Question
A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees
A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees with II vertices.
(a) By drawing out all full binary trees with 3. 5. or 7 vertices, determine the exact values of 83. B5, and 87. Why have we left out even numbers of vertices, like B49
(b) For general n. derive a recurrence relation for Bn.
(c) Show by induction that Bn is 20(n).
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a The following figures show all the binary trees with 3 5 and 7 nodes The binary tree with three ve...
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Discrete and Combinatorial Mathematics An Applied Introduction
Authors: Ralph P. Grimaldi
5th edition
201726343, 978-0201726343
