Efficient Algorithms

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Department of Theoretical Computer Science

Synopsis:

Students get an overview of efficient algorithms and data structures for solving classical algorithmic problems, such as searching and sorting, on dynamically changing data sets. Students are able to design and implement such algorithms, to use methods for analysing their computational and memory complexity. They understand the sorting algorithms with O(n.log n) time complexity, special sorting algorithms with linear complexity, algorithms for associative and address searching. They are able to use the efficient dynamic data structures, such as hash tables, search trees, balanced search trees, heaps, B-trees, and others. They are able to work with recursive algorithms and dynamic programming.

Requirements:

An ability to solve basic algorithmic problems actively, to express the algorithmic solution in a high-level programming language (Java, C++), and knowledge of basic notions from calculus and combinatorics is assumed.

Syllabus of lectures:

1. Data structures I: Fundamental ADTs.^2. Data structures II: Hash tables.^3. Sorting algorithms I.^4. Data structures III: Trees, heaps.^5. Sorting algorithms II.^6. Data structures IV: Advanced heaps.^7. Searching and search trees.^8. Recursive algorithms.^9. B-trees and their variants.^10. Balanced search trees. ^11. Dynamic programming.^12. Computational geometry algorithms.2. Data structures II: Hash tables.1. Data structures I: Fundamental ADTs

2. Data structures II: Hash tables

3. Sorting algorithms I

4. Data structures III: Trees, heaps

5. Sorting algorithms II

6. Data structures IV: Advanced heaps

7. Searching and search trees

8. Recursive algorithms

9. B-trees and their variants

10. Balanced search trees.

11. Dynamic programming.

12. Computational geometry algorithms.

Syllabus of tutorials:

1. Algorithms on arrays, multidimensional arrays and mapping functions. mathematics. ^2. ADT stack, queue, list. ^3. ADT table, set. ^4. Hash tables. ^5. Basic sorting algorithms. ^6. Trees and binary heaps. ^7. Sorting algorithms II. ^8. Binomial and Fibonnaci heaps.^9. Searching and binary search trees.^10. Recursive algorithms.^11. B-trees.^12. Balanced search trees.^13. Dynamic programming.^4. Data structures III: Trees, heaps.1. Algorithms on arrays, multidimensional arrays and mapping functions. mathematics.

2. ADT stack, queue, list.

3. ADT table, set.

4. Hash tables.

5. Basic sorting algorithms.

6. Trees and binary heaps.

7. Sorting algorithms II.

8. Binomial and Fibonnaci heaps.

9. Searching and binary search trees.

10. Recursive algorithms.

11. B-trees.

12. Balanced search trees.

13. Dynamic programming.

Study Objective:

The goal of the course is to equip the student with a set of well-known standard algorithms and to help him/her recognize a proper algorithm variant for any specific usage. At the same time, the student will learn basic methods of algorithm analysis to be used as a main efficiency criterion.

Study materials:

Cormen, T. H., Leiserson, C. E., Rivest, R. L. Introduction to Algorithms. The MIT Press, 2001. ISBN 0262032937.

Note:

Further information:

https://courses.fit.cvut.cz/BI-EFA/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (elective course)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (elective course)
• Bachelor branch Computer Science, in English, 2015-2020 (elective course)
• Bachelor branch Computer Science, in English, 2015-2020 original version (elective course)