(a) Describe the structure of a complete binary tree of height h with maximum number of nodes. Derive the minimum number of nodes, n(max) (h), of this tree as a function of h. (b) Describe the structure of a complete binary tree of height h with minimum number of nodes. Derive the maximum number of nodes, n(min)(h), of this tree as a function of h. (c) Derive an expression for the height of a binary tree h in terms of the number of nodes, n.
(a) Describe the structure of a complete binary tree of height h with maximum number of nodes. Derive the minimum number of nodes, n(max) (h), of this tree as a function of h. (b) Describe the structure of a complete binary tree of height h with minimum number of nodes. Derive the maximum number of nodes, n(min)(h), of this tree as a function of h. (c) Derive an expression for the height of a binary tree h in terms of the number of nodes, 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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(a) Describe the structure of a complete binary tree of height h with maximum number of nodes.
Derive the minimum number of nodes, n(max) (h), of this tree as a function of h.
(b) Describe the structure of a complete binary tree of height h with minimum number of nodes.
Derive the maximum number of nodes, n(min)(h), of this tree as a function of h.
(c) Derive an expression for the height of a binary tree h in terms of the number of nodes, n.
![[Note: Assume height of leaf node = 0 and height of root node = h. For (a) and (b), you need to
explain the number of nodes at each level of the binary tree. For answering part (c), use the results
in (a) and (b)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c99683-a01b-4e64-96f8-7137fedec6c4%2F04a5ad94-0295-4b9c-a733-1566adb3bad4%2Ffau8hh_processed.png&w=3840&q=75)
Transcribed Image Text:[Note: Assume height of leaf node = 0 and height of root node = h. For (a) and (b), you need to
explain the number of nodes at each level of the binary tree. For answering part (c), use the results
in (a) and (b)]
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