1. CSE 20 DISCRETE MATH Prof. Shachar Lovett http://cseweb.ucsd.edu/classes/wi15/cse20-a/ Clicker frequency: CA

2. Todays topics Order relations Section 6.3 in Jenkyns, Stephenson

3. Order relations

4. Partial order

6. Definition: reflexive, transitive, anti-symmetric Equality relation: xRy if x=y Is it a partial order? A. Yes B. No

7. Partial order

9. Total order

12. Lexicographic order

13. Orders on sequences Which one of the following is the largest one? A. (1,2,5,10) B. (10,5,2,1) C. (5,100,3,3) D. (10,7,100,1000)

14. Maximal / maximum elements

17. There could be multiple maximal elements in a set, but the maximal element (if it exists) must be unique Lets prove it

18. Maximal / maximum elements

19. Minimal / minimum elements

20. Maximum/maximal/minimum/minimal

23. Back to total orders

24. Sorting Sorting is a basic primitive used by many algorithms Most sorting algorithms are “abstract”, in the sense that they can apply to any partial order Naïve sorting on n elements requires comparing all pairs of elements, which takes ~n 2 comparisons Fast sorting algorithms (for example, quicksort) can do it using only n log n comparisons This can be proven to be tight!

25. Next class Knights and knaves