1. Lecture 16
CSE 331
Oct 4, 2017

2. Mini Project Pitch due TODAY
Some of the chosen algorithm are now up!
Form your group on Autolab BEFORE submitting
your pitch
Do not forget to add URL to your references

3. Quiz 1 on Monday

4. Directed Acyclic Graph (DAG)
No directed cycles
Precedence relationships are consistent

5. Topological Sorting of a DAG
Order the vertices so that all edges go “forward”
Topological sorting  DAG

6. TopOrd(G=(V,E)) If |V| = {u}, return u
Let w be a node with no incoming edges
Let G’ be G\{w}
Return w; TopOrd(G’)

7. Run of TopOrd algorithm

8. Todays’ agenda Prove Lemma 3 Run time analysis of TopOrd
Greedy algorithms

9. Mid-term material
Everything we have covered so far (essentially Chaps 1-3 except Sec 1.2)
See piazza post on how to prepare for the mid-terms

10. Questions?

11. Main Steps in Algorithm Design
Problem Statement
Problem Definition n!
Algorithm
“Implementation”
Data Structures
Analysis
Correctness+Runtime Analysis

12. A tool to define problems
Where do graphs fit in?
Problem Statement
A tool to define problems
Problem Definition
Algorithm
“Implementation”
Data Structures
Analysis
Correctness+Runtime Analysis

13. Three general techniques
Rest of the course
Problem Statement
Problem Definition
Three general techniques
Algorithm
“Implementation”
Data Structures
Analysis
Correctness+Runtime Analysis

14. Greedy algorithms Build the final solution piece by piece
Being short sighted on each piece
Never undo a decision
Know when you see it

15. End of Semester blues
Can only do one thing at any day: what is the maximum number of tasks that you can do?
Write up a term paper
Party!
331 homework
Exam study
331 HW
Project
Monday
Tuesday
Wednesday
Thursday
Friday

16. Greedily solve your blues!
Arrange tasks in some order and iteratively pick non-overlapping tasks
Write up a term paper
Party!
Exam study
331 HW
Project
Monday
Tuesday
Wednesday
Thursday
Friday

17. Ordering is crucial Order by starting time Write up a term paper
Algo =1
Party!
Exam study
331 HW
Project
Monday
Tuesday
Wednesday
Thursday
Friday

18. Ordering by least conflicts doesn’t work
Another attempt
Order by duration
Ordering by least conflicts doesn’t work
Algo =1
Monday
Tuesday
Wednesday
Thursday
Friday

19. Order tasks by their END time
The final algorithm
Order tasks by their END time
Write up a term paper
Party!
Exam study
331 HW
Project
Monday
Tuesday
Wednesday
Thursday
Friday

20. Questions?

21. Rest of today’s agenda
Prove the correctness of the algorithm