Modern Database Management
13th Edition
ISBN: 9780134773650
Author: Hoffer
Publisher: PEARSON
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Chapter 4, Problem 4.27RQ
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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)
Design a dynamic programming algorithm for the problem described below
Input: A list of numbers A = = [a1,..., an].
Output: A contiguous subsequence of numbers with the maximum sum.
The algorithm must take O(n) time. You must also write and explain the recurrence.
(I am looking for an i ≥ 1 and k ≥ 0 such that a + ai+1 + ···ai+k has the largest possible sum among all
possible values for i and k.)
Example 1:
Input: A[5, 15, -30, 10, -5, 40, 10].
Output: [10, 5, 40, 10]
Example 2:
Input: A = [7, 5, 7, 4, -20, 6, 9, 3, -4, -8, 4]
Output: [6,9,3]
Chapter 4 Solutions
Modern Database Management
Ch. 4 - Define each of the following terms: determinant...Ch. 4 - Prob. 4.2RQCh. 4 - Prob. 4.3RQCh. 4 - Describe the primary differences between the...Ch. 4 - Summarize six important properties of relations.Ch. 4 - Describe two properties that each candidate key...Ch. 4 - Describe the three types of anomalies that can...Ch. 4 - Demonstrate each of the anomaly types with an...Ch. 4 - Fill in the blanks in each of the following...Ch. 4 - What is a well-structured relation? Why are...
Ch. 4 - Prob. 4.11RQCh. 4 - Describe how the following components of an E-R...Ch. 4 - Prob. 4.13RQCh. 4 - Prob. 4.14RQCh. 4 - Briefly describe four typical problems that often...Ch. 4 - Prob. 4.16RQCh. 4 - Explain how each of the following types of...Ch. 4 - Prob. 4.18RQCh. 4 - Prob. 4.19RQCh. 4 - Prob. 4.20RQCh. 4 - Prob. 4.21RQCh. 4 - What is the relationship between the primary key...Ch. 4 - Prob. 4.23RQCh. 4 - Explain what can be done with primary keys to...Ch. 4 - Prob. 4.25RQCh. 4 - Explain three conditions that suggest a surrogate...Ch. 4 - Prob. 4.27RQCh. 4 - For each of the following E-R diagrams from...Ch. 4 - Prob. 4.29PAECh. 4 - Prob. 4.30PAECh. 4 - For your answers to the following Problems and...Ch. 4 - Figure 4-3212 shows a class list for Millennium...Ch. 4 - Prob. 4.33PAECh. 4 - Prob. 4.34PAECh. 4 - Prob. 4.35PAECh. 4 - Prob. 4.36PAECh. 4 - Prob. 4.37PAECh. 4 - Prob. 4.38PAECh. 4 - Prob. 4.39PAECh. 4 - Transform Figure 2-15a, attribute version, to 3NF...Ch. 4 - The Public Safety office at Millennium College...Ch. 4 - Prob. 4.42PAECh. 4 - Prob. 4.43PAECh. 4 - Prob. 4.44PAECh. 4 - For your answers to Problem and Exercise 3-33 from...Ch. 4 - Prob. 4.46PAECh. 4 - Prob. 4.47PAECh. 4 - Figure 4-38 includes an EER diagram for a...Ch. 4 - Prob. 4.49PAECh. 4 - Prob. 4.50PAECh. 4 - Prob. 4.51PAECh. 4 - Prob. 4.52PAECh. 4 - Figure 4-40 shows an EER diagram for a university...Ch. 4 - Explore the data included in Table 4-9. Assume...Ch. 4 - Prob. 4.55PAECh. 4 - Prob. 4.56PAECh. 4 - Prob. 4.57PAECh. 4 - Prob. 4.58PAE
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