Problem Solving with C++ (9th Edition)
9th Edition
ISBN: 9780133591743
Author: Walter Savitch
Publisher: PEARSON
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Chapter 15, Problem 11PP
The computer player in
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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 15 Solutions
Problem Solving with C++ (9th Edition)
Ch. 15.1 - Is the following program legal (assuming...Ch. 15.1 - Prob. 2STECh. 15.1 - Is the following a legal definition of the member...Ch. 15.1 - The class SalariedEmployee inherits both of the...Ch. 15.1 - Give a definition for a class TitledEmployee that...Ch. 15.1 - Give the definitions of the constructors for the...Ch. 15.2 - You know that an overloaded assignment operator...Ch. 15.2 - Suppose Child is a class derived from the class...Ch. 15.2 - Give the definitions for the member function...Ch. 15.2 - Define a class called PartFilledArrayWMax that is...
Ch. 15.3 - Prob. 11STECh. 15.3 - Why cant we assign a base class object to a...Ch. 15.3 - What is the problem with the (legal) assignment of...Ch. 15.3 - Suppose the base class and the derived class each...Ch. 15 - Write a program that uses the class...Ch. 15 - Listed below are definitions of two classes that...Ch. 15 - Solution to Programming Project 15.1 Give the...Ch. 15 - Create a base class called Vehicle that has the...Ch. 15 - Define a Car class that is derived from the...Ch. 15 - Prob. 4PPCh. 15 - Consider a graphics system that has classes for...Ch. 15 - Flesh out Programming Project 5. Give new...Ch. 15 - Banks have many different types of accounts, often...Ch. 15 - Radio Frequency IDentification (RFID) chips are...Ch. 15 - The goal for this Programming Project is to create...Ch. 15 - Solution to Programming Project 15.10 Listed below...Ch. 15 - The computer player in Programming Project 10 does...Ch. 15 - Prob. 12PP
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