1. Lecture 15
CSE 331
Oct 5, 2012

2. HW 4 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 stuff HW 5 has been posted online: see blog/piazza
Solutions to HW 4 at the END of the lecture
Graded HW 3: pickup from TAs next week

4. 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)

5. HW 4 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

6. Questions?

7. 2 # edges = sum of # neighbