The course objective is to provide the foundamental tools to design algorithmic solutions for concrete programs. The algorithms are evaluated and compared based required amount of resources. At the end of the course the student will have to demonstrate knowledge and understanding of the main algorithms for the problems of sorting, selection, priority queues, visit of graphs, shortest paths, minimum spanning trees, maximum flow; have ability to apply acquired knowledge and understanding skills to compare algorithms on the basis of their complexity; know how to choose the right algorithm for a specific situation; know how to develop the skills necessary to expand the knowledge learned in order to understand algorithmic solutions to new problems.
Complexity: complexity of algorithms, asymptotic notation, resolution of recurrence equations.
Sorting and selection: insertion sort, merge sort, heap sort, quick sort, randomized quick sort. Linear algorithms, counting sort, radix sort, bucket sort. Selection algorithms.
Data structures: heap, binary search trees, RB-trees, B-trees, binomial heaps, hash tables, priority queues, disjoint sets, extension of data structures, graphs.
Design and analisis of alsorithms: divide et impera, greedy, dynamic programming, local serch, backtracking, branch and bound.
Foundamental algorithms: minimum spanning tree (Prim and Kruskal), linear programing (simplex and basic elements of the elipsoid method) shortest path with single source (Dijkstra and Bellman-Ford) and multiple source (Floyd-Warshall and Johnson), maximum flow (Ford-Fulkerson, Karp), maximnal matching on bipartite graph.
|T. Cormen, C. Leiserson, R. Rivest, C. Stein||Introduzione agli Algoritmi e Strutture Dati (Edizione 2)||McGraw-Hill||2005||88-386-6251-7|
The exam consists of a writtene test of three hours, divided into two parts, and possibly of an oral colloquium.
The forst part of the written test consists of several questions with multiple choices. It produces a valuation from 0 to 30. The exam is not passed if the evaluation is below 18. The exam ends if the evaluation is between 18 and 23. The second part of the written test, available only if the evaluation of the first part is at least 24, consists of one or more exercises of increasing complexity. The evaluation is between 24 and 30.
The optional oral examination is available only if the evaluation of the second part of the written test is at least 27.
The evaluation scale is the following. 18-28 (pure notionistic knowledge), 22-24 (acceptable understanding of the arguments), 25-27 (ability to apply the concepts learned in the course), 28-30 (ability to elaborate autonomous ideas based on the concepts learned in the course).