1. Lecture 33
CSE 331
Nov 15, 2013

2. HW 8 due today Place Q1, Q2 and Q3 in separate piles
I will not accept HWs after 1:15pm
DO NOT FORGET TO WRITE DOWN YOUR SOURCES

3. Related HW stuff HW 9 has been posted on piazza
Solutions to HW 8 at the END of the lecture
Can pick up graded HW 7 from Monday

4. Closest pairs of points
Input: n 2-D points P = {p1,…,pn}; pi=(xi,yi)
d(pi,pj) = ( (xi-xj)2+(yi-yj)2)1/2
Output: Points p and q that are closest

5. Dividing up P Q R
First n/2 points according to the x-coord

6. Recursively find closest pairsQ R
δ = min (blue, green)

7. An easy case R > δ Q All “crossing” pairs have distance > δ
δ = min (blue, green)

8. Life is not so easy thoughQ R
δ = min (blue, green)

9. Life is not so easy thoughδ Q R
> δ
> δ
> δ
δ = min (blue, green)

10. All we have to do now δ R Q S
Figure if a pair in S has distance < δ S
δ = min (blue, green)

11. Rest of today’s agenda
Prove the Kickass Property Lemma

12. HW 8 due today Place Q1, Q2 and Q3 in separate piles
I will not accept HWs after 1:15pm
DO NOT FORGET TO WRITE DOWN YOUR SOURCES

13. Three general techniques
High level view of CSE 331
Problem Statement
Problem Definition
Three general techniques
Algorithm
“Implementation”
Data Structures
Analysis
Correctness+Runtime Analysis

14. Greedy Algorithms Natural algorithms
Reduced exponential running time to polynomial

15. Divide and Conquer Recursive algorithmic paradigm
Reduced large polynomial time to smaller polynomial time

16. A new algorithmic technique
Dynamic Programming

17. Dynamic programming vs. Divide & Conquer

18. Same same because
Both design recursive algorithms

19. Different because
Dynamic programming is smarter about solving recursive sub-problems

20. Using Memory to be smarter
Pow (a,n)
// n is even and ≥ 2
return t * t
t= Pow(a,n/2)
Pow (a,n)
// n is even and ≥ 2
return Pow(a,n/2) * Pow(a, n/2)
O(n) as we recompute!
O(log n) as we compute only once

21. End of Semester blues
Can only do one thing at any day: what is the optimal schedule to obtain maximum value?
Write up a term paper
(30)
(3)
(2)
(5)
(10)
Party!
Exam study
331 HW
Project
Monday
Tuesday
Wednesday
Thursday
Friday

22. Previous Greedy algorithm
Order by end time and pick jobs greedily
Greedy value = 5+2+3= 10
Write up a term paper
(10)
OPT = 30
Party!
(2)
Exam study
(5)
331 HW
(3)
Project
(30)
Monday
Tuesday
Wednesday
Thursday
Friday

23. Today’s agenda Formal definition of the problem
Start designing a recursive algorithm for the problem