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Algorithms and Data Structures 2 - NTIN061

Title:	Algoritmy a datové struktury 2
Guaranteed by:	Department of Applied Mathematics (32-KAM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Martin Mareš, Ph.D. prof. RNDr. Ondřej Čepek, Ph.D. doc. Mgr. Jan Hubička, Ph.D.
Class:	Informatika Bc.
Classification:	Informatics > Theoretical Computer Science
Incompatibility :	NTIX061
Interchangeability :	NTIX061
Is incompatible with:	NTIX061
Is interchangeable with:	NTIX061
In complex interchangeability with:	NUIN021

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Pavel Töpfer, CSc. (01.02.2018)

Lecture about various types of algorithms and their time complexity (follows NTIN060 Algorithms and data structures 1).

Course completion requirements - Czech

Last update: Mgr. Martin Mareš, Ph.D. (26.09.2023)

Je třeba získat zápočet a složit zkoušku (v libovolném pořadí).

Pro zápočet je třeba získat 100 bodů z alespoň 150 možných udělovaných průběžně za řešení domácích úloh, písemné testy a další aktivity. Z průběžné povahy kontroly neplyne nárok na vypisování opravných termínů testů ani zadání náhradních domácích úloh.

V důvodných případech (dlouhodobá nemoc, pobyt v zahraničí, apod.) může cvičící stanovit individuální podmínky na udělení zápočtu.

Zkouška může být písemná, ústní nebo kombinovaná. Zkouška může mít kontaktní nebo distanční formu. Formu zkoušky určuje vyučující.

Literature -

Last update: prof. Mgr. Milan Hladík, Ph.D. (22.11.2012)

Aho, Hopcroft, Ullman : The design and analysis of computer algorithms, Addison-Wesley 1976

T.Cormen, Ch.Leiserson, R. Rivest, C. Stein : Introduction to Algorithms (2nd Edition), McGraw-Hill 2001

http://kam.mff.cuni.cz/~ludek

Requirements to the exam - Czech

Last update: Mgr. Martin Mareš, Ph.D. (11.10.2017)

Je třeba rozumět teorii z přednášky a být schopen ji aplikovat na řešení algoritmických úloh.

Syllabus -

Last update: doc. RNDr. Pavel Töpfer, CSc. (01.02.2018)

Optional topics in square brackets, the rest is mandatory.

1. Searching in text

Knuth-Morris-Pratt algorithm

Aho-Corasick algorithm

[Rabin-Karp algorithm]

2. Flows in networks

augmenting path algorithm

Dinic's algorithm

Goldberg's algorithm

matching in bipartite graph

[search for maximum flow of minimum price]

3. Algebraic algorithms

discrete Fourier transformation, its motivation and application

the FFT algorithm and its implementation by the "butterfly"

[related transformations (cosine transformation - JPEG compression)]

4. Parallel arithmetic algorithms

sorting networks (implementation of one sorting algorithm - either merge-sort or bitonic-sort)

carry look-ahead algorithm for addition

5. Basic geometric algorithms in a plane

convex hull

the principle of plane sweeping driven by events

[Voronoi diagram and Delaunay triangulation (Fortune's algorithm)]

6. Transferability of problems and classes of time complexity

polynomial transformation and reduction between decision problems

non-deterministic algorithms, Class P and NP

NP-completeness

7. Approximation algorithms

use of approximation algorithms, ratio and relative error

one or two simple examples of approximation algorithms (knapsack, bin-packing, scheduling on parallel machines) including an upper estimate for their ratio (or relative) error

approximation scheme: principle and example

8. Probabilistic algorithms and cryptography

Monte Carlo algorithms (Rabin-Miller's Primality Test)

public key cryptography (RSA algorithm)