ALGORITMI E LABORATORIO

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.

• Algorithms Lab

  Conoscenza e capacità di comprensione (knowledge and understanding): we will focus on the implementation of the main data stuttures analyzed during the theoretical module of Algorithms
  Capacità di applicare conoscenza e comprensione (applying knowledge and understanding): we will focus on the implementation skills and on the algorithmic solutions design.
  Autonomia di giudizio (making judgements): The student will be able to judge the effectiveness of its implementation and of their project work.
  Capacità di apprendimento (learning skills): the student will be able to adapt to other contexts all solutions and algorithms.

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)
  Open addressing

  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
  Breadth-first search
  Depth-first search (edges classification)
  Topological sorting
  Strongly connected components

• Algorithms Lab

  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