# Assignment No. 8 EECS 210 Discrete Structures

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Assignment No. 8
EECS 210
Discrete Structures

Submit deliverables in a single zip file to Canvas
Name of the zip file: FirstnameLastname_Assignment8 (with your first and last name)
Name of the Assignment folder within the zip file: FirstnameLastname_Assignment8
Deliverables:
1. Copy of Rubric8.docx with your name and ID filled out (do not submit a PDF).
2. Source code.
3. Screen print showing the successful execution of your code or copy and paste the
output from a console screen to a Word document and PDF it.
Assignment:
• You may use any language you want, but if you want help from me or one of the
SIs, you should probably use C++, Python, or Haskell.
• Your output should make it easy for the grader to determine which part of the
assignment it is for.
1. Write a program for finding an Euler circuit, if one exists, using the algorithm
from the lecture on Euler circuits and paths. If an Euler circuit does not exist,
print out the vertices with odd degrees (see Theorem 1). If an Euler circuit does
exist, print it out with the vertices of the circuit in order, separated by dashes, e.g.,
a-b-c.
a) Debug your program with the Example 1 graphs G1, G2, G3, and the graph
of the Bridges of Kӧnigsberg from the “Euler, Hamilton, & Shortest Path
Problems” lecture slides.
b) Test your program with this graph:
2. Write a program that uses Dirac’s theorem to determine if a graph has a Hamilton
circuit. You do not have to find the circuit.
a) Debug your program with the Example 5 graphs G1, G2, and G3 from the
“Euler, Hamilton, & Shortest Path Problems” lecture slides.
b) Test your program with this graph:
3. Write a program that uses Ore’s theorem to determine if a graph has a Hamilton
circuit. You do not have to find the circuit.
a) Debug your program with the Example 5 graphs G1, G2, and G3 from the
“Euler, Hamilton, & Shortest Path Problems” lecture slides.
b) Test your program with this graph:
4. Write a program that creates a min-max strategy for the game of Nim. Display the
strategy in a manner that will be clear to the grader and includes all of the
elements shown in the “Minmax Strategy for Nim (11.2.5)” slide in the
“Application of Trees” lecture.
a) Debug your program with a version of Nim with the starting position
where there are 3 piles of stones containing 2, 2, and 1 stone each,
respectively (same as one in the “Minmax Strategy for Nim (11.2.5)”
slide.
b) Test your program with a version of Nim with the starting position
consists of three piles with one, two, and three stones, respectively. When
drawing the tree represent by the same vertex symmetric positions that
result from the same move.
c) Who wins the game if both players follow an optimal strategy?
5. Provide comments that explain what each line of code is doing. See rubric below.
Exceeds Expectations
(90-100%)
Meets Expectations
(80-89%)
Unsatisfactory
(0-79%)
commented with prologue
summarizing major blocks of
line.
but missing some items or some
major blocks of code are not
commented or there are
line.
all together or there are no
code or there are very few
• Name of program contained in the file (e.g., EECS 210 Assignment 3)
• Brief description of the program, e.g.:
o Python code for demonstrating operations on relations and properties of
relations.
• Inputs (e.g., none, for a function, it would be the parameters passed to it)
• Output, e.g.,
o Print out of the name of each exercise, followed by the exercise’s output.
• Author’s full name
• Creation date: The date you first create the file, i.e., the date you write this
comment