Systems Architecture
Systems Architecture
7th Edition
ISBN: 9781305080195
Author: Stephen D. Burd
Publisher: Cengage Learning
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Chapter 4, Problem 2RQ

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Reason for the increasing speed of program execution

  • The program execution speed increases as the number of general purpose registers increases because access to data stored in registers is immediate but access to data stored in memory locations causes some delay...

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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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