1. Lecture 14
CSE 331
Sep 30, 2011

2. HW 3 due today I will not take any HW after 1:15pm
Q1, Q2 and Q3 in different piles
I will not take any HW after 1:15pm

3. Other HW related annoucements
Solutions to HW 3 handed out at the
END of the lecture
Pick up graded HW 2 from recitation/TA office hours
next week
HW 4 (and rubric) has been posted (link on the blog)

4. Mid-term related stuff
Sample mid term posted (link on the blog)
Blog entry on mid-term exam prep.

5. On Friday, Oct 7 hours-a-thon Atri: 2:00-3:00 (Bell 123)
Jiun-Jie: 4:00-5:00 (Commons 9)
Jesse: 5:00-6:00 (Bell 224)

6. Empty Slots Coming up…

7. Computing Connected Component
Explore(s)
Start with R = {s}
While exists (u,v) edge v not in R and u in R
Add v to R
Output R

8. Explore(s) = Connected Comp.(s)
Lemma 1: If w is in R then s is connected to w
Lemma 2: If s is connected to w then w is in R

9. Also argued that
m ≤ n(n-1)/2

10. HW 3 due today I will not take any HW after 1:15pm
Q1, Q2 and Q3 in different piles
I will not take any HW after 1:15pm

11. Questions?

12. BFS
all

13. Depth First Search (DFS)

14. DFS(u) Mark u as explored and add u to R For each edge (u,v)
If v is not explored then DFS(v)

15. Why is DFS a special case of Explore?

16. Every non-tree edge is between a node and its ancestor
A DFS run
Every non-tree edge is between a node and its ancestor
DFS(u)
u is explored
For every unexplored
neighbor v of u
DFS(v) 1 1 7 2 2 3 8 4 4 5 5
DFS tree 6 6 3 8 7

17. Questions?

18. Connected components are disjoint
Either Connected components of s and t are the same or are disjoint
Algorithm to compute ALL the connected components?
Run BFS on some node s. Then run BFS on t that is not connected to s

19. Reading Assignment
Sec 3.2 in [KT]

20. Rest of today’s agenda
Run-time analysis of BFS (DFS)

21. Stacks and Queues
Last in First out
First in First out

22. But first…
How do we represent graphs?

23. Graph representations1
Better for sparse graphs and traversals
Adjacency matrix
Adjacency List
(u,v) in E?
O(1)
O(n) [ O(nv) ]
All neighbors of u?
O(n)
O(nu)
O(n2)
Space?
O(m+n)