84745 - INTRODUZIONE AGLI ALGORITMI

Learning outcomes

Knowing the main data structures (like sequences, trees, dictionaries, priority queues, graphs) and the main algorithms for solving some basic computational problems (like searching, sorting, tree and graph visits, minimum spanning trees, shortest paths, matrix multiplication) . Understanding and using the main methodologies (e.g. divide-&-conquer, dynamic programming, greedy, backtracking, local search) for designing efficient iterative and recursive algorithms. Understanding and using the main techniques for analyzing iterative and recursive algorithms. Knowing the basic computational classes (P, NP, NP-hardness) and evaluating the inherent difficulty of basic computational problems.

Course contents

Data structures. Arrays, records, lists, stacks, queues. Trees. Tree visits (preorder, inorder, postorder). Sets. Dictionaries. Binary search. Hash tables. Priority queues. Heaps. Heapsort. Balanced search trees. MFSET. Graphs. DFS and BFS. Design and analysis of algorithms. Computational complexity. Order of growth. Recurrence equations. Lower bounds. Design techniques: divide-&-conquer, backtrack, greedy, local search, dynamic programming. Sorting: Mergesort, Quicksort, Shellsort. Complexity. The P and NP classes. NP-completeness. Pseudo-polynomial, approximate, branch-&-bound, and probabilistic algorithms. Heuristics.

Readings/Bibliography

A.A. Bertossi & A. Montresor, Algoritmi e Strutture di Dati, Citta' Studi Edizioni, Torino, 2014.

Teaching methods

The course is taught during the second semester, and it comprises lessons and lectures. First, theoretical foundations are presented. After base notions are introduced, the main data structures and computational problems are presented. Algorithms for solving such problems are designed, pointing out the design techniques employed. For each proposed algorithm, theorems are stated, and sometimes proved, showing their correctness and temporal computational complexity. Next, several exercises are solved.

Assessment methods

The assessment consists in a final written examination, lasting 3 hours, during which no books, notes, calculatora and electronic devices are allowed. The written exam consists of 6 questions, some of which are exercises whose purpose is to check the practical ability to design correct and efficient algorithms to solve computational problems, while other are open-answer questions whose objective is to verify that the expected theoretical knowledge has been acquired.

Teaching tools

Projector.

Office hours

See the website of Alan Albert Bertossi