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(a) Describe the structure of a complete binary tree of heighth with maximum number of nod- Derive the minimum number of nodes, nmax (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 nod- Derive the maximum number of nodes, n(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 heighth with maximum number of nod- Derive the minimum number of nodes, nmax (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 nod- Derive the maximum number of nodes, n(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
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
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[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)]

(a) Describe the structure of a complete binary tree of height h with maximum number of nodes. Derive the minimum number of nodes, nmax (h), of this tree as a function of h. (b) Describe the structure of a complete binary tree of heighth with minimum number of nodes Derive the maximum number of nodes, nmin (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.
Transcribed Image Text:(a) Describe the structure of a complete binary tree of height h with maximum number of nodes. Derive the minimum number of nodes, nmax (h), of this tree as a function of h. (b) Describe the structure of a complete binary tree of heighth with minimum number of nodes Derive the maximum number of nodes, nmin (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.
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