C241 PLTL SESSION –
2/22/2015
Graph Theory & Binary Search Trees
Warm-Up Exercise
• Grab a worksheet
• Begin completing the worksheet in pairs or small groups
Problem 1
Put the following sequence of numbers into a binary search tree
data structure:
8, 7, 9, 5, 20, 12, 1, 4
What is the root of your tree?
What is the depth of the resulting tree?
Problem 2
Consider the binary search tree data structure. What other sorts
of data could it be useful for storing? Come up with three
different situations in which you would use a binary search tree
(BST) to represent your data.
Problem 3
Draw the following situation as a graph, (like the one from class
today): In the domain of all people, everyone is mortal. Alex is
nice and he trusts everyone, but no one trusts Alex. Ben and
Chris trust each other, but only Ben is nice. Also, assume that
everyone trusts themselves. (Note: In this context, “everyone”
means Alex, Ben, and Chris. Also, think of the truth relation as a
two-way street).
T(x, y) = x trusts y
M(x) = x is mortal
N(x) = x is nice
Problem 4
Given the situation drawn above, translate the following into
statements of predicate logic, and then assess the truth of each
statement:
• A. Everyone is mortal.
• B. Everyone is mortal or nice.
• C. Everyone trusts someone.
• D. Everyone who is trustworthy is also nice.
• E. Someone trusts everyone.
• F. Everyone trusts someone nice, excluding themselves.