Starting Out with C++ from Control Structures to Objects Plus MyLab Programming with Pearson eText -- Access Card Package (9th Edition)
9th Edition
ISBN: 9780134544847
Author: Tony Gaddis
Publisher: PEARSON
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Chapter 20, Problem 12PC
Ackermann’s Function
Ackermann’s Function is a recursive mathematical
If m = 0 then return n + 1
If n = 0 then return A(m−1, 1)
Otherwise, return A(m−1, A(m, n−1))
Test your function in a driver
A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
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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.
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CodeWorkout
X267: Recursion Programming Exercise:
Cumulative Sum
For function sumtok, write the missing recursive call. This function returns the sum of the
values from1 to k.
Examples:
sumtok(5) -> 15
Your Answer:
1 public int sumtok(int k) {
2.
} (0 => )
return 0;
3.
} else {
return >
6.
{
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Chapter 20 Solutions
Starting Out with C++ from Control Structures to Objects Plus MyLab Programming with Pearson eText -- Access Card Package (9th Edition)
Ch. 20.2 - What happens if a recursive function never...Ch. 20.2 - What is a recursive functions base case?Ch. 20.2 - Prob. 20.3CPCh. 20.2 - What is the difference between direct and indirect...Ch. 20 - What is the base case of each of the recursive...Ch. 20 - What type of recursive function do you think would...Ch. 20 - Which repetition approach is less efficient, a...Ch. 20 - When should you choose a recursive algorithm over...Ch. 20 - Explain what is likely to happen when a recursive...Ch. 20 - The _____________ of recursion is the number of...
Ch. 20 - Prob. 7RQECh. 20 - Prob. 8RQECh. 20 - Prob. 9RQECh. 20 - Write a recursive function to return the number of...Ch. 20 - Write a recursive function to return the largest...Ch. 20 - #include iostream using namespace std; int...Ch. 20 - Prob. 13RQECh. 20 - #include iostream #include string using namespace...Ch. 20 - Iterative Factorial Write an iterative version...Ch. 20 - Prob. 2PCCh. 20 - Prob. 3PCCh. 20 - Recursive Array Sum Write a function that accepts...Ch. 20 - Prob. 5PCCh. 20 - Prob. 6PCCh. 20 - Prob. 7PCCh. 20 - Prob. 8PCCh. 20 - Prob. 9PCCh. 20 - Prob. 10PCCh. 20 - Prob. 11PCCh. 20 - Ackermanns Function Ackermanns Function is a...
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- Ackermann’s Functionarrow_forwardWrite 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.arrow_forwardConsider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).arrow_forward
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