EBK STARTING OUT WITH PYTHON
3rd Edition
ISBN: 9780100794351
Author: GADDIS
Publisher: YUZU
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Textbook Question
Chapter 12, Problem 2SA
In this chapter, the rules given for calculating the factorial of a number are as follows:
If n = 0 then factorial (n) = 1
If n . 0 then factorial (n) = n × factorial (n - 1)
If you were designing a function from these rules, what would the base case be? What would the recursive case be?
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In this chapter, the rules given for calculating the factorial of a number are as follows:If n = 0 then factorial(n) = 1If n . 0 then factorial(n) = n × factorial(n – 1)If you were designing a function from these rules, what would the base case be? What wouldthe recursive case be?
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.
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 12 Solutions
EBK STARTING OUT WITH PYTHON
Ch. 12.2 - It is said that a recursive algorithm has more...Ch. 12.2 - Prob. 2CPCh. 12.2 - What is a recursive case?Ch. 12.2 - What causes a recursive algorithm to stop calling...Ch. 12.2 - What is direct recursion? What is indirect...Ch. 12 - Prob. 1MCCh. 12 - A function is called once from a program's main...Ch. 12 - Prob. 3MCCh. 12 - Prob. 4MCCh. 12 - Prob. 5MC
Ch. 12 - Prob. 6MCCh. 12 - Any problem that can be solved recursively can...Ch. 12 - Actions taken by the computer when a function is...Ch. 12 - A recursive algorithm must _______ in the...Ch. 12 - A recursive algorithm must ______ in the base...Ch. 12 - An algorithm that uses a loop will usually run...Ch. 12 - Some problems can be solved through recursion...Ch. 12 - It is not necessary to have a base case in all...Ch. 12 - In the base case, a recursive method calls itself...Ch. 12 - In Program 12-2 , presented earlier in this...Ch. 12 - In this chapter, the rules given for calculating...Ch. 12 - Is recursion ever required to solve a problem?...Ch. 12 - When recursion is used to solve a problem, why...Ch. 12 - How is a problem usually reduced with a recursive...Ch. 12 - What will the following program display? def...Ch. 12 - Prob. 2AWCh. 12 - The following function uses a loop. Rewrite it as...Ch. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Largest List Item Design a function that accepts a...Ch. 12 - Recursive List Sum Design a function that accepts...Ch. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Ackermann's Function Ackermann's Function is a...
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