Question: Each deleteMin operation uses 2 logN comparisons in the worst case. a. Propose a scheme so that the deleteMin operation uses only logN + log

Each deleteMin operation uses 2 logN comparisons in the worst case.
a. Propose a scheme so that the deleteMin operation uses only logN + log logN + O(1) comparisons between elements. This need not imply less data movement.
b. Extend your scheme in part (a) so that only logN + log log logN + O(1) comparisons are performed.
c. How far can you take this idea?
d. Do the savings in comparisons compensate for the increased complexity of your algorithm?

Step by Step Solution

★★★★★

3.33 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a If the heap is organized as a min heap then starting at the hole at the root find a path down to a ... 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(380).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

Show that the second smallest of n elements can be found with n + lg n - 2 comparisons in the worst case.

Prove that any comparison-based sorting algorithm requires (N logN) comparisons on average.

The worst-case number T(n) of comparisons used by SELECT to select the ith order statistic from n numbers was shown to satisfy T(n) = Θ(n), but the constant hidden by the Θ-notation is...

Each deleteMin operation uses 2logN comparisons in the worst case. N is the number of nodes in the heap structure. 1. Propose a scheme so that the deleteMin operation uses only logN+loglogN+O(1)...

Each deleteMin operation uses 2 logN comparisons in the worst case. N is the number of nodes in the heap structure. Propose a scheme so that the deleteMin operation uses only logN + loglogN + O ( 1 )...

Each deletMin operation uses 2longN comparisons in the worst case. a. Propose a scheme so that the deleteMin operation uses only logN + longlongN +O(1) comparisons between elements. This need not...

make a project on topic priority queue using binary heap help with the research paper giving above to implementation code in python data structure do it in one day S.L. Graham, R.L. Rivest Editors...

Developments in Technology Light is incident from air on the end face of a multimode optical fibre at angle of incidence as shown below. n n 1 2 The refractive indices of the core and cladding are...

What differences do you see between the U.S. version of American Idol and the version in other countries? Use material from this chapter to explain the reason for those differences.

Explain why the MP/P relation is deficient as the sole mechanism for determining the optimal level of resource employment.

What type of transmission lines were used in early telegraphy over land? Two wire PVC insulated lines Two wire ait insutated tines Two wire Gutta - Percha insulated lines Coaxdal cables

2. The following table gives your marginal utilities for three desserts: pie, ice cream, and custard. Each dessert is priced at $1. Suppose you had $10 to spend on desserts. How much of each dessert...

Design a form that requests the user to type in two numbers. When the user clicks on the submit button, the server returns their sum. Write the server side as a PHP script.

For each of the following applications, tell whether it would be (1) possible and (2) better to use a PHP script or JavaScript and why. (a) Displaying a calendar for any requested month since...

Write a program in JavaScript that accepts an integer greater than 2 and tells whether it is a prime number. Note that JavaScript has if and while statements with the same syntax as C and Java. The...

5-5 You plan to buy a new car. The price is $30,000 and you will make a down payment of $4,000. Your annual interest rate is 10% and you intend to pay for the car over five years. What will be your...

A one-year European call option on ABX corporation with a strike price of $50 is currently trading for $1.45, and a one-year European put option on ABX with the same strike price is currently trading...

A 13-year annuity pays $3,000 per month, and payments are made at the end of each month. The interest rate is 9 percent compounded monthly for the first six years, and 7 percent compounded monthly...