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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025
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Welcome page > Faculty of Information Technology > Department of Theoretical Computer Science > Algorithms and Graphs 1

Algorithms and Graphs 1

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Code Completion Credits Range Language
BI-AG1.21 Z,ZK 5 2P+2C Czech
Relations:
It is not possible to register for the course BI-AG1.21 if the student is concurrently registered for or has already completed the course BIE-AX1.24 (mutually exclusive courses).
Course guarantor:
Dušan Knop
Lecturer:
Dušan Knop, Michal Opler
Tutor:
Suzan Catay, Patrik Drbal, Michal Dvořák, Radek Hušek, Dušan Knop, Daniel Král, Michal Opler, Matěj Ptáček, Josef Erik Sedláček, Martin Slávik, Ondřej Suchý, Ondřej Šofr, Petr Šťastný, Tomáš Valla
Supervisor:
Department of Theoretical Computer Science
Synopsis:

The course covers the basics of efficient algorithm design, data structures, and graph theory, belonging to the core knowledge of every computing curriculum.

It links and partially develops the knowledge from the course BI-DML.21, in which students acquire the knowledge and skills in combinatorics necessary for evaluating the time and space complexity of algorithms. The course also follows up knowledge from BI-MA1.21, the practical usage of asymptotic mathematics, in particular, the asymptotic notation.

Requirements:

Active algorithmic skills for solving basic types of computational tasks, programming skills in C++ (e.g., the level needed for passing BIE-PA1.21 and BIE-PA2.21) , and knowledge of basic notions from mathematical analysis and combinatorics are expected (e.g., by passing BIE-DML.21 a BIE-MA1.21). Students are expected to take the concurrent course BIE-AAG.21 and BIE-MA2.21.

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 partially ordered structure, HeapSort.

5. Extendable array, amortized complexity. Binomial Heaps.

6. Operations and properties of binary search trees, balancing strategies, and 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. Shortest paths algorithms on edge-labeled graphs.

Syllabus of tutorials:

1. Motivation and Elements of Graph Theory I.

2. Elements of Graph Theory II.

3. Elements of Graph Theory III.

4. Sorting Algorithms O(n^2). Binary Heaps.

5. Extendable Array, Amortized Complexity, Binomial Heaps.

6. Search Trees and Balance Strategies.

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.

13. Minimum Spanning Trees, Shortest Paths.

Study Objective:

Students learn basic techniques for proving the correctness of algorithms and techniques of asymptotic mathematics for estimation of their complexity in the best, worst, or average case.

Study materials:

1. Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms (4th Edition). MIT Press, 2022. ISBN 978-0262033848.

2. J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, 2008, 2th edition, Oxford University Press. (Available online in English.)

3. R. Diestel: Graph Theory, 2010, 4th edition, Springer-Verlag, Berlin. (Available online, new edition released in 2017.)

Note:
Further information:
https://courses.fit.cvut.cz/BI-AG1
Time-table for winter semester 2024/2025:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
roomTK:BS
Opler M.
09:15–10:45
(lecture parallel1)
Dejvice roomTH:A-1247
Dvořák M.
11:00–12:30
(parallel nr.1)
Thákurova 7 (budova FSv) roomT9:302
Slávik M.
12:45–14:15
(parallel nr.2)
Dejvice roomT9:302
Slávik M.
14:30–16:00
(parallel nr.3)
Dejvice roomTH:A-1242
Ptáček M.
16:15–17:45
(parallel nr.4)
Thákurova 7 (budova FSv) roomTH:A-1242
Ptáček M.
18:00–19:30
(parallel nr.5)
Thákurova 7 (budova FSv)
roomTK:BS
Knop D.
16:15–17:45
(lecture parallel2)
Dejvice roomTH:A-1247
Dvořák M.
18:00–19:30
(parallel nr.6)
Thákurova 7 (budova FSv)
Tue
roomT9:301
Catay S.
07:30–09:00
(parallel nr.7)
Dejvice roomTH:A-1247
Knop D.
09:15–10:45
(parallel nr.9)
Thákurova 7 (budova FSv) roomT9:302
Valla T.
11:00–12:30
(parallel nr.10)
Dejvice roomTH:A-942
Král D.
12:45–14:15
(parallel nr.11)
Thákurova 7 (budova FSv)
roomTH:A-1247
Knop D.
07:30–09:00
(parallel nr.8)
Thákurova 7 (budova FSv)
Wed
roomT9:347
Hušek R.
16:15–17:45
(parallel nr.12)
Dejvice roomT9:347
Hušek R.
18:00–19:30
(parallel nr.13)
Dejvice
Thu
roomT9:301
Sedláček J.
07:30–09:00
(parallel nr.14)
Dejvice roomT9:301
Sedláček J.
09:15–10:45
(parallel nr.16)
Dejvice roomT9:347
Šofr O.
16:15–17:45
(parallel nr.18)
Dejvice roomT9:347
Šofr O.
18:00–19:30
(parallel nr.20)
Dejvice
roomT9:347
Drbal P.
07:30–09:00
(parallel nr.15)
Dejvice roomT9:347
Drbal P.
09:15–10:45
(parallel nr.17)
Dejvice roomTH:A-1247
Šťastný P.
16:15–17:45
(parallel nr.19)
Thákurova 7 (budova FSv)
Fri
roomTH:A-1442
Suchý O.
12:45–14:15
(parallel nr.22)
Thákurova 7 (budova FSv)
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-12-12
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