MATH 368 Design & Analysis Algorithms

James Skon
Spring 2019
Location: Hayes 203, Time: 9:10-10:00, Days: MWF

"People who analyze algorithms have double happiness. First of all they experience the sheer beauty of elegant mathematical patterns that surround elegant computational procedures. Then they receive a practical payoff when their theories make it possible to get other jobs done more quickly and more economically.'' Donald E. Knuth


This course introduces students to the analysis and design of computer algorithms. Upon completion of this course, students will be able to do the following:

  1. analyze the asymptotic performance of algorithms;
  2. demonstrate a familiarity with major algorithms and data structures;
  3. apply important algorithmic design paradigms and methods of analysis; and
  4. synthesize efficient algorithms in common engineering design situations.
Prerequisite: MATH 222 and SCMP 118 or PHYS 270 or equivalent, or permission of instructor

Course Information

  • James Skon
  • Office Hayes Hall 309c
  • Office Hours: MTWHF 10:00-11:00
  • Phone: (740) 427-5369
  • Textbook: Introduction to Algorithms, 3rd Edition, MIT Press, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, ISBN 0262033844
  • Room and Time: Hayes 203, Time: 8:10-9:00, Days: MWF
  • Paperless: This course is intentionally paperless. All assignments are turned in online through Moodle. The instructor will normally not accept work written or printed on paper. (Any exceptions must be pre-approved by the instructor).

Course Grades

Class Attendance/Participation 10%
Problem Sets 30%
LeetCode Assignments 20%
Exams 20%
Final Project/Presentation 20%

Email help

While students are encouraged to use office hours instead of email, the instructor will respond to short questions when appropriate. In order to ensure that they will be correctly handled by the instructor’s filter, the subject of all emails must start with “MATH 391:”; any email without this header runs the risk of being filtered.

Lectures and Lecture Slides

Lecture slides will be available on this site by the day of the presentation. They are intended to help you reconstruct the work from class, but are not intended as a substitute for taking notes.


It is expected that you have read the assigned reading BEFORE class. We will be discussing the topic, and each student is expected to contribute to the conversations. Your participation grade will be partially dependent on your involvement in the discussions.

Problem Sets

Due date: Unless otherwise stated, Problem Sets are due by 5:00pm the day before they will be presented in class. There will be a 12 hour grace period during which the student will received a penalty equal to 5% of the value of the assignment; any assignments submitted more than 12 hours late will not be accepted. Exception: Each student may have a 24 hour extension on one assignment without penalty. This extension will be applied to the first assignment submitted outside the grace period (or retroactively used to cancel one grace-period penalty if not used by the end of the semester.)

Submission Methods: Assignments must be typed and submitted through the Moodle website. The instructor will not accept submissions through email, Moodle submissions in any format other than pdf, or hard copies submitted directly to him.

Missing Assignments: Problem sets are an important part of this class; the effort spent on them is a crucial part of the learning process. Failure to submit assignments is unacceptable: students earning 0s on two assignments cannot receive a grade higher than a B- for the course; students earning three 0s will receive an automatic F for the course.

Problem Set Work Teams: Two person teams may be randomly assigned for some problem sets. The teams should work together, discussing the solutions. However, each team member is responsible to write up their own solution and turn is in. Thus while teams may share the same solution, they also may might be the same. Each assignment will include an estimation of the percentage of work done but each member (from the perspective of each person). For example: "Work distribution: Carmen: 55%, myself: 45%". The instructor will monitor this for patterns across multiple partners.

Problem Set Presentations: Each team must prepare to make a presentation of each problem. The instructor will review these before class, and determine which team will present which problems. The students class participation grade will depend in part of the level of preparation for the solution presentation.

Presentations: Students should be prepared to present and discuss their solutions formally in class the day specifies in the schedule.

LeetCode Assignments

Due Date: As with problem sets, the assignments are due by 5:00pm the day before they will be presented in class, with wth same rules for lateness.

Submission Methods: Assignments ust be submitted online with source code, runs showing a variety of test cases that demonstrate all major aspects of the problem space, a writeup of the computational and space complexity as requested in the assignments.

Collaboration: Students should conform to the "group work" policy below.

Presentations: Students should be prepared to present and discuss their solution formally in class the day specifies in the schedule. Be prepared to justify the solutions correctness as well as it computational analysis.


In order to facilitate learning, students are encouraged to discuss homework and LeetCode problems amongst themselves. Copying a solution is not, however, the same as “discussing.'' A good rule of thumb is the “cup of coffee'' rule. After discussing a problem, you should not take away any written record or notes of the discussion. Go have a cup of coffee or cocoa, and read the front page of the newspaper. If you can still re-create the problem solution afterward from memory, then you have learned something, and are not simply copying. (The “group problems” are exempt from this, as they are intended to be done together.)

Term Project

20% of your grade will consist of a semester long research project, collimating in a 30 minute presentation at the end of the class. This project can be one of the following two types:

  1. (Theory) A review, analysis, and presentation of a relatively recent algorithm of some notability (something from the past 5-10 years). This should include a comprehensive explanation of the algorithm operation and complexity (space and time), a comparison with other techniques, and a review of the proof of both the analysis and the correctness of the algorithm.
  2. (Practice) The implementation, analysis, and testing of some significant algorithm technique or method not explored in this class. You find a problem from this class, or from work you have done or are doing elsewhere, and explore the use of one or more advanced algorithmic technique. This should also include an actual comparative runtime comparison with other techniques varying both the problem size, and the type, of the datasets.
The results of either will be presented during the finals period in a 30 minute time slot. The presentation will be evaluated by both the instructor, and the other students.

Two person teams can be considered for this project, but you must justify this option with clear evidence that it is significantly more work then a single person project. For example, you could explore and compare two distinct approaches, or do a combination of 1 & 2 above, or explore something that has significant complexity in and of itself.

Possible Sources: link


All work turned in is expected to be your own. It is likely that proof, algorithm and code solutions for most problems exist online. Generally you should not search for any of these solutions. If you do use online or written documents, you must fully disclose and reference everything used, and be prepared to lose some credit if the help is deemed to be beyond that which you should used. The rule of thump is you can use references to help understand the problems and terminology, but should not use (and copy or modify) complete or partial solutions found online. Plagiarism detection methods may be used for detection of copying, and student will be subject to AIB notification in such cases.


Date Lecture Content Reading Notes/Links Slides Assignment Due
  Review the slides. It is you responsibility to be familiar with the following:
  • Logarithms
  • Graphs
  • Proof notation
  • Pseudocode
  • Heaps
  • Array v. Lists
    Review Slides  
Jan 14 Introduction
  • Joseph Flavius
  • Course Details
Ch 1 Josephus
Information Form
Jan 16

Programming Environment

  • LeetCode
  Bring Laptop to class!
Jan 18 Proof By Induction
  • Proof: Tiling
  • Proof: A tree of n nodes has n-1 edges
Ch 2   Induction LeetCode0
Jan 21 Algorithm Proof by Loop Invarient Ch 2   Proofs of Algorithms  
Jan 23 Present LeetCode1 solutions
Algorithm Proof By Induction:
    Proofs of Algorithms LeetCode1
Jan 25 Graph Theory Ch 22   Graph Theory  
Jan 28 Graph Theory Proof Example Ch 23 Course Project Instructions    
Jan 30 Cold Day!       Problem Set 1, tex, Teams
Feb 1 Present Problem Set 1 Solutions
Greedy Algorithms

  • Disjkstra's Algorithm
    Dijkstra's Algorithm Problem Set 1, tex, Teams
Feb 4

Greedy Algorithms

  • Classroom Scheduling
    Interval Scheduling
Fractional Knapsack
Feb 6 Runtime Analysis
  • Asymptotic notation
  • Worst-case analysis
  • Binary search
  • Problem bounds
Ch 3      
Feb 8 Present LeetCode2 solutions
Runtime Analysis
Ch 3   Asymptotic Analysis LeetCode2
Feb 11
Runtime Analysis
Present Problem Set 2 Solutions
    Asymptotic Analysis
Big-O, Little-O, Theta, Omega
Problem Set 2, Teams, moodle
Feb 13 Runtime Analysis CH 16   Greedy Algorithms  
Feb 15 Presentation Overview
Runtime Analysis
Ch 17      
Feb 18 Huffman Codes
Heaps and Priority Queues

Ch 22, 23   Kruskal LeetCode3

Feb 20 More on Union-Find and MST
Midterm Questions
  01UnionFind.pdf Kruskal Problem Set 3, Teams, moodle
Feb 22 Minimum Spanning Trees
Prim’s Algorithm

Union-Find Structure
  Exam Study Guide   Presentation Topic Submit
Feb 25   Ch 4, 7      
Feb 27 Exam 1 CH 4.5      
Mar 1 Art Gallary Visit - Art and Algorithms        
  Spring Break        
Mar 18

Divide and conquer

CH 4    
Mar 20 Sorting with divide and conquer CH 4 DivideAndConquerNotes.pdf Divide & Conquer sorting Problem Set 4, Teams
Mar 22 Analyzing Recurrence relations CH 4   Bounding Recurrences Relations  
Mar 25 Analyzing Recurrence relations 4 Master Theorem   LeetCode4
Mar 27 Divide and Conquer 8 InversionCounting Code (n^2)

Presentation Status Report

Mar 29 Linear Sorting 15 Linear Sorting

Problem Set 5, Teams, Moodle
Apr 1

Dynamic Programming

  • Linear Sorting
15   Dynamic Programming  
Apr 3

Dynamic Programming

  • Rodcutting
15   RodCutting LeetCode5
Apr 5

Dynamic Programming

  • Weighted Interval Selection
    weighted_interval_selection LeetCode6
Apr 8

Dynamic Programming

  • Russian Doll Envelope
15 Russian Doll Envelope   LeetCode7
Apr 10 Searching
  • Hashing
11 Hashing Animation Hashing Problem Set 6 , Teams , Moodle
Apr 12


  • Hashing Consideration
11   HashingConsiderations LeetCode8
Apr 15
  • Present Problem Set 6 Solutions
  • Present LeetCode 8 solutions
  Exam 2 Study Guide Trees Presentation Outline
Apr 17 Tree Structures 12&18 B-Tree Simulation
B+ Tree Simulation
Apr 19         Problem Set 7, Moodle, Teams
This problem set is optional and extra credit.
Apr 22

Exam 2

Apr 24 P and NP, nondeterminism, reductions 34   AlgorithmicIntractability LeetCode9
Apr 26 P and NP, nondeterminism, reductions 34 Reduction Video AlgorithmicIntractability Problem Set 7B
Apr 29 Reductions
  • Subset Sum
  • Hamiltonian Path
May 1 Final Presentations        
May 3 Final Presentations       Problem Set 8 (Extra Credit) Moodle
May 9 Final Presentations 8:30   Presentation Time Sign Up



Moodle link to turn in presentation

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Team Selector - Students

-- Jim Skon - 2016-08-08

Topic attachments
I Attachment History Action Size Date Who Comment
JPEGjpg Algorithms.jpg r1 manage 30.1 K 2018-12-17 - 03:10 JimSkon  
PDFpdf PS01.pdf r3 r2 r1 manage 114.2 K 2019-01-16 - 20:39 JimSkon  
Compressed Zip archivezip r1 manage 2.2 K 2019-01-16 - 19:23 JimSkon  
PDFpdf PS02.pdf r1 manage 90.2 K 2019-01-28 - 18:26 JimSkon  
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PDFpdf PS04.pdf r1 manage 158.0 K 2019-02-11 - 17:26 JimSkon  
PDFpdf PS05.pdf r1 manage 103.3 K 2019-03-24 - 19:18 JimSkon  
PDFpdf PS06.pdf r1 manage 120.6 K 2019-03-24 - 19:47 JimSkon  
PDFpdf PS07.pdf r1 manage 107.1 K 2019-03-24 - 20:00 JimSkon  
PDFpdf PS07B.pdf r1 manage 90.0 K 2019-04-18 - 20:02 JimSkon  
PDFpdf PS08.pdf r1 manage 119.8 K 2019-04-22 - 12:39 JimSkon  
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