COP 3530 Spring2012 Data Structures & Algorithms

1. COP 3530 Spring2012Data Structures & Algorithms Discussion Session

3. Sort • What is sort? • Why sort? • Examples • Dictionary • Search (Google)

4. Sorting Algorithms • Quicksort • Merge sort • Heapsort • Insertion sort • Selection sort • Shell sort • Bubble sort • Strand sort • Smoothsort • Tournament sort • Cocktail sort • Comb sort • Gnome sort • Bogosort • Slowsort • Cycle sort Topological sort

5. Directional Acyclic Graph (DAG) • A set of vertices / directed edges • Directional • Acyclic

6. Directional Acyclic Graph (DAG) • Why directional? • Relation between objects are asymmetric • E.g., parent to child, predecessor to successor

7. Directional Acyclic Graph (DAG) • Why acyclic? • A collection of tasks • Ordered, s.t., certain tasks must be performed earlier than others T1 T2 T4 T3 T1 T7 T6 T3 T2 T5 T8

8. Directional Acyclic Graph (DAG) • Applications? • Program language processing (fundamental in CS) • Real-world traffic scheduling • Computer network traffic scheduling • So on

9. Topological Order • Topological ordering of a directed acyclic graph is a linear ordering of its vertices such that, for every edge uv, u comes before v in the ordering u v

10. Topological Order • Left to right first, then top to bottom • 7, 5, 3, 11, 8, 2, 9, 10 • smallest-numbered available vertex first • 3, 5, 7, 8, 11, 2, 9, 10 • fewest edges first • 5, 7, 3, 8, 11, 10, 9, 2 • largest-numbered available vertex first • 7, 5, 11, 3, 10, 8, 9, 2

11. Topological Sort

12. Example

13. Time Complexity • O(|N|+|E|)