Starting Out with Java: From Control Structures through Objects (6th Edition)
6th Edition
ISBN: 9780133957051
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 16, 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)
Solve in javaFX
JAVA
Question 2:
For two integers m and n, their GCD (Greatest Common Divisor) can be computed by a recursive method. Write a recursive method gcd(m,n) to find their Greatest Common Divisor.
Method body:
If m is 0, the method returns n. If n is 0, the method returns m. If neither is 0, the method can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n (or m % n). The recursive method cannot have loops.
Note: although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit.
main method:
Prompt and read in two numbers to find the greatest common divisor.
Call the gcd method with the two numbers as its argument. Print the result to the monitor.
Example program run:
Enter m:
12
Enter n:
28
GCD(12,28) = 4
And here is what I have so far,
package CSCI1302;import java.util.*;public class RecursionDemo {
public static void…
Chapter 16 Solutions
Starting Out with Java: From Control Structures through Objects (6th Edition)
Ch. 16.2 - It is said that a recursive algorithm has more...Ch. 16.2 - Prob. 16.2CPCh. 16.2 - What is a recursive case?Ch. 16.2 - What causes a recursive algorithm to stop calling...Ch. 16.2 - What is direct recursion? What is indirect...Ch. 16 - Prob. 1MCCh. 16 - This is the part of a problem that can be solved...Ch. 16 - This is the part of a problem that is solved with...Ch. 16 - This is when a method explicitly calls itself. a....Ch. 16 - Prob. 5MC
Ch. 16 - Prob. 6MCCh. 16 - True or False: An iterative algorithm will usually...Ch. 16 - True or False: Some problems can be solved through...Ch. 16 - True or False: It is not necessary to have a base...Ch. 16 - True or False: In the base case, a recursive...Ch. 16 - Find the error in the following program: public...Ch. 16 - Prob. 1AWCh. 16 - Prob. 2AWCh. 16 - What will the following program display? public...Ch. 16 - Prob. 4AWCh. 16 - What will the following program display? public...Ch. 16 - Convert the following iterative method to one that...Ch. 16 - Write an iterative version (using a loop instead...Ch. 16 - What is the difference between an iterative...Ch. 16 - What is a recursive algorithms base case? What is...Ch. 16 - What is the base case of each of the recursive...Ch. 16 - What type of recursive method do you think would...Ch. 16 - Which repetition approach is less efficient: a...Ch. 16 - When recursion is used to solve a problem, why...Ch. 16 - How is a problem usually reduced with a recursive...Ch. 16 - Prob. 1PCCh. 16 - isMember Method Write a recursive boolean method...Ch. 16 - String Reverser Write a recursive method that...Ch. 16 - maxElement Method Write a method named maxElement,...Ch. 16 - Palindrome Detector A palindrome is any word,...Ch. 16 - Character Counter Write a method that uses...Ch. 16 - Recursive Power Method Write a method that uses...Ch. 16 - Sum of Numbers Write a method that accepts an...Ch. 16 - Ackermarms Function Ackermanns function is a...Ch. 16 - Recursive Population Class In Programming...
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