Answered: Problem 5: Disjoint sets. Consider a…

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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Problem 5: Disjoint sets. Consider a list of cities c1, c2, . . . , cn. Assume we have a relation
R such that, for any i, j, R(ci
, cj ) is 1 if cities ci and cj are in the same province, and 0
otherwise.
(i) Using a disjoint set data structure, write an algorithm that puts each city in a set
such that ci and cj are in the same set if and only if they are in the same province.
Justify corectness of your algorithm.
(ii) If a disjoint set data structure is implemented by trees and in union the name of the
new set is always the name of the larger set, what is the worst-case running time of
your algorithm.

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