Starting Out with Programming Logic and Design (4th Edition)
4th Edition
ISBN: 9780133985078
Author: Tony Gaddis
Publisher: PEARSON
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Chapter 13, Problem 6PE
Ackermann’s Function
7. 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))
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8. Ackerman's Function
Ackermann's Function is a recursive mathematical algorithm that can be used to test how well a system optimizes its performance of recursion. Design a function ackermann(m, n), which solves Ackermann's function. Use the following logic in your function:
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))
Once you've designed yyour function, test it by calling it with small values for m and n.
Use Python.
java C++
Ackermann’s FunctionAckermann’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s Function. Use the following logic in your function:If m = 0 then return n + 1If n = 0 then return A(m−1, 1) Otherwise, return A(m−1, A(m, n−1))Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
SAMPLE RUN #0: ./AckermannRF
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Highlight: Show Highlighted Only
The·value·of·A(0,·0)=·1↵ The·value·of·A(0,·1)=·2↵ The·value·of·A(1,·1)=·3↵ The·value·of·A(1,·2)=·4↵ The·value·of·A(1,·3)=·5↵ The·value·of·A(2,·2)=·7↵ The·value·of·A(3,·2)=·29↵
Write the definition of a recursive function
int simpleSqrt(int n)
The function returns the integer square root of n, meaning the biggest integer whose square is less than or equal to n. You may
assume that the function is always called with a nonnegative value for n.
Use the following algorithm:
If n is 0 then return 0.
Otherwise, call the function recursively with n-1 as the argument to get a number t. Check whether or not t+1 squared is strictly
greater than n. Based on that test, return the correct result.
For example, a call to simpleSqrt(8) would recursively call simpleSqrt(7) and get back 2 as the answer. Then we would square (2+1)
= 3 to get 9. Since 9 is bigger than 8, we know that 3 is too big, so return 2 in this case.
On the other hand a call to simpleSqrt(9) would recursively call simpleSqrt(8) and get back 2 as the answer. Again we would square
(2+1) = 3 to get back 9. So 3 is the correct return value in this case.
Chapter 13 Solutions
Starting Out with Programming Logic and Design (4th Edition)
Ch. 13.2 - It is said that a recursive algorithm has more...Ch. 13.2 - Prob. 13.2CPCh. 13.2 - What is a recursive case?Ch. 13.2 - What causes a recursive algorithm to stop calling...Ch. 13.2 - What is direct recursion? What is indirect...Ch. 13 - Prob. 1MCCh. 13 - A module is called once from a programs main...Ch. 13 - The part of a problem that can be solved without...Ch. 13 - Prob. 4MCCh. 13 - Prob. 5MC
Ch. 13 - Prob. 6MCCh. 13 - Any problem that can be solved recursively can...Ch. 13 - Actions taken by the computer when a module is...Ch. 13 - A recursive algorithm must _______ in the...Ch. 13 - A recursive algorithm must _____ in the base case....Ch. 13 - An algorithm that uses a loop will usually run...Ch. 13 - Some problems can be solved through recursion...Ch. 13 - It is not necessary to have a base case in all...Ch. 13 - In the base case, a recursive method calls itself...Ch. 13 - In Program 13-2, presented earlier in this...Ch. 13 - In this chapter, the rules given for calculating...Ch. 13 - Is recursion ever required to solve a problem?...Ch. 13 - When recursion is used to solve a problem, why...Ch. 13 - How is a problem usually reduced with a recursive...Ch. 13 - What will the following program display? Module...Ch. 13 - What will the following program display? Module...Ch. 13 - The following module uses a loop. Rewrite it as a...Ch. 13 - Prob. 1PECh. 13 - Prob. 2PECh. 13 - Recursive Array Sum Design a function that accepts...Ch. 13 - Prob. 4PECh. 13 - Prob. 5PECh. 13 - Ackermanns Function 7. Ackermanns Function is a...
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