Problem Solving with C++ (9th Edition)
9th Edition
ISBN: 9780133591743
Author: Walter Savitch
Publisher: PEARSON
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Textbook Question
Chapter 1.1, Problem 5STE
What is the role of a compiler?
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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
Problem Solving with C++ (9th Edition)
Ch. 1.1 - Prob. 1STECh. 1.1 - What would be the data for a program to add two...Ch. 1.1 - Prob. 3STECh. 1.1 - What is the difference between a machine-language...Ch. 1.1 - What is the role of a compiler?Ch. 1.1 - What is a source program? What is an object...Ch. 1.1 - What is an operating system?Ch. 1.1 - What purpose does the operating system serve?Ch. 1.1 - Prob. 9STECh. 1.1 - Prob. 10STE
Ch. 1.1 - Prob. 11STECh. 1.2 - An algorithm is approximately the same thing as a...Ch. 1.2 - Prob. 13STECh. 1.2 - Prob. 14STECh. 1.2 - Prob. 15STECh. 1.3 - If the following statement were used in a C++...Ch. 1.3 - What is the meaning of \n as used in the following...Ch. 1.3 - What is the meaning of the following statement...Ch. 1.3 - What is the meaning of the following statement...Ch. 1.3 - What is the meaning of this directive? # include...Ch. 1.3 - What, if anything, is wrong with the following...Ch. 1.4 - Prob. 22STECh. 1.4 - Prob. 23STECh. 1.4 - If you omit a punctuation symbol (such as a...Ch. 1.4 - Omitting the final brace } from a program produces...Ch. 1.4 - Prob. 26STECh. 1.4 - Suppose you write a program that is supposed to...Ch. 1 - Using your text editor, enter (that is, type in)...Ch. 1 - Modify the C++ program you entered in Practice...Ch. 1 - Further modify the C++ program that you already...Ch. 1 - Modify the C++ program that you entered in...Ch. 1 - Modify the C++ program that you entered in...Ch. 1 - Prob. 6PCh. 1 - Write a C++ program that reads in two integers and...Ch. 1 - Write a program that prints out C S ! in large...Ch. 1 - Write a program that allows the user to enter a...Ch. 1 - Write a program that allows the user to enter a...Ch. 1 - Write a program that inputs a character from the...
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