1. Lecture 34
CSE 331
Nov 26, 2012

2. Online OH

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

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

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

6. A new algorithmic technique
Dynamic Programming

7. Dynamic programming vs. Divide & Conquer

8. Same same because
Both design recursive algorithms

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

10. 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

11. 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

12. 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

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