Systems Architecture
Systems Architecture
7th Edition
ISBN: 9781305080195
Author: Stephen D. Burd
Publisher: Cengage Learning
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Chapter 2, Problem 2RP

Tables 2.2 and 2.3 will probably be out of date by the time this book is published. Research current computer hardware offerings and update Tables 2.2 and 2.3 with current representative models for each computer class/type.

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Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)
Design a dynamic programming algorithm for the Coin-change problem described below: Input: An amount of money C and a set of n possible coin values with an unlimited supply of each kind of coin. Output: The smallest number of coins that add up to C exactly, or output that no such set exists. The algorithm must take O(n C) time. You must also write and explain the recurrence. Example 1: Input: C24, Coin values = = [1, 5, 10, 25, 50] Output: 6 (since 24 = 10+ 10+1+1 +1 + 1) Example 2: Input: C = 86, Coin values = [1, 5, 6, 23, 35, 46, 50] Output: 2 (since 86 = 46+35+5)
Design a dynamic programming algorithm for the Longest Common Subsequence problem de- scribed below Input: Two strings x = x1x2 xm and y = Y1Y2... Yn Output: The length of the longest subsequence that is common to both x and y. . The algorithm must take O(m n) time. You must also write and explain the recurrence. (I want the largest k such that there are 1 ≤ i₁ < ... < ik ≤ m and 1 ≤ j₁ < ... < jk ≤ n such that Xi₁ Xi2 Xik = Yj1Yj2 ··· Yjk) Example 1: Input: x = 'abcdefghijklmnopqrst' and y = 'ygrhnodsh ftw' Output: 6 ('ghnost' is the longest common subsequence to both strings) Example 2: Input: x = 'ahshku' and y = ‘asu' Output: 3 ('asu' is the longest common subsequence to both strings)
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