1. Topological Sort Neil Tang 03/02/2010
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Class Overview
Basic concepts
An application
Algorithm 1
Algorithm 2
CS223 Advanced Data Structures and Algorithms

3. CS223 Advanced Data Structures and Algorithms
Basic Concepts
A topological sort is an ordering of vertices in a DAG, such that if there is a path from vi to vj, then vj appears after vi in the ordering.
The topological sort may not be unique for a DAG.
Indegree/outdegree: the number of incoming/outgoing edges
CS223 Advanced Data Structures and Algorithms

4. CS223 Advanced Data Structures and Algorithms
An Example
Ordering 1: 1,2,5,4,3,7,6
Ordering 2: 1,2,5,4,7,3,6
CS223 Advanced Data Structures and Algorithms

5. CS223 Advanced Data Structures and Algorithms
An Application
CS223 Advanced Data Structures and Algorithms

6. Topological Sort: Algorithm 1
Time complexity: O(|V|2)
CS223 Advanced Data Structures and Algorithms

7. Topological Sort: Algorithm 2
Time complexity: O(|V|+|E|)
CS223 Advanced Data Structures and Algorithms

8. Topological Sort: Algorithm 2
CS223 Advanced Data Structures and Algorithms