*Data Structures and Algorithm Professor Holmes came up with the idea of a sorting algorithm that he calls Trinary Sort which he claims is asymptotically faster than merge sort, despite being similar in logic. Unlike merge sort, trinary sort splits the input list into three roughly equal parts at each step of the recursion as long as the list is splittable (i.e., has at least 3 elements in this case). The merge operation, similar to what it does in mergeSort, takes three already sorted subarrays, and merges them. (a) In merge sort, merge operation makes exactly n−1 comparisons in total to merge two lists of size n/2 in the worst case, which takes O(n) time. How many comparisons will the merge operation of Trinary sort make in the worst case to merge three sublists of size (n/3) (give an exact number)? Why? What would be the asymptotic bound? (b) What is the total running time of the Trinary Search algorithm? Show it using the tree expansion method.

*Data Structures and Algorithm Professor Holmes came up with the idea of a sorting algorithm that he calls Trinary Sort which he claims is asymptotically faster than merge sort, despite being similar in logic. Unlike merge sort, trinary sort splits the input list into three roughly equal parts at each step of the recursion as long as the list is splittable (i.e., has at least 3 elements in this case). The merge operation, similar to what it does in mergeSort, takes three already sorted subarrays, and merges them. (a) In merge sort, merge operation makes exactly n−1 comparisons in total to merge two lists of size n/2 in the worst case, which takes O(n) time. How many comparisons will the merge operation of Trinary sort make in the worst case to merge three sublists of size (n/3) (give an exact number)? Why? What would be the asymptotic bound? (b) What is the total running time of the Trinary Search algorithm? Show it using the tree expansion method.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter17: Linked Lists

Section: Chapter Questions

Problem 18SA

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1. The sorted values array contains 16 integers 5, 7, 10, 13, 13, 20, 21, 25, 30,32, 40, 45, 50, 52, 57, 60. Indicate the sequence of recursive calls that are made tobinaraySearch, given an initial invocation of binarySearch(32, 0, 15).show only the recursive calls. For example, initial invocation is binarySearch(45,0,15)where the target is 45, first is 0 and last is 15.
def removeMultiples(x, arr) - directly remove the multiples of prime numbers (instead of just marking them) by creating a helper function. This recursive function takes in a number, n, and a list and returns a list that doesn’t contain the multiples of n.def createList(n) - a recursive function, createList(), that takes in the user input n and returns an array of integers from 2 through n (i.e. [2, 3, 4, …, n]). def Sieve_of_Eratosthenes(list) - a recursive function that takes in a list and returns a list of prime numbers from the input list.Template below: def createList(n): #Base Case/s #ToDo: Add conditions here for base case/s #if <condition> : #return <value> #Recursive Case/s #ToDo: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once all ToDo is completed return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your…
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15.14 LAB: Binary search Binary search can be implemented as a recursive algorithm. Each call makes a recursive call on one-half of the list the call received as an argument. Complete the recursive function BinarySearch() with the following specifications: Parameters: a target integer a vector of integers lower and upper bounds within which the recursive call will search Return value: the index within the vector where the target is located -1 if target is not found The template provides the main program and a helper function that reads a vector from input. The algorithm begins by choosing an index midway between the lower and upper bounds. If target == integers.at(index) return index If lower == upper, return -1 to indicate not found Otherwise call the function recursively on half the vector parameter: If integers.at(index) < target, search the vector from index + 1 to upper If integers.at(index) > target, search the vector from lower to index - 1 The vector…
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