Algorithms and Graphs 1

Garant předmětu:

Dušan Knop

Lecturer:

Radek Hušek

Tutor:

Radek Hušek

Supervisor:

Department of Theoretical Computer Science

Synopsis:

The course is presented in Czech.

The course covers the basics from the efficient algorithm design, data structures, and graph theory, belonging to the core knowledge of every computing curriculum. Students learn techniques of proofs of correctness of algorithms and techniques of asymptotic mathematics for estimation of their complexity in the best, worse, or average case (the course includes basics from probability theory needed for understanding randomized algorithms). Within exercises students learn applications of studied algorithms for solving practical problems.

Requirements:

Entry knowledge: Active algorithmic skills for solving basic types of computational tasks, programming skills in some HLL (Java, C++), and knowledge of basic notions from the mathematical analysis and combinatorics are expected. Students are expected to take concurrent courses BIE-AAG and BIE-ZDM.

Syllabus of lectures:

1. Motivation, graph definition, important types of graphs, undirected graphs, graph representation, subgraphs.

2. Connectivity, connected components, DFS, directed graphs, trees.

3. Spanning trees, distances in graphs, BFS, topological ordering.

4. Basic sorting algorithms with the quadratic time complexity. Binary heap as a partial ordered structure, HeapSort.

5. Extendable array, amortized complexity. Binomial Heaps.

6. Operations and properties of binary search trees, balancing strategies, AVL trees.

7. Randomized algorithms. Introduction to probability theory. Hash tables and strategies of collision resolving.

8. Recursive algorithms and Divide and Conquer algorithms.

9. QuickSort. Lower bound of complexity for sorting problem in the comparison model. Special sorting algorithms.

10. Dynamic programming.

11. Minimum spanning trees of edge-labelled graphs. Jarník’s algorithm and Kruskal’s algorithm and their implementations.

12. [2] Shortest paths algorithms on edge-labelled graphs.

Syllabus of tutorials:

1. Implementation of FA.

2. Examples of formal languages. Intuitive considerations of grammars for given languages. Estimation of the classification of a given language in Chomsky hierarchy.

3. Intuitive creation of finite automata (DFA, NFA, with epsilon transitions) for a given langauage.

4. Transformations and compositions of FA.

5. FA with output function and its implementation.

6. Conversions of grammars to FA and vice versa.

7. Considerations, modifications and transformations of regular expressions.

8. Use of regular expressions for text processing tasks (e.g. sh, grep, sed, perl).

9. Creation and implementation of lexical analyzers.

10. Classification of languages.

11. Examples of context-free languages, creation of pushdown automata.

12. Examples of deterministic parsing of context-free languages (e.g. LL, yacc, bison).

13. Examples of context-sensitive and recursively enumerable languages, creation of grammars, creation of Turing machines.

Study Objective:

The course covers the most basic of effective algorithms, data structures and graph theory, which should be known to every computer scientist. they will learn to use asymptotic mathematics practically.

Study materials:

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.

Note:

Further information:

https://courses.fit.cvut.cz/BIK-AG1/index.html

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor specialization Information Security, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor specialization Software Engineering, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor specialization Computer Networks and Internet, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor specialization Computer Systems and Virtualization, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor program, unspecified specialization, part-time, in Czech, 2021 (compulsory course in the program)