# ALGORITMI E LABORATORIO A - L

Academic Year 2019/2020 - 2° Year - Curriculum A and Curriculum B
Teaching Staff Credit Value: 9
Scientific field: INF/01 - Informatics
Taught classes: 36 hours
Exercise: 24 hours
Laboratories: 12 hours
Term / Semester:

## Learning Objectives

• Algorithms

Knowledge and understanding: students will acquire knowldege relative to the main methodologies for the design of efficient algorithms (incremental, recursion, dynamic programming, greedy algorithms), as well as the techniques for their computational analysis, both in the worst and in the average cases.
Applying knowledge and understanding: students will acquire the ability to solve problems of low difficulty, requiring the design and analysis of elementary algorithmic solutions.
Making judgements: students will be able to evaluate the quality of an algorithmic solution in terms of efficiency and reuse.
Communication skills: students will acquire the necessary communication skills and expressive ability in communicate problems regarding the algorithmic studies, also to non-expert interlocutors.
Learning skills: students will have the ability to adapt the knowledge acquired also in new contexts and to advance his/her knowledge through the consultation of specialist sources in the algorithmic field.

• LABORATORIO

Knowledge and understanding: we will focus on the implementation of the main data stuttures analyzed during the theoretical module of Algorithms
Applying knowledge and understanding: we will focus on the implementation skills and on the algorithmic solutions design.
Making judgements: the student will be able to judge the effectiveness of its implementation and of their project work.
Learning skills: the student will be able to adapt to other contexts all solutions and algorithms.

## Course Structure

• Algorithms

Classroom-taught lessons

• LABORATORIO

Practical laboratory

## Detailed Course Content

• Algorithms

General description

The course presents the main design methodoligies (incremental, recursion, dynamic programming, greedy algorithms) and the techniques for their complexity analysis, both in the worst and average cases.

DETAILED SYLLABUS

Introduction
Computational problems and algorithms: the sorting problem
Algorithms as technology
Incremental methodology: Insertion-Sort (correctness and complexity)
Divide-and-Conquer methodology: Merge-Sort (complexity)
Asymptotic notations and relationships among them
Standard notations and common functions.

Recurrences
The substitution method
The iterative method and the recursion tree
The master theorem

Sorting and order statistics
Heaps and their construction
Priority queues
Quicksort and its randomized version
Analysis of Quicksort in the worst- and average case
Lower bounds for sorting
Sorting in linear time: Counting-Sort, Radix-Sort, Bucket-Sort
Medians and order statistics

Hashing
Hash table
Hash functions (division method, multiplication method, universal hashing)

Red-black trees
Rotations, insertions, deletions
Complexity analysis

Elements of dynamic programming
Optimal substructure, overlapping subproblems, reconstructing an optimal solution
Some case studies: assembly line scheduling, matrix-chain multiplication, longest common subsequence, editing distance

Elements of the greedy strategy
Greedy-choice property, optimal substructure
Some case studies: the activity-selection problem, Huffman codes

Elementary graph algorithms
Single-source shortest paths: the Bellman-Ford algorithm, single-source shortest paths in oriented acyclic graphs, Dijkstra's algorithm
All-pairs shortest paths: the Floyd-Warshall algorithm, transitive closure of oriented graphs

• LABORATORIO
• The aim of Algorithms Laboratory is to provide the tools for the implementation of the algorithms and the data structures discussed in the Algorithms class. It will be done through the use of an object-oriented programming language. The C ++ language will be used as the main tool to present the implementations of data structures and algorithms.

## Textbook Information

• Algorithms

T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein. Introduction to algorithms (Third Edition), The MIT Press, Cambridge - Massachusetts, 2009

• LABORATORIO

T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein. Introduction to algorithms (Third Edition), The MIT Press, Cambridge - Massachusetts, 2009