CSC 320: Summer 2017
Tutorial #1, Tues. May 9, 1:30pm or 2:30pm
If you feel you need extra help, you are welcome to attend
both tutorial sections.
Learning Objectives:

To make sure you understand the Hamilton Path/Hamilton Cycle
question on Assignment #1.

To provide a review of induction.
You should have already
studied induction in Math 122, and either Math 222 or CSC 225/226.
Do these questions before the tutorial but you
do not have to write them up as a formal submission.
It's better to have incorrect solutions
then to just passively absorb it at the tutorial as this will
give you more information as to your strong
and weak points.
Tutorial Part 1: Graph Theory Review
Before coming to the tutorial:

Read the directions on the assignment for the Hamilton Path/
Hamilton cycle programming questions. Download the code
(your choice, C or java) and make sure when you run it
you get a correct output file.

Print the file
out.txt
(from assignment #1).
Draw pictures of all of the graphs
If they have a Hamilton cycle, indicate one
with a highlighter. Otherwise, if they have a Hamilton
Path, indicate one with a highlighter.
For the remaining ones, try to figure out why
they have no Hamilton Path.
Graphs 1012 contain a
Petersen graph
with the outer 5cycle labelled as
0, 1, 2, 3, 4 as a subgraph.
Tutorial Part 2: Induction Proofs

(a)
Give an inductive definition of the
even length strings over the alphabet {a, b}.
(b)
Use your definition from (a) to
prove by induction that the number of
strings of even length n= 2k for some integer k >= 0 is equal to 4^{k}.

Consider the following recurrence relation which is
only defined for n= 2^{k} for integers k >= 0.
T(1)= 5, and for n >= 2, T(n) = n + T(n/2).
Choose either (a) or (b) as the correct formula and
then prove that your answer is correct by induction.
For the incorrect answer, carry out the steps of an
induction proof until the proof fails.
(a) T(n)= n + log_{2}n + 4
(b) T(n)= 2n + 3