Algorithms and Graphs 1
Code  Completion  Credits  Range  Language 

BIKAG1.21  Z,ZK  5  14KP+4KC  Czech 
 Course guarantor:
 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 BIEAAG and BIEZDM.
 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 edgelabelled graphs. Jarník’s algorithm and Kruskal’s algorithm and their implementations.
12. [2] Shortest paths algorithms on edgelabelled 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 contextfree languages, creation of pushdown automata.
12. Examples of deterministic parsing of contextfree languages (e.g. LL, yacc, bison).
13. Examples of contextsensitive 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 9780262033848.
2. Wengrow J. : A CommonSense Guide to Data Structures and Algorithms: Level Up Your Core Programming Skills (2nd Edition). Pragmatic Bookshelf, 2020. ISBN 9781680507225.
3. Sedgewick R. : Algorithms (4th Edition). AddisonWesley, 2011. ISBN 9780321573513.
4. Deo N. : Graph Theory with Applications to Engineering and Computer Science. Dover Publications, 2016. ISBN 978048680793.
5. Bickle A. : Fundamentals of Graph Theory. AMS, 2020. ISBN 9781470453428.
 Note:
 Further information:
 https://courses.fit.cvut.cz/BIKAG1/index.html
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Bachelor Specialization Information Security, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor Specialization Software Engineering, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor Specialization Computer Networks and Internet, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor Specialization Computer Systems and Virtualization, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor program, unspecified specialization, parttime, in Czech, 2021 (compulsory course in the program)