Problem 4. Let S be a dynamic set of integers. At the beginning, S is empty. Then, new integers are added to it one by one, but never deleted. Let k be a fixed integer. Describe an algorithm to maintain the k largest integers in S. Your algorithm must use O(k) space at all times, no matter how large |S| is (note that |S| increases continuously, but your space cannot). Furthermore, it must process every integer insertion in O(log k) time. For example, suppose that k = 3, and that the sequence of integers inserted is 83, 21, 66, 5, 24, 76, 92, 32, 43... Your algorithm must be keeping {83,66, 24} after the insertion of 24, {83, 66, 76} after the insertion of 76, and {83, 76, 92} after the insertion of 43.

Problem 4. Let S be a dynamic set of integers. At the beginning, S is empty. Then, new integers are added to it one by one, but never deleted. Let k be a fixed integer. Describe an algorithm to maintain the k largest integers in S. Your algorithm must use O(k) space at all times, no matter how large |S| is (note that |S| increases continuously, but your space cannot). Furthermore, it must process every integer insertion in O(log k) time. For example, suppose that k = 3, and that the sequence of integers inserted is 83, 21, 66, 5, 24, 76, 92, 32, 43... Your algorithm must be keeping {83,66, 24} after the insertion of 24, {83, 66, 76} after the insertion of 76, and {83, 76, 92} after the insertion of 43.

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

Problem 4. Let S be a dynamic set of integers. At the beginning, S is empty. Then, new integers
are added to it one by one, but never deleted. Let k be a fixed integer. Describe an algorithm to
maintain the k largest integers in S. Your algorithm must use O(k) space at all times, no matter
how large |S| is (note that |S| increases continuously, but your space cannot). Furthermore, it must
process every integer insertion in O(log k) time.
For example, suppose that k = 3, and that the sequence of integers inserted is 83, 21, 66, 5, 24,
76, 92, 32, 43.. Your algorithm must be keeping {83, 66, 24} after the insertion of 24, {83, 66, 76}
after the insertion of 76, and {83, 76, 92} after the insertion of 43.

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