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irga5000 [103]
3 years ago
7

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 wit

h n vertices.
(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?


(b) For general n, derive a recurrence relation for Bn.

(c) Show by induction that Bn is (2n). 2.14. You are given an array of n elements, and

Computers and Technology
1 answer:
Arlecino [84]3 years ago
7 0

Answer:

(a) B_3 = 1\\B_5 = 2\\B_7 = 5

(b) See attached

(c) B_n = 2^{(n-3)/2}

Explanation:

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