C How To Program Plus Mylab Programming With Pearson Etext -- Access Card Package (8th Edition)
8th Edition
ISBN: 9780134227023
Author: Paul J. Deitel; Harvey Deitel
Publisher: PEARSON
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Chapter 7, Problem 7.18E
(Card Shuffling and Dealing Modification) Modify the card shuffling and dealing
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2, Towers of Hanoi Problem. (10 points)
The Towers of Hanoi is a famous problem for studying recursion in
computer science and searching in artificial intelligence. We start with N
discs of varying sizes on a peg (stacked in order according to size), and two
empty pegs. We are allowed to move a disc from one peg to another, but we
are never allowed to move a larger disc on top of a smaller disc. The goal is
to move all the discs to the rightmost peg (see figure). To solve the problem
by using search methods, we need first formulate the problem. Supposing
there are K pegs and N disk. Answer the following questions.
(1) Determine a state representation for this problem. (4points)
(2) What is the size of the state space? (3 points)
(3) Supposing K=3, N=4, what is the start state by using your proposed
state representation method and what is the goal state? (3 points)
(Visualizing Recursion) It’s interesting to watch recursion “in action.” Modify the factorialfunction of Fig. 5.18 to print its local variable and recursive call parameter. For each recursive call,display the outputs on a separate line and add a level of indentation. Do your utmost to make theoutputs clear, interesting and meaningful. Your goal here is to design and implement an output format that helps a person understand recursion better. You may want to add such display capabilitiesto the many other recursion examples and exercises throughout the text.
(Recursive Exponentiation) Write a recursive function power(base, exponent) that wheninvoked returnsbaseexponentFor example, power(3, 4) = 3 * 3 * 3 * 3. Assume that exponent is an integer greater than or equalto 1. Hint: The recursion step would use the relationshipbaseexponent = base * baseexponent–1and the terminating condition occurs when exponent is equal to 1 becausebase1 = base
Chapter 7 Solutions
C How To Program Plus Mylab Programming With Pearson Etext -- Access Card Package (8th Edition)
Ch. 7 - Answer each of the following: The _____ operator...Ch. 7 - Prob. 7.10ECh. 7 - Do each of the following: Write the function...Ch. 7 - (Simulation: The Tortoise and the Hare) In this...Ch. 7 - (Card Shuffling and Dealing Modification) Modify...Ch. 7 - What does this program do, assuming that the user...Ch. 7 - What does this program do?Ch. 7 - Find the error in each of the following program...Ch. 7 - (Maze Traversal) The following grid is a...Ch. 7 - Prob. 7.23E
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- 14. (7 points) Write a recursive function count_odds(Ist) which takes as parameter a list of numbers (1st) and counts the odd numbers in it. Example: >>> count_odds ([2, 5, 7, 6, 4]) 2arrow_forwardQ2) (Perfect Numbers) An integer number is said to be a perfect number if its factors, including 1 (but not the number itself), sum to the number. For example, 6 is a perfect number because 6 = 1 + 2 + 3. Write a function perfect that determines if parameter number is a perfect number. Use this function in a program that determines and prints all the perfect numbers between 1 and 1000. Print the factors of each perfect number to confirm that the number is indeed perfect. Challenge the power of your computer by testing numbers much larger than 1000.arrow_forwardthe following 12. (Greatest Common Divisor) Given two integers x and recursive definition determines the greatest common divisor of x and y, written gcd(x,y): Y, if y = 0 gcd(x, y) = %3D gcd(y, x%y) if yチ0 Note: In this definition, % is the mod operator. write a recursive function, gcd, that takes as parameters two integers and returns the greatest common divisor of the numbers. Also, write a pro- gram to test your function.arrow_forward
- Problem 4 (Count Token) Write a function called count_token(source, token) that takes two strings as input; a source and a token. The function should use a recursive process to count the number of times the token appears in the source string. You may assume the token is only a single character long. Sample run: >> print(count_token('peter piper picked a peck of pickled peppers', 'p')) 9. >>> print(count_token ("betty botter bought some butter", 'b’) 4 >>> print(count_token ("betty botter bought some butter", 't') 7arrow_forward(GREATEST COMMON DIVISOR) The greatest common divisor of integers x and y is the largest integer that evenly divides into both x and y. Write and test a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equal to 0, then gcd (x, y) is x; otherwise, gcd (x, y) is gcd (y, x % y), where % is the remainder operator.arrow_forward(Displaying a Square of Any Character) Modify the function created in Exercise 5.19 toform the square out of whatever character is contained in character parameter fillCharacter. Thusif side is 5 and fillCharacter is “#”, then this function should print: ##### ##### ##### ##### #####arrow_forward
- (Modifying Class GradeBook) Modify class GradeBook (Figs. 16.11–16.12) as follows:a) Include a second string data member that represents the course instructor’s name.b) Provide a set function to change the instructor’s name and a get function to retrieve it.c) Modify the constructor to specify course name and instructor name parameters.d) Modify function displayMessage to output the welcome message and course name,then the string "This course is presented by: " followed by the instructor’s name.Use your modified class in a test program that demonstrates the class’s new capabilities.arrow_forward6. Sum of Numbers Design a function that accepts an integer argument and returns the sum of all the integers from 1 up to the number passed as an argument. For example, if 50 is passed as an argument, the function will return the sum of 1, 2, 3, 4, . . . 50. Use recursion to calculate the sum.arrow_forwardProblem 3 (Filter Vowels) Write a function called filter_vowels(string) that takes a string as input and returns a string with all vowels removed. Your function should make use of a recursive process, and should not use the str.replace() function. Sample run: >>> print(filter_vowels ("Winter is almost here!")) Wntr s 1mst hr! >>> print(filter_vowels(""The quick brown fox jumps over the lazy dog.")) Th gck brwn fx jmps vr th lzy dg. Page 2 of 4arrow_forward
- (2) Create an iterative and a recursive function in pseudo-code which calculates the ele- ments of the sequence given on the following drawing. The green numbers mean the index (Oth element, 1st element, 2nd element, etc.) and the black mean the actual va- lue. Note: I did not calculate all the values, just the "necessary" ones.: 27 2 2 7arrow_forward(b) Good Programming practices help in improving programs readability and understandability both for a programmer and for a general user. What changes would you make in the following program, written by a beginner, keeping in view the good programming practices. You are also required to write the output of the program if a user wants to find factorial of number 6. Note: The Program finds/calculates factorial of a number using a user defined recursive function. #include using namespace std; int f(int n); int main() { int n; cout > n; cout 1) return n * f(n - 1); else return 1; }arrow_forward17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.arrow_forward
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