What are the rules for writing a recursive algorithm? a) Base case needs to be tested first b) Reduction should solve a problem with smaller size. c) We should always attempt reducing the problem to a smaller problem. d) The problem should be divided into two equal parts, otherwise recursion will not work.

What are the rules for writing a recursive algorithm? a) Base case needs to be tested first b) Reduction should solve a problem with smaller size. c) We should always attempt reducing the problem to a smaller problem. d) The problem should be divided into two equal parts, otherwise recursion will not work.

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
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
er 3) The algorithm solves the problem of 4) size n by dividing it into 64 sub- problems of size n/8, recursively solving each sub-problem, and then combining the solutions in O(n²) time 5) The algorithm solves the problem by breaking it into 8 sub-problems of 1/4 the scale, recursively solving each sub-maze, and then combining the solutions in linear time Th of sub the Q(r Rago 4 of E
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.
Problem 2 -- Recursive Palindrome (Grey + Scarlet) Write a recursive method, isPalindrome, which takes a String as a parameter, and returns true if the String is a palindrome. For the purposes of this method, you may assume Strings with a length of o or 1 are palindromes.
T/F 9. As loop variables and recursive solutions are also not used for iterative solutions, the recursive solution generally makes memorization more effective (use fewer stored) than the corresponding iterative solution.
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
3) Tail Recursion Homework • Unanswered Tail recursion Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation. SHOW MORE v always takes more time than regular recursion b can be transformed into an iterative algorithm – algorithmically is just as problematic as redundant recursion is rarely worth the extra effort to develop requires the single recursive invocation to be at the last line of the algorithm
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2. Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size. Please be sure to give an English description of the algorithm along with pseu- docode, explaining the main points of its design, and a concise inductive argument for its correctness (i.e., say…
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.
Consider the following sequence and answer the questions 3, 12, 27, 48, 75, . (1) Develop the recursive solution to identify numbers in the list. (2) Develop the closed-form solution of the recursive solution you made in the previous question.