A very balanced rooted plane binary tree (VBRPBT for short) is defined to be either An
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Question:
A very balanced rooted plane binary tree (VBRPBT for short) is defined to be either
• An empty tree, or
• A single node, attached to two subtrees L and R, both of which are VBRPBTs, where the difference between the number of nodes in L and the number of nodes in R is at most 1. (As a formula, |s(L) − s(R)| ≤ 1.)
(a) How many VBRPBTs with 10 nodes are there? (There is 1 with 1 node, 2 with 2 nodes, 1 with 3 nodes, and 4 with 4 nodes, as drawn below.)
(b) Prove that, for any number n, there are 2k VBRPBTs for some k (which you don’t have to figure out explicitly). (You probably want to use induction. Hopefully in doing the previous part you have figured out a recursive formula (with two recursive cases) for the numberof VBRPTs of size n.)
Expert Answer:
determine if a binary tree is heightbalanced ORvery balanced rooted plane binary tree A tree where no leaf is much farther away from the root than any other leaf Different balancing schemes allow diff... View the full answer
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