Learning outcomes

The student will be able to :
  • formalize a problem described informally (specify) ;
  • 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 and its improvements : branch-and-bound, propagation
 
 

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

Assessment method

10% Small homeworks along the semester
20% A project with 3 problems to solve, to finish by the end of the teaching semester
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. 
 
 

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

Français
Training Study programme Block Credits Mandatory
Bachelor in Computer Science Standard 0 5
Bachelor in Computer Science Standard 2 5