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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BIE-AG1 Algorithms and Graphs 1 Extent of teaching: 2P+2C

Instructor: Completion: Z,ZK

Department: 18101 Credits: 6 Semester: Z

Annotation:
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.

Lecture syllabus:

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.

Seminar syllabus:

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.

Literature:

[1] Cormen, T. H. - Leiserson, C. E. - Rivest, R. L. - Stein, C.: Introduction to Algorithms, 3rd Edition, MIT Press, 2009, 978-0262033848,

[2] Gibbons, A.: Algorithmic Graph Theory, Cambridge University Press, 1985, 978-0521288811,

[3] Gross, J. L. - Yellen, J. - Zhang, P.: Handbook of Graph Theory, 2nd Edition (Discrete Mathematics and Its Applications), Chapman and Hall/CRC, 2013, 978-1439880180,

Requirements:
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.

Information about the course and courseware are available at https://courses.fit.cvut.cz/BIE-AG1/

The course is also part of the following Study plans:

Study Plan Study Branch/Specialization Role Recommended semester

BIE-BIT.2015 Computer Security and Information technology (Bachelor, in English) PP 3

BIE-TI.2015 Computer Science (Bachelor, in English) PP 3

BIE-WSI-SI.2015 Software Engineering (Bachelor, in English) PP 3

Page updated 24. 4. 2024, semester: Z/2020-1, Z/2019-20, Z/2023-4, Z/2021-2, L/2022-3, Z/2024-5, L/2019-20, Z/2022-3, L/2020-1, L/2021-2, L/2023-4, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška

BIE-AG1	Algorithms and Graphs 1			Extent of teaching:	2P+2C
Instructor:				Completion:	Z,ZK
Department:	18101	Credits:	6	Semester:	Z

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.

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.

[1]		Cormen, T. H. - Leiserson, C. E. - Rivest, R. L. - Stein, C.: Introduction to Algorithms, 3rd Edition, MIT Press, 2009, 978-0262033848,
[2]		Gibbons, A.: Algorithmic Graph Theory, Cambridge University Press, 1985, 978-0521288811,
[3]		Gross, J. L. - Yellen, J. - Zhang, P.: Handbook of Graph Theory, 2nd Edition (Discrete Mathematics and Its Applications), Chapman and Hall/CRC, 2013, 978-1439880180,