There are n number of students in a class. Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion. b) Consider this Algorithm-Z , Taking list of integer as input List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i < number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X (i) Explain what Algorithm Z is doing? (ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexity

There are n number of students in a class. Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion. b) Consider this Algorithm-Z , Taking list of integer as input List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i < number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X (i) Explain what Algorithm Z is doing? (ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexity

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 1TF

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Question-3 There are n number of students in a class.Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion. b) Consider this Algorithm-Z , Taking list of integer as input List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i< number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X (i) Explain what Algorithm Z is doing? (ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexity
Use 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.
Question-3 There are n number of students in a class. Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion.
Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1
(Recursive Greatest Common Divisor) The greatest common divisor of integers x and y isthe largest integer that evenly divides both x and y. Write a recursive function gcd that returns thegreatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equalto 0, then gcd(x, y) is x; otherwise gcd(x, y) is gcd(y, x % y), where % is the remainder operator.
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
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,…
T/F 7. The recursive procedure for solving the Towers of Hanoi can only be used if the number of discs parameter is 7 or less.
The 4th problem mimics the situation where eagles flying in the sky can be spotted and counted.FindEagles: a recursive function that examines and counts the number of objects (eagles) in aphotograph. The data is in a two-dimensional grid of cells, each of which may be empty (value 0) orfilled (value 1 to 9). Maximum grid size is 50 x 50. The filled cells that are connected form an object(eagle). Two cells are connected if they are vertically, horizontally, or diagonally adjacent. Thefollowing figure shows 3 x 4 grids with 3 eagles. 0 0 1 21 0 0 01 0 3 1 FindEagle function takes as parameters the 2-D array and the x-y coordinates of a cell that is a part ofan eagle (non-zero value) and erases (change to 0) the image of an eagle. The function FindEagleshould return an integer value that counts how many cells has been counted as part of an eagle and havebeen erased. The following sample data has two pictures, the first one is 3 x 4, and the second one is 5 x 5 grids. Notethat your program…
Algorithm problem w/ recurrence: Frying pancakes: a small pan can only hold two pancakes at a time. Each pancake needs to be fried on both sides. Frying one side takes 1 minute, no matter how many pancakes are on the pan. Consider this recursive algorithm: If n <= 2, fry the pancakes or the two pancakes together on each side. If n > 2, fry any two pancakes together on each side and then apply the same process recursively to the remaining n-2 pancakes. a. Set up and solve the recurrence for the amount of time this algorithm needs to fry n pancakes. b. Explain why this algorithm does not fry the pancakes in the minimum time for all n > 0. c. Give a correct recursive algorithm that executes the task in the minimum amount of time. > I was not sure how to start this. I have had trouble with recurrence in the past. Also from the work that I did do, I didn't know how there could be a better algorithm. Thanks in advance
Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val): if exponent_val == 0: result_val = 1 else: result_val = base_val * Your solution goes here return result_val user_base = int(input())user_exponent = int(input()) print('%d^%d = %d' % (user_base, user_exponent, raise_to_power(user_base, user_exponent)))
Computer Science A) If the values of c and d are given and the function Euclid(c,d) below is executed, multiple recursive calls (Bolded at function) are performed to obtain gcd(c,d) and terminate. Give examples of c and d that make exactly 7 recursive calls, and show the process. However, c>d>=1. Euclid(c,d) if d=0 then return c else return Euclid(d,c mod d)

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Question-3 There are n number of students in a class. Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2ⁿ
a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion.
b) Consider this Algorithm-Z , Taking list of integer as input
List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i < number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X
(i) Explain what Algorithm Z is doing?
(ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexity