3rd Edition

ISBN: 9780133582734

Author: Tony Gaddis

Publisher: PEARSON

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The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set o…

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Textbook Question

Chapter 12, Problem 8PE

Ackermann'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 your function, test it by calling it with small values for m and n.

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Chapter 12, Problem 7PE

Chapter 13.1, Problem 1CP

Students have asked these similar questions

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>>;}

The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.)

Chapter 12 Solutions

Starting Out with Python (3rd Edition)

Ch. 12.2 - It is said that a recursive algorithm has more...Ch. 12.2 - Prob. 2CP Ch. 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. 1MC Ch. 12 - A function is called once from a program's main...Ch. 12 - Prob. 3MC Ch. 12 - Prob. 4MC Ch. 12 - Prob. 5MC

Ch. 12 - Prob. 6MC Ch. 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. 2AW Ch. 12 - The following function uses a loop. Rewrite it as...Ch. 12 - Prob. 1PE Ch. 12 - Prob. 2PE Ch. 12 - Prob. 3PE Ch. 12 - Largest List Item Design a function that accepts a...Ch. 12 - Recursive List Sum Design a function that accepts...Ch. 12 - Prob. 6PE Ch. 12 - Prob. 7PE Ch. 12 - Ackermann's Function Ackermann's Function is a...

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