1 / 4

Graph Algorithms 1

Topological sort is a fundamental algorithm used to arrange courses in an order based on their prerequisites. In this directed graph representation, each node represents a course, and each edge (U, V) signifies that U is a prerequisite for V. The objective is to find a linear ordering such that for every directed edge (U, V), U appears before V in the order. This algorithm only works for Directed Acyclic Graphs (DAGs), as cycles prevent a proper ordering. Explore the algorithm through a detailed example to master this essential concept in graph theory.

moira
Télécharger la présentation

Graph Algorithms 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Graph Algorithms 1 http://www.flickr.com/photos/zubrow/6865196143/sizes/o/in/photostream/ Topological sort

  2. Course Prerequisite Example • Each node is a course • Each edge (U, V) denotes that U is a pre-req for V • Find an order in which these courses can be taken

  3. Topological sort • Topological sort: a linear ordering of vertices such that for every arc (u, v), u comes before v in the ordering • Any linear ordering in which all the arrows go “right” is a valid solution. • Any linear ordering in which an arrow goes “left” is invalid. • Any directed graph with a cycle cannot be topologically sorted

  4. Algorithm module topologicalSort(G) { L ← An empty list S ← A list of all nodes in G with in-degree 0 while S is notempty do • M← S.removeFirst() L.append(M) foreach node N with an edge Efrom M to N do remove edge E from G if N has in-degree 0 then S.append(N) endif endforeach endwhile if the size of G is greater than 0 then return error (G is not acyclic) else return L

More Related