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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
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Algorithms and Graphs 1

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Code Completion Credits Range Language
BI-AG1.21 Z,ZK 5 2P+2C Czech
Garant předmětu:
Dušan Knop
Lecturer:
Dušan Knop, Tomáš Valla
Tutor:
Michal Dvořák, Radek Hušek, Dušan Knop, Daniel Král, Jan Matyáš Křišťan, Xuan Thang Nguyen, Michal Opler, Vojtěch Rozhoň, Martin Slávik, Ondřej Šofr, Tomáš Valla
Supervisor:
Department of Theoretical Computer Science
Synopsis:

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:

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-DML.

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. 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.W

Study Objective:
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/BI-AG1
Time-table for winter semester 2022/2023:
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
Valla T.
09:15–10:45
(lecture parallel1)
Dejvice
NTK Ballingův sál
roomT9:301
Dvořák M.
11:00–12:30
(parallel nr.1)
Dejvice
NBFIT učebna
roomT9:301
Dvořák M.
12:45–14:15
(parallel nr.3)
Dejvice
NBFIT učebna
roomT9:347
Nguyen X.
14:30–16:00
(parallel nr.5)
Dejvice
NBFIT učebna
roomT9:347
Slávik M.
16:15–17:45
(parallel nr.7)
Dejvice
NBFIT učebna
roomT9:347
Slávik M.
18:00–19:30
(parallel nr.9)
Dejvice
NBFIT učebna
roomT9:347
Šofr O.
11:00–12:30
(parallel nr.2)
Dejvice
NBFIT učebna
roomT9:347
Šofr O.
12:45–14:15
(parallel nr.4)
Dejvice
NBFIT učebna
roomTH:A-1442
Opler M.
14:30–16:00
(parallel nr.6)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Opler M.
16:15–17:45
(parallel nr.8)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Křišťan J.
18:00–19:30
(parallel nr.10)
Thákurova 7 (FSv-budova A)
roomTK:BS
Knop D.
16:15–17:45
(lecture parallel2)
Dejvice
NTK Ballingův sál
Tue
roomT9:347
Valla T.
11:00–12:30
(parallel nr.11)
Dejvice
NBFIT učebna
Wed
roomT9:302
Hušek R.
16:15–17:45
(parallel nr.12)
Dejvice
NBFIT učebna
roomT9:302
Hušek R.
18:00–19:30
(parallel nr.13)
Dejvice
NBFIT učebna
Thu
roomT9:346
Rozhoň V.
07:30–09:00
(parallel nr.14)
Dejvice
NBFIT učebna
roomT9:347
Nguyen X.
09:15–10:45
(parallel nr.16)
Dejvice
NBFIT učebna
roomTH:A-1247
Knop D.
07:30–09:00
(parallel nr.15)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Knop D.
09:15–10:45
(parallel nr.17)
Thákurova 7 (FSv-budova A)
seminární místnost
Fri
roomT9:346
Opler M.
07:30–09:00
(parallel nr.18)
Dejvice
NBFIT učebna
roomTH:A-1247
Král D.
09:15–10:45
(parallel nr.19)
Thákurova 7 (FSv-budova A)
seminární místnost
roomT9:346
Opler M.
11:00–12:30
(parallel nr.20)
Dejvice
NBFIT učebna
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-05-30
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6546906.html