C How to Program (8th Edition)
8th Edition
ISBN: 9780133976892
Author: Paul J. Deitel, Harvey Deitel
Publisher: PEARSON
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Textbook Question
Chapter 5, Problem 5.48E
(Research Project: 1m proving the Recursive Fibonacci Implementation) In Section 5.15, the recursive
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Using Python
Recursion is the concept of a function calling itself until the problem is solved when the Base Case is met.
Study Recursion: See slides in Modules, Practice Slides, lab12 and also Recursion is in chapter 9 of the textbook.
Some examples of recursion are: compute [ factorial of a number, towers of Hanoi, fractals (as shown in the textbook), and many more].
Example: See slides Page 2
For this assignment we'll use Collatz Cojecture (see Wikipedia).
Collatz Conjecture algorithm:
Given a number n, first call to the function: f(n):
In the function:
if n == 1 return 1:
if n is even then f(n/2), i.e. call self with the new value.
else (n is odd) call self with the new value, f((n*3)+1) and repeat. All numbers eventually end up with 1.
The program should test for the base case which is: if n == 1, in which case it returns to the caller with 1.
This problem is perfect to demonstrate Recursion.Create a list with random numbers (you can just do this part manually) in the list as 1,…
Ex. 01 : Recursion
About
So far, we have learned that we can perform repetitive tasks using loops. However, another way is by creating methods that call themselves. This programming technique is called recursion
and, a method that calls itself within it's own body is called a recursive method. One use of recursion is to perform repetitive tasks instead of using loops, since some problems seem to be
solved more naturally with recursion than with loops.
To solve a problem using recursion, it is broken down into sub-problems. Each sub-problem is similar to the original problem, but smaller in size. You can apply the same approach to each
sub-problem to solve it recursively.
All recursive methods use conditional tests to either
1. stop or
2. continue the recursion.
Each recursive method has the following characteristics:
1. end/terminating case: One or more end cases to stop the recursion.
2. recursive case: reduces the problem in to smaller sub-problems, until it reaches (becomes) the end…
is it possible to change this function from recursive to iterative one? Any help would be greatly appreciated.
Chapter 5 Solutions
C How to Program (8th Edition)
Ch. 5 - Show the value of x after each of the following...Ch. 5 - (Parking Charges) A parking garage charges a $2.00...Ch. 5 - (Rounding Numbers) An application of function...Ch. 5 - (Rounding Numbers) Function floor may be used to...Ch. 5 - Write statements that assign random integers to...Ch. 5 - For each of the following sets of integers, write...Ch. 5 - (Hypotenuse Calculations) Define a function called...Ch. 5 - (Exponentiation) Write a function...Ch. 5 - Prob. 5.17ECh. 5 - Prob. 5.18E
Ch. 5 - Prob. 5.19ECh. 5 - (Displaying a Square of Any Character) Modify the...Ch. 5 - Prob. 5.21ECh. 5 - (Separating Digits) Write program segments that...Ch. 5 - (Time in Seconds) Write a function that takes the...Ch. 5 - (Temperature Conversions) Implement the following...Ch. 5 - (Find the Minimum) Write a function that returns...Ch. 5 - (Perfect Numbers) An integer number is said to be...Ch. 5 - Prob. 5.27ECh. 5 - (Reversing Digits) Write a function that takes an...Ch. 5 - (Greatest Common Divisor) The greatest common...Ch. 5 - (Quality Points for Students Grades) Write a...Ch. 5 - (Coin Tossing) Write a program that simulates coin...Ch. 5 - (Guess the Number) Write a C program that plays...Ch. 5 - (Guess the Number Modification) Modify the program...Ch. 5 - (Recursive Exponentiation) Write a recursive...Ch. 5 - (Fibonacci) The Fibonacci series 0, 1, 1, 2, 3, 5,...Ch. 5 - (Towers of Hanoi) Every budding computer scientist...Ch. 5 - Prob. 5.37ECh. 5 - Prob. 5.38ECh. 5 - Prob. 5.39ECh. 5 - Prob. 5.40ECh. 5 - (Distance Between Points) Write a function...Ch. 5 - Prob. 5.42ECh. 5 - Prob. 5.43ECh. 5 - After you determine what the program of Exercise...Ch. 5 - (Testing Math Library Functions) Write a program...Ch. 5 - Find the error in each of the following program...Ch. 5 - Prob. 5.47ECh. 5 - (Research Project: 1m proving the Recursive...Ch. 5 - (Global Warming Facts Quiz) The controversial...Ch. 5 - Prob. 5.50MDCh. 5 - Prob. 5.51MDCh. 5 - (Computer-Assisted Instruction: Monitoring Student...Ch. 5 - (Computer-Assisted Instruction: Difficulty Levels)...Ch. 5 - (Computer-Assisted Instruction: Varying the Types...
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- (You need to have first completed Programming Project 13.1 to work on this project.) In this exercise, you will compare the efficiency of a recursive and an iterative function to compute the Fibonacci number.a. Examine the recursive function computation of Fibonacci numbers. Note that each Fibonacci number is recomputed many times. To avoid this recomputation, do Programming Project 13.1 iteratively, rather than recursively; that is, do the problem with a loop. You should compute each Fibonacci number once on the way to the number requested and discard the numbers when they are no longer needed. b. Time the solution for Programming Project 13.1 and Part a of this project in finding the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th Fibonacci numbers. Determine how long each function takes. Compare and comment on your results. Hints: If you are running Linux, you can use the bash time utility. It gives real time (as in wall clock time), user time (time measured by cpu cycles devoted to…arrow_forwardOne-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.arrow_forwardUse back substitution method to compute the following recursive function. Note that final results must be presented as a function of n. Show at least three substitutions before moving to k steps to get credit.arrow_forward
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