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Suppose that you have the following recursive function written in C++. I've intentionally written the function so that it doesn't use descriptive names for anything, though that's obviously not a good design practice, but I aim not to bias your understanding of the techniques you'll be using by assuming anything about what the function's goal is; to stay "on task" here, you should resist the temptation to try to figure that out first. void kaboom( const std::vector& v, std::vector& w, unsigned int i) { if (i < w.size()) { int q = 0; for (int j : v) { q += j; } w.at(i) - kaboom(v, w, i + 1); } = q; } 1. Using the techniques from our discussion of the Asymptotic Analysis of Recursion, write a recurrence that describes the time required to run the following call to kaboom for two vector v and w whose sizes are the same. Use the variable s in your recurrence to denote that size. kaboom(v, w, 0) 2. Using the repeated substitution technique, reduce the recurrence to a closed form, then give…

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1) The newton function returns the square root of 'x' 2) The limitReached function returns True if the estimate is within the tolerance, if not, False 3) The improveEstimate function returns an improved estimate

a) Write down a tail recursive implementation of the function sum in python language or programming language of your choice. You may use the helper function in your solution. b) Write down a tail recursive implementation of the function factorial in pythonlanguage or programming language of your choice. You may use the helper function in yoursolution.

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,…

QUESTION 9 There are several rules to keep in mind when writing a recursive function. Select all of them from the following list. of al Tust A. The recursive function may not call any other function or method. B. The value of all arguments passed to the recursive function must change for every recursive call. C. The recursive method must cal the main function in order to begin. D.There must be a clearly stated base case. CE. The function must contain a break statement to end the recursion. OF. The recursive function may not include a return statement. G. Recursive calls to the function must converge on the base case. is called. H.One or more arguments passed to the function must change in value each time the function i

Question 5 When writing a recursive method, O you do not need to know ahead of time exactly how many levels of recursion will occur. O you must keep count of how many recursion call levels you have traversed. O you must make sure the method does not take any input parameters.

Python only*  Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle   Do not use any kind of loop Within the definition of…

Python only*  Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle   Do not use any kind of loop Within the definition of…

Write a recursive function that returns a value of 1 if its string argument is apalindrome and zero otherwise.* Note that for the function parameters, you need to accommodate for the shrinkingstring, so that the string shrinks both from beginning and end after each recursive call.** Think about the simple cases or base cases. The 2 base cases have conditions thatwould return 0 and return 1 independently.For the palindrome, create a driver program. First ask the user to enter anystring through the keyboard. Then remove all the spaces and punctuations from thestring. Also, remove any letter capitalization from the string. Finally, pass the string tothe palindrome function through a function call.

use C Program Online compilation Recamán's Sequence Implement this in a program. Write two functions, one for solving it iteratively, one for solving it recursively. Take two arguments from the command-line: an "i" or "r", and the term number (how many terms to print). Print out which method executed (was selected) and all the terms (and the number of terms）

QUESTION 9 There are several rules to keep in mind when writing a recursive function. Select all of them from the following list. Lun A. The recursive function may not call any other function or method. B. The value of all arguments passed to the recursive function must change for every recursive calL OC. The recursive method must call tie main function in order to begin. D. There must be a clearly stated base case. CE. The function must contain a break statement to end the recursion. OF. The recursive function may not include a return statement. OG. Recursive calls to the function must converge on the base case. H. One or mare arguments passed to the function must change in value each time the function is called.

