Starting Out with C++ from Control Structures to Objects (9th Edition)
9th Edition
ISBN: 9780134498379
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 1.5, Problem 1.22CP
What happens to a variable’s current contents when a new value is stored there?
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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 1 Solutions
Starting Out with C++ from Control Structures to Objects (9th Edition)
Ch. 1.2 - Why is the computer used by so many different...Ch. 1.2 - List the five major hardware components of a...Ch. 1.2 - Internally, the CPU consists of what two units?Ch. 1.2 - Prob. 1.4CPCh. 1.2 - Prob. 1.5CPCh. 1.2 - Prob. 1.6CPCh. 1.2 - Prob. 1.7CPCh. 1.2 - Prob. 1.8CPCh. 1.2 - What do you call a program that performs a...Ch. 1.2 - Word processing programs, spreadsheet programs,...
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