Description:

The course covers the basics from the efficient algorithm design, data structures, and graph theory, belonging to the core knowledge of every computing curriculum. It is interlinked with the concurrent BIE-AAG and BIE-ZDM courses in which the students gain the basic skills and knowledge needed for time and space complexity of algorithms and learn to handle practically the asymptotic mathematics.

Contents:

1. Motivation and Elements of Graph Theory.
2. Basic Definitions and Elements of Graph Theory I.
3. Basic Definitions and Elements of Graph Theory II.
4. Sorting Algorithms O(n^2). Binary Heaps and HeapSort.
5. Extendable Array, Amortized Complexity, Binomial Heaps.
6. Search Trees and Balance Strategies.
7. Introduction to Randomization, Hashing.
8. Recursive algorithm and the Divide-and-Conquer method.
9. Probabilistic Algorithms and Their Complexity. QuickSort.
10. Dynamic Programming.
11. Minimum Spanning Trees.
12. Shortest Paths Algorithms on Graphs.

Seminar contents:

1. Motivation and Elements of Graph Theory I.
2. Elements of Graph Theory II.
3. Elements of Graph Theory III. 1st ProgTest.
4. Sorting Algorithms O(n^2). Binary Heaps.
5. Extendable Array, Amortized Complexity, Binomial Heaps.
6. Search Trees and Balance Strategies. 2nd ProgTest.
7. Hashing and Hash tables.
8. Recursive Algorithms and Divide et Impera Method.
9. Probabilistic Algorithms and their Complexity. QuickSort.
10. Semestral test.
11. Dynamic Programming. 3rd ProgTest.
13. Minimum Spanning Trees, Shortest Paths.

Recommended literature:

1. Cormen T.H., Leiserson C.E., Rivest R.L., Stein C. : Introduction to Algorithms (3rd Edition). MIT Press, 2016. ISBN 978-0262033848.
2. Wengrow J. : A Common-Sense Guide to Data Structures and Algorithms: Level Up Your Core Programming Skills (2nd Edition). Pragmatic Bookshelf, 2020. ISBN 978-1680507225.
3. Sedgewick R. : Algorithms (4th Edition). Addison-Wesley, 2011. ISBN 978-0321573513.
4. Deo N. : Graph Theory with Applications to Engineering and Computer Science. Dover Publications, 2016. ISBN 978-048680793.
5. Bickle A. : Fundamentals of Graph Theory. AMS, 2020. ISBN 978-1470453428.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar