# Coursebooks

## Algorithms

#### Lecturer(s) :

Svensson Ola Nils Anders

English

#### Summary

The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, sorting and searching, and graph algorithms.

#### Content

Mathematical Induction

• Mathematical background, Euler's formula for trees, Schwartz-Zippel lemma.

Analysis of Algorithms

• O-notation, time and space complexity, recurrence relations, probabilistic analysis.

Data structures

• Arrays, linked lists, trees, heaps, hashing, graphs.

Design of algorithms by induction

• Evaluating polynomials, divide-and-conquer algorithms, dynamic programming.

Greedy Algorithms

• Spanning tree and shortest path algortihms

Sorting and searching

• Merge sort, bucket sort, quicksort, heapsort, binary search.

Graphs algorithms and data structures

• Graphs traversals, shortest paths, spanning trees, transitive closure, decompostitions, matching, network flows.

Complexity

• Polynomial reductions, NP-completeness.

#### Keywords

algorithms, data structures, efficiency, problem solving

#### Learning Outcomes

By the end of the course, the student must be able to:
• Illustrate the execution of algorithms on example inputs
• Describe basic data structures such as arrays, lists, stacks, queues, binary search trees, heaps, and hash tables
• Analyze algorithm efficiency
• Compare alternative algorithms and data structures with respect to efficiency
• Choose which algorithm or data structure to use in different scenarios
• Use algorithms and data structures taught in the course on concrete problem instances
• Design new algorithms and data structures based on known methods
• Prove the correctness of an algorithm

#### Teaching methods

Ex cathedra lecture, exercises in classroom

#### Assessment methods

• Programming exercises (15%)
• Theoretical homework (15%)
• Final exam (70%)

#### Resources

##### Bibliography

Thomas Cormen, Charles Leiserson, Ronald Rivest, Clifford Stein: Introduction to algorithms, Third Edition, MIT Press, 2009.

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14    CO1
14-15SG1
15-16
16-17GCA331
GCB330
GCB331
GRA330
GRB330

17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

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• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German