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Chapter 7: Problem 24

Give two instances for which Quicksort algorithm is the most appropriate choice.

Short Answer

Expert verified
QuickSort is most appropriate when dealing with large, unordered datasets and when memory availability is not a constraint.

Step by step solution

01

Understanding when Quicksort is appropriate

QuickSort is a Divide and Conquer algorithm that creates two empty arrays to hold elements less than the pivot value and elements greater than the pivot value, and then recursively sorts the sub arrays. There are few situations where QuickSort becomes the most appropriate choice. QuickSort is best suited when:
02

Instance 1: Large Data sets

When you need to sort a large, unordered dataset, QuickSort is an excellent option. This is due to QuickSort's performance—specifically, its average and best case time complexity of O(n log n). This lower time complexity makes it more effective at sorting large datasets compared to other sorting algorithms like bubble sort or insertion sort that have a time complexity of O(n^2).
03

Instance 2: Memory is not a constraint

QuickSort requires space to store the auxiliary arrays that are created during the sorting process. As a result, it may not be the best choice for systems where memory is a significant constraint. However, if memory is not a limiting factor, QuickSort's efficiency makes it an appropriate choice.

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Most popular questions from this chapter

Write an algorithm that checks if an essentially complete binary tree is a heap. Analyze your algorithm and show the results using order notation.

Write a nonrecursive Quicksort algorithm. Analyze your algorithm, and show the results using order notation. Note that it will be necessary to explicitly maintain a stack in your algorithm.

Another way to sort a list by exchanging out-of-order keys is called Bubble Sort. Bubble Sort scans adjacent pairs of records and exchanges those found to have out-of-order keys: After the first time through the list, the record with the largest key (or the smallest key) is moved to its proper position. This process is done repeatedly on the remaining, unsorted part of the list until the list is completely sorted. Write the Bubble Sort algorithm. Analyze your algorithm, and show the results using order notation. Compare the performance of the Bubble Sort algorithm to those of Insertion Sort, Exchange Sort, and Selection Sort.

Show that there is a case for Heapsort in which we get the worst-case time complexity of \(W(n) \approx 2 n \lg n \in \Theta(n \lg n)\)

Show that the worst-case and average-case time complexities for the number of assignments of records performed by the Insertion Sort algorithm (Algorithm 7.1) are given by $$W(n)=\frac{(n+4)(n-1)}{2} \approx \frac{n^{2}}{2} \quad \text { and } \quad A(n)=\frac{n(n+7)}{4}-1 \approx \frac{n^{2}}{4}$$
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