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Chapter 2: Problem 24

Assuming that Quicksort uses the first item in the list as the pivot item: a. Give a list of \(n\) items (for example, an array of 10 integers) representing the worst-case scenario. b. Give a list of \(n\) items (for example, an array of 10 integers) representing the best-case scenario.

Short Answer

Expert verified
Worst-case scenario array: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]. Best-case scenario array: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Step by step solution

01

Worst Case Scenario

To represent the worst-case scenario, provide an array that is already sorted in descending order. For example, an array of 10 integers in descending order could be: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
02

Best Case Scenario

To represent the best-case scenario, provide an array where the pivot divides the array into two nearly equal halves. An example could be a list that is already sorted or the pivot being the median of the array. Here's an example of an array of 10 integers: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

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Most popular questions from this chapter

Use the divide-and-conquer approach to write a recursive algorithm that finds the maximum sum in any contiguous sublist of a given list of \(n\) real values. Analyze your algorithm, and show the results in order notation.

Suppose that, even unrealistically, we are to search a list of 700 million items using Binary Search, Recursion (Algorithm 2.1). What is the maximum number of comparisons that this algorithm must perform before finding a given item or concluding that it is not in the list?

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Write a recursive \(\Theta(n \lg n)\) algorithm whose parameters are three integers \(x, n,\) and \(p,\) and which computes the remainder when \(x^{n}\) is divided by \(p\) For simplicity, you may assume that \(n\) is a power of \(2-\) that is, that \(n=2^{k}\) for some positive integer \(k\)
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