Fundamentals of Information Systems (Looseleaf)
9th Edition
ISBN: 9781337099042
Author: STAIR
Publisher: Cengage
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Chapter 7, Problem 1.1RQ
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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)
Chapter 7 Solutions
Fundamentals of Information Systems (Looseleaf)
Ch. 7 - Prob. 1LOCh. 7 - Prob. 2LOCh. 7 - Prob. 3LOCh. 7 - Prob. 4LOCh. 7 - Prob. 5LOCh. 7 - Prob. 6LOCh. 7 - Prob. 7LOCh. 7 - Prob. 8LOCh. 7 - Prob. 9LOCh. 7 - Prob. 1.1RQ
Ch. 7 - Prob. 1.2RQCh. 7 - Prob. 1.1CTQCh. 7 - Prob. 1.2CTQCh. 7 - Prob. 2.1RQCh. 7 - Prob. 2.2RQCh. 7 - Prob. 2.1CTQCh. 7 - Prob. 2.2CTQCh. 7 - Prob. 3.1RQCh. 7 - Prob. 3.2RQCh. 7 - Prob. 3.1CTQCh. 7 - Prob. 3.2CTQCh. 7 - What sort of training and experience is needed by...Ch. 7 - Prob. 4.2RQCh. 7 - Prob. 4.1CTQCh. 7 - Prob. 4.2CTQCh. 7 - Prob. 1SATCh. 7 - Prob. 2SATCh. 7 - Prob. 3SATCh. 7 - Prob. 4SATCh. 7 - Prob. 5SATCh. 7 - Prob. 6SATCh. 7 - Prob. 7SATCh. 7 - Prob. 8SATCh. 7 - Prob. 9SATCh. 7 - Prob. 10SATCh. 7 - Prob. 11SATCh. 7 - Prob. 12SATCh. 7 - Prob. 13SATCh. 7 - Prob. 14SATCh. 7 - Prob. 15SATCh. 7 - Prob. 16SATCh. 7 - Prob. 17SATCh. 7 - Prob. 1RQCh. 7 - Prob. 2RQCh. 7 - Prob. 3RQCh. 7 - Prob. 4RQCh. 7 - Prob. 5RQCh. 7 - Prob. 6RQCh. 7 - Prob. 7RQCh. 7 - Prob. 8RQCh. 7 - Prob. 9RQCh. 7 - Prob. 10RQCh. 7 - Prob. 11RQCh. 7 - Prob. 12RQCh. 7 - Prob. 13RQCh. 7 - Prob. 14RQCh. 7 - Prob. 15RQCh. 7 - Prob. 16RQCh. 7 - Prob. 17RQCh. 7 - Prob. 18RQCh. 7 - Prob. 19RQCh. 7 - Prob. 20RQCh. 7 - Prob. 21RQCh. 7 - Prob. 22RQCh. 7 - Prob. 23RQCh. 7 - Prob. 1DQCh. 7 - Prob. 2DQCh. 7 - Prob. 3DQCh. 7 - Prob. 4DQCh. 7 - Prob. 5DQCh. 7 - Prob. 6DQCh. 7 - Prob. 7DQCh. 7 - Prob. 8DQCh. 7 - Prob. 9DQCh. 7 - Prob. 10DQCh. 7 - Prob. 11DQCh. 7 - Prob. 12DQCh. 7 - Prob. 13DQCh. 7 - Prob. 1PSECh. 7 - Prob. 2PSECh. 7 - Prob. 3PSECh. 7 - Prob. 1WECh. 7 - Prob. 2WECh. 7 - Prob. 3WECh. 7 - Prob. 1CECh. 7 - Prob. 2CECh. 7 - Prob. 3CECh. 7 - Prob. 1.1CSCh. 7 - Prob. 1.2CSCh. 7 - Prob. 1.3CSCh. 7 - Prob. 1.4CSCh. 7 - Prob. 1.5CSCh. 7 - Prob. 2.1CSCh. 7 - Prob. 2.2CSCh. 7 - Prob. 2.3CS
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