Transcribed Image Text:(50 MARKS) (Greedy Algorithms.) A group of friends is organizing a bike racing competition. There are n friends and m bikes, but bikes ate not equal, some of them perform better and some of them perform worse. You may think that each bike has a performance factor pi, 1 ≤ i ≤ m in the range (1,100) where 1 is the worst and 100 is the best. Each frieng has a greed factor 9i, 1 ≤ i ≤ n which is the minimum bike performace this firend will be content with. Your goal is to maximize the number of content friends, i.e., friends i assigned a bike j with gi ≤ pj. Give a correct greedy algorithm for this problem (15 marks), prove that it finds the optimal solution (20 marks), and give an efficient implementation (15 marks).
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