Assignment 01 - max Aj-Ai (Solution)

Assignment 01 - max Aj-Ai (Solution) - The Hong Kong...

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COMP 271: Design and Analysis of Algorithms Fall 2007 Solution to Assignment 1 Idea of the algorithm : If we divide A into two roughly equal size sub-arrays, each with approximately n/ 2 elements, we observe that the maximum value of A [ j ] - A [ i ] must be one of the following: 1. The maximum value of A [ j ] - A [ i ] in A [1 .. b n/ 2 c ] where 1 i j ≤ b n/ 2 c . 2. The maximum value of A [ j ] - A [ i ] in A [ b n/ 2 c + 1 ..n ] where b n/ 2 c + 1 i j n . 3. The maximum value of A [ j ] - A [ i ] where A [ i ] is the minimum value of A [1 .. b n/ 2 c ] and A [ j ] is the maximum value of A [ b n/ 2 c + 1 ..n ]. Details of algorithm : Input : A is an array of positive integers; p is the start index of A ; r is the end index of A . Output : An integer array [MaxAll, MinAll, ValAll] where MaxAll and MinAll are the maximum and minimum value of the input array respectively. ValAll
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Assignment 01 - max Aj-Ai (Solution) - The Hong Kong...

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