Learning outcomes

The student will be able to :

- formalize a problem described informally ;

- systematically build a correct and efficient program solving this problem.

 
 

Goals

Learn rigourous methods for efficient algorithm construction.

 
 

Content

We base our methods on formal proofs, of runtime and memory consumption. We use recursivity systematically. The methods selected are: 1- divide-and-conquer 2- memoization and dynamic programming 3- the greedy method 4- generate-and-test.

We study the main data structures : lists, hash tables, trees, binary search trees, red/black trees, B-trees.

 
 

Table of contents

Part O. Specification by pre- and post-conditions, of proofs by invariants and variants. Runtime evaluation (complexity). Recursivity.

Part I. Programming methods: 1- divide-and-conquer 2- memoization and dynamic programming 3- the greedy method 4- generate-and-test 5- constraint-based programming 6- heuristic methods

Part II. Data structures. Data types. Lists. Hash tables. Binary search trees. Red-black trees. B-trees.

 
 
 

Assessment method

70% A written examination, where new problems are posed and new, efficient solutions should be discovered by the students on basis of the methods learned in the course.

The rest will be evaluated through a project and small assignments.

 
 

Sources, references and any support material

The course follows a selection of chapters from: Introduction to Algorithms ( Second Edition), T. Cormen, C. Leiserson, R. Rivest, C. Stein, MIT Press.

 
 

Language of instruction

Anglais