Question

A binary tree isfullif every non-leaf node has exactly two children. For context, recallthat we saw in lecture that a binary tree of heighthcan have at most 2h+1−1 nodes, and thatit achieves this maximum if it iscomplete, meaning that it is full and all leaves are at the samedistance from the root. Findμ(h), theminimumnumber of nodes that a full tree of heighthcan have, and prove your answer using ordinary induction onh. Note that tree of height of 0 isa single (leaf) node

Answer #1

Prove that a full non-empty binary tree must have an odd number
of nodes via induction

Problem 4. Convert RE to CFG
We saw in class how to construct CFGs
for U, *, and
o operations for existing CFL's. We
also saw how to construct CFG's for regular expressions
empty-set, e, and c (where c is
some member of S).
a) Using these constructions, create
CFG for the RE R = x ((yx)* U
y). This is an algorithm for converting any RE to
a CFG with start variable S0. It works as follows:
create an...

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