Problem 6: Red black trees. Let D be a data structure on the set of positive integers, which supports the following operations: - Insert(D, x): insert x in D. - Remove(D, x): remove x from D. - Find(D, x): find x in D. - Count(D, x): returns the number of elements in D that are larger then x. We would like to implement D by using red black trees. Describe how can we modify a red black tree such that all four operations have time complexity O(log n), where n denotes the number of elements in the structure. Elaborate why time complexity of all four operations is O(log n).
Problem 6: Red black trees. Let D be a data structure on the set of positive integers, which supports the following operations: - Insert(D, x): insert x in D. - Remove(D, x): remove x from D. - Find(D, x): find x in D. - Count(D, x): returns the number of elements in D that are larger then x. We would like to implement D by using red black trees. Describe how can we modify a red black tree such that all four operations have time complexity O(log n), where n denotes the number of elements in the structure. Elaborate why time complexity of all four operations is O(log n).
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 6: Red black trees. Let D be a data structure on the set of positive integers,
which supports the following operations:
- Insert(D, x): insert x in D.
- Remove(D, x): remove x from D.
- Find(D, x): find x in D.
- Count(D, x): returns the number of elements in D that are larger then x.
We would like to implement D by using red black trees. Describe how can we modify a red
black tree such that all four operations have time complexity O(log n), where n denotes the
number of elements in the structure. Elaborate why time complexity of all four operations
is O(log n).
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