Solve the following exercises in Sorting Algorithms:a. Recall that a sorting algorithm is said to be stable if the original ordering forduplicate keys is preserved. Of the sorting algorithms Insertion Sort, BubbleSort, Selection Sort, Shell sort, Merge sort, Quicksort, Heapsort, Binsort, andRadix Sort, which of these are stable, and which are not? For each one,describe either why it is or is not stable. If a minor change to theimplementation would make it stable, describe the change.b. Which of the following operations are best implemented by first sorting thelist of numbers? For each operation, briefly describe an algorithm toimplement it, and state the algorithm's asymptotic complexity.i.ii.iii.Find the minimum value.Find the maximum value.Compute the arithmetic mean.iv.Find the median (i.e., the middle value).Find the mode (i.e., the value that appears the most times).V.

sorting algorithm: A Sorting Algorithm is used to rearrange a given array or list elements according…

Answered: a. Recall that a sorting algorithm is…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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3 illustrates the counting sort algorithm. For simplicity ofimplementation and understanding, the range (a, b) within which the unordered setof keys lie is assumed to be within (0, k).
Question 6: Professor Holmes has come up with a new sorting algorithm. He calls it Trinary Sort and "claims" that it is asymptotically faster than Merge Sort, despite the fact both the algorithms operate using similar logic. But, unlike Merge Sort, Trinary Sort splits the input array into (roughly) 3 equal parts at each step of the recursion as long as the array is splittable (i.e., has at least 3 elements). Trinary Sort's merge subroutine, similar in principle to the one used by Merge Sort, takes 3 sorted subarrays and merges them to produce a single sorted array. Given all of this, answer the following questions. (a) In Merge Sort, the merge subroutine makes n-1 comparisons to merge 2 arrays of size n/2, which takes (n) time. How many comparisons will the merge subroutine of Trinary Sort make to merge 3 arrays of size n/3? What would be the (...) bound on the running time for this subroutine? (b) What is the (...) bound on the running time of the Trinary Sort algorithm? Come up with…
1. Write the Insertion Sort algorithm. 2. Analyze the algorithm time complexity at the best case, what are the total running time for this algorithm at the best case
Present an example of walking through the merge sort or the quick sort algorithm (your choice) This is an algorithm tracing activity, not a coding exercise. Do not post any code or code output. Post the following for merge sort: Start with an unordered list of at least NINE elements. List all the recursive calls that would be made to sort the list, going forward. Show which pair of sub-lists will be merged each time, going back. Show the ordering of the sub-list after each recursive call returns. Post the following for quick sort: Start with an unordered list of at least NINE elements. State what element will be the pivot value (use only low index or median-of-three). List all the recursive calls that would be made to sort the list. Show the ordering of the sub-list after each recursive call returns.
AssuAssume we want to analyze empirically 4 variants of the Quicksort algorithm by varying the selection of the pivot and the recursive call as follows: ● Try the following values when selecting a pivot: - Pick the last element as pivot - Pick a random element as pivot ● Do not make a recursive call to QuickSort when the list size falls below a given threshold, and use Insertion Sort to complete the sorting process instead. Try the following values for the threshold size: - Log2(N) - Sqrt(N) Therefore, you are asked: a. (12 points) Write the java code for the 4 Quicksort implementations. b. (5 points) Write a driver program that allows you to measure the running time in milliseconds of the 4 implementations for N = 10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 107 and use the same list to measure the running time of the 4 implementations. Present the results in the following table:me we want to analyze…
Subj:- Design & Anal Algorithms Please compelete all the three questions since it has to be answereda once. Thank you in advance. Three animals stand next to each other by size, as follows: An Elephant, followed by a Hippo, followed by a Panda bear, [E, H, P]. Your goal is to re-arrange them so that they are sorted in the opposite size-based order. You are only allowed to switch positions of neighboring animals. Do not use Insertion or Merge sort. Try to use your own strategy to re-arrange the array. (a) How many operations do you need to reverse the order of the three animals? (b) Let’s generalize the above. You have an array of n elements whose ordering you want to revers. Write pseudo code to do this. (c) How many operations do you need to reverse the ordering of an array of n? Your answer should be a function of n.
Make pseudocode to illustrates the counting sort algorithm. For simplicity of implementation and understanding, the range (a, b) within which the unordered set of keys lie is assumed to be within (0, k).
Explain the running time of Tim sort Algorithm if the input data array is Sorted (ascending) and Sorted (descending) and not sorted. 2. Explain the running time of tree Sort Algorithm if the input dada array is Sorted (ascending) and sorted (descending) and not sorted. 3. Explain the running time of counting Sort Algorithm if the input data array is Sorted (ascending) and Sorted (descending) and not Sorted. 4. Explain the running time of Block Sort Algorithm if the input data array is Sorted (ascending) and Sorted (descending) and not Sorted. 5. Explain the running time of Bucket Sort Algorithm if the input data array is Sorted (ascending) and Sorted (descending) and not Sorted.
Stable algorithmsa. Explain the meaning of stability in a sorting algorithm. b. Explain a situation why stability in sorting is desired. c. State which algorithms are stable i. selection sort ii. bubble sort ii. insertion sort iii. merge sort iv. quick sort
subject: data structure and algorithms Q: Suppose a list of 650 elements is sorted using Bubble sort i. What is the total number of Passes?ii. What is the total number of steps in all Passes?iii. What is the number of steps in Pass# 34, Pass# 134 and Pass# 434?
Answer the given question with a proper explanation and step-by-step solution. Class Activity - Sorting Sort the list 19, 22, 8, 90, 13 using the stated method, showing the result after each pass (not each comparison!) Selection sortInsertion sortBubble sortQuicksort (underline the pivot at each step)Merge Sort (Show the decomposition & the merge)
Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] Consider a list of numbers A {55,12,53,56,24,1,7,42}. Sort is by using Merge Sort. Show each step in dividing the list and conquering/combining it.

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