Starting Out with Java: Early Objects (6th Edition)
6th Edition
ISBN: 9780134462011
Author: Tony Gaddis
Publisher: PEARSON
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Chapter 14, Problem 9PC
Ackermarm’s Function
Ackermann’s function is a recursive mathematical
If m = 0 then return n + 1
If n = 0 then return ackermann(m - 1, 1)
Otherwise, return ackermann(m - 1, ackermann(m, n - 1))
Test your method in a program that displays the return values of the following method calls:
ackermann(0, 0) ackermann(0, 1) ackermann(1, 1) ackermann(1, 2)
ackermann(1, 3) ackermann(2, 2) ackermann(3, 2)
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In Java
Ackermann’s Function
Ackermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion.
Write a method ackermann(m, n), which solves Ackermann’s function. Use the following logic in your method:
If m = 0 then return n + 1
If n = 0 then return ackermann(m - 1, 1)
Otherwise, return ackermann(m - 1, ackermann(m, n - 1))
Test your method in a program that displays the return values of the following method calls:
ackermann(0, 0) ackermann(0, 1) ackermann(1, 1) ackermann(1, 2)ackermann(1, 3) ackermann(2, 2) ackermann(3, 2)
For function addOdd(n) write the missing recursive call. This function should return the sum of all postive odd numbers less than or equal to n.
Examples:
addOdd(1) -> 1addOdd(2) -> 1addOdd(3) -> 4addOdd(7) -> 16
public int addOdd(int n) { if (n <= 0) { return 0; } if (n % 2 != 0) { // Odd value return <<Missing a Recursive call>> } else { // Even value return addOdd(n - 1); }}
For function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101".
Examples: decToBinary(13) -> "1101"
public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}
Chapter 14 Solutions
Starting Out with Java: Early Objects (6th Edition)
Ch. 14.2 - It is said that a recursive algorithm has more...Ch. 14.2 - Prob. 14.2CPCh. 14.2 - What is a recursive case?Ch. 14.2 - What causes a recursive algorithm to stop calling...Ch. 14.2 - What is direct recursion? What is indirect...Ch. 14 - Prob. 1MCCh. 14 - This is the part of a problem that can be solved...Ch. 14 - This is the part of a problem that is solved with...Ch. 14 - This is when a method explicitly calls itself. a....Ch. 14 - Prob. 5MC
Ch. 14 - Prob. 6MCCh. 14 - True or False: An iterative algorithm will usually...Ch. 14 - True or False: Some problems can be solved through...Ch. 14 - True or False: It is not necessary to have a base...Ch. 14 - True or False: In the base case, a recursive...Ch. 14 - Find the error in the following program: public...Ch. 14 - Prob. 1AWCh. 14 - Prob. 2AWCh. 14 - What will the following program display? public...Ch. 14 - Prob. 4AWCh. 14 - What will the following program display? public...Ch. 14 - Convert the following iterative method to one that...Ch. 14 - Write an iterative version (using a loop instead...Ch. 14 - What is the difference between an iterative...Ch. 14 - What is a recursive algorithms base case? What is...Ch. 14 - What is the base case of each of the recursive...Ch. 14 - What type of recursive method do you think would...Ch. 14 - Which repetition approach is less efficient: a...Ch. 14 - When recursion is used to solve a problem, why...Ch. 14 - How is a problem usually reduced with a recursive...Ch. 14 - Prob. 1PCCh. 14 - isMember Method Write a recursive boolean method...Ch. 14 - String Reverser Write a recursive method that...Ch. 14 - maxElement Method Write a method named maxElement,...Ch. 14 - Palindrome Detector A palindrome is any word,...Ch. 14 - Character Counter Write a method that uses...Ch. 14 - Recursive Power Method Write a method that uses...Ch. 14 - Sum of Numbers Write a method that accepts an...Ch. 14 - Ackermarms Function Ackermanns function is a...Ch. 14 - Recursive Population Class In Programming...
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