Demonstrate Recursion Assignment Instructions Overview The programs we’ve discussed so far are generally structured as methods that call one another in a hierarchical manner. For some problems, it’s useful to have a method call itself—this is known as a recursive method. Such a method can call itself either directly or indirectly through another method. Recursion is an important topic discussed at length in upper-level computer-science courses. Instructions Write a recursive method printArray() that displays all the elements in an array of integers, separated by spaces. The array must be 100 elements in size and filled using a for loop and a random number generator. The pseudo-code for this is as follows:   //Instantiate an integer array of size 100 //fill the array For (int i=0; i<array.length; i++) Array[i] = random number between 1 and 100 inclusive printArray(integer array);   For this assignment make sure that your screen shots show your program running and that your runtime…

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Recursive Exponentiation (using c language) Write a recursive function power(base, exponent) that when invoked returns baseexponent.   For example, power(3, 4) = 3 * 3 * 3 * 3. Assume that exponent is an integer greater than or equal to 1.   Then, write a demo program that uses the power function and test it out for a number of inputs.   Hint: The recursion step would use the relationship baseexponent = base * baseexponent–1   and the terminating condition occurs when exponent is equal to 1 because base1 = base

Python program (recursive function)   A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. Write a python recursive functionprod that takes x as an argument, and returns the result where, result=1*1/2*1/3*….*1/n Include a screenshot that shows a python program that uses the above function and prints the rounded result to three decimal placesafter prompting the user to enter a number, x. Use x=3.    N.B: The code should be included please.

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Please can be handwritten. Question 2: Implementing a Recursive Function . Write recursive function, recursionprob(n), which takes a positive number as its argument and returns the output as shown below. The solution should clearly write the steps as shown in an example in slide number 59 and slide number 60 in lecture slides. After writing the steps, trace the function for “recursiveprob(5)” as shown in an example slide number 61. Function Output: >> recursionprob(1) 1 >> recursionprob(2) 1 4 >> recursionprob(3) 1 4 9 >>recrusionprob(4) 1 4 9 16

Which of the following is/are true regarding the characteristics of recursion? a.Every recursive call reduces the original problem, bringing it increasingly closer to a base case until it becomes that case. b.Recursive method requires less memory than an iterative method. c. It is possible to convert every recursive method to an iterative method. d.The method is implemented using an if-else or a switch statement that leads to different cases. e.One or more base cases are used to stop recursion.

Python only** Use recursive function* Define countBetween with 2 parameters Use def to define countBetween with 2 parameters thas two parameters: a starting number and an ending number, and counts up (i.e., prints consecutive integers) from the starting number to the ending number. If the numbers are the same, it just prints that number; if the ending number is lower than the starting number, it prints nothing.   Do not use any kind of loop Within the definition of countBetween with 2 parameters, do not use any kind of loop.   Call countBetween Within the definition of countBetween with 2 parameters, call countBetween in at least one place.     Python only** Use recursive function* Define countThereAndBack with 2 parameters Use def to define countThereAndBack with 2 parameters   after reaching the ending number, it also counts back down to the starting number. It accepts the same two parameters defining starting and ending numbers it should print nothing if the starting number is…

Write factorial1 function in python 3.8 follow the directions provided below, don't need anything else as long as it meets all the requirements below. Function: factorial1 The function implements an iterative factorial. It takes an integer n as argument and returns n! The method needs to be computed interactively (not recursively

program in C++ with the name, towers.cpp which helps to solve the Towers of Hanoi puzzle using this recursive approach. The main() routine should make a single call to the recursive member function do Towers(). This function then calls itself recursively until the puzzle is solved. Note: solve as soon as possible

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Objective: Practice writing recursive functions in python3  Make the five recursive functions described below in python3 by using the starter code recursive_functions.py. For each function, figure out how to solve it conceptually : write down the base case (when recursion stops) and how each recursive function-call moves towards the base case. The functions should not print anything (except you may add temporary print statements to help debug them). You can test your program by using the provided program test_recursive_functions.py. Don't edit the test program. Put it into the same directory (folder) with your recursive_functions.py and run it. It will import your functions as a module, test your functions, and tell you when each function is returning correct results. 1. Factorial In math, if you have a number n, the factorial function (written n!) computes n x (n-1) x (n-2) x (n-3) x ... x 1. For example: 0! is defined to be 1 1! = 1 2! = 2 x 1=2 3! = 3 x 2 x 1=6 4! = 4 x 3…

Please provide step by step solution. And provide screen shoot of running code Thank you