Problem 1: Patricia trees. In this problem we assume that there are n ≥ 2 elements inserted into a Patricia tree over an alphabet Σ and that no element is a prefix of some other element. (i) If Σ = {0, 1}, show that the Patricia tree has precisely n − 1 internal nodes. (ii) If Σ = {0, 1, X}, what is the greatest possible height of the Patricia tree and what is the smallest possible? Elaborate.
Problem 1: Patricia trees. In this problem we assume that there are n ≥ 2 elements inserted into a Patricia tree over an alphabet Σ and that no element is a prefix of some other element. (i) If Σ = {0, 1}, show that the Patricia tree has precisely n − 1 internal nodes. (ii) If Σ = {0, 1, X}, what is the greatest possible height of the Patricia tree and what is the smallest possible? Elaborate.
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 1: Patricia trees. In this problem we assume that there are n ≥ 2 elements
inserted into a Patricia tree over an alphabet Σ and that no element is a prefix of some
other element.
(i) If Σ = {0, 1}, show that the Patricia tree has precisely n − 1 internal nodes.
(ii) If Σ = {0, 1, X}, what is the greatest possible height of the Patricia tree and what is
the smallest possible? Elaborate.
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