Answered: Given a set of n numbers, we wish to…

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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Question

Given a set of n numbers, we wish to find the i largest in sorted order using a comparison-based algorithm. Find the algorithm that implements each of the following methods with the best asymptotic worst-case running time, and analyze the running times of the algorithms in terms of n and i.

a. Sort the numbers, and list the i largest.

Group of answer choices

1. O(ni)

2. O(nlg(n))

3. O(n + ilg(n))

4. O(i + nlg(n))

5. O(n + ilg(i))

b. Build a max-priority queue from the numbers, and call EXTRACT-MAX i times.

Group of answer choices

1. O(i + nlg(n))

2. O(n + ilg(n))

3. O(nlg(n))

4. O(ni)

5. O(n + ilg(i))

c. Use an order-statistic algorithm to find the ith largest number, partition around that number, and sort the i largest numbers.

Group of answer choices

1. O(n + ilg(i))

2. O(n + ilg(n))

3. O(nlg(n))

4. O(i + nlg(n))

5. O(ni)

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