Question: The following divide-and-conquer algorithm is proposed for finding the simultaneous maximum and minimum: If there is one item, it is the maximum and minimum, and

The following divide-and-conquer algorithm is proposed for finding the simultaneous maximum and minimum: If there is one item, it is the maximum and minimum, and if there are two items, then compare them and in one comparison you can find the maximum and minimum. Otherwise, split the input into two halves, divided as evenly as possibly (if N is odd, one of the two halves will have one more element than the other). Recursively find the maximum and minimum of each half, and then in two additional comparisons produce the maximum and minimum for the entire problem.
a. Suppose N is a power of 2. What is the exact number of comparisons used by this algorithm?
b. Suppose N is of the form 3 ∙ 2k. What is the exact number of comparisons used by this algorithm?
c. Modify the algorithm as follows: When N is even, but not divisible by four, split the input into sizes of N/2 − 1 and N/2 + 1. What is the exact number of comparisons used by this algorithm?

Step by Step Solution

★★★★★

3.39 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Here is a Java implementation import javautilRandom public class Exercise740 public static int numComparisons public static final int N 1048576 Let N ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1486-C-S-A(436).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

Many computer applications involve searching through a set of data and sorting the data. A number of efficient searching and sorting algorithms have been devised in order to reduce the runtime of...

Consider the following recursive mergesort algorithm (another classic divide and conquer algorithm). Mergesort was first described by John Von Neumann in 1945. The basic idea is to divide an unsorted...

This exercise develops a space-efficient variant of the forward'backward algorithm described in Figure. We wish to compute P (X k?e l; t) for k = 1... t. This will be done with a divide-and-conquer...

Table of Contents Main Objective of the assessment 1 Description of the Assessment 1 Learning Outcomes and Marking Criteria. 4 Format of the Assessment 6 Submission Instructions. 7 Avoiding...

Q4: Highs and lows(Loop algorithms: Maximum/minimum) Instructions Today well carry on working through some common loop algorithms. Our second one will be finding both the maximum and minimum of a set...

Alicia Fuentes owns 15 shares of stock in the Shale Oil Company, a large corporation that deals with oil and gas products. Hugh Jones, a friend of Alicia's, owns 20 shares. Today they both received...

What is the relationship between business modeling and system design? How would an information system, including timely and accurate accounting information, improve the business decision-making...

Question 3 2 of 7 5 . Gustavo is a partner in an architectural design firm. He is active in the business and serves as the partnership's chief technology officer. He receives a guaranteed payment of...

3. Supposing you own a pastry shop. Using any numbers you wish, construct a table showing your market-day, short-run, and long-run supply of chocolate clairs. Explain the differences.

The off-line minimum problem asks us to maintain a dynamic set T of elements from the domain {1, 2, ..., n} under the operations INSERT and EXTRACT-MIN. We are given a sequence S of n INSERT and m...

In the depth-determination problem, we maintain a forest F = (Ti) of rooted trees under three operations: MAKE-TREE (v) creates a tree whose only node is v. FIND-DEPTH (v) returns the depth of node...

Consider the problem of neatly printing a paragraph on a printer. The input text is a sequence of n words of lengths l1, l2, ..., ln, measured in characters. We want to print this paragraph neatly on...

Paladin Furnishings generated million in sales during 2019, and its year and total assets were $2.8 million. Also, at year-end 2019, current liabilities were $500.000. consisting of $200,000 of notes...

(1 point) Random samples of female and male drivers are asked to estimate the number of miles that each drives in a year. The data is below: Females (Population 1): 9100, 8100, 9500, 790, 8100, 8400,...

How to calculate the content of green grid? Thank you 12. After saving diligently throughout your entire career, you and your spouse are finally ready to retire with a nest egg of $1,000,000. You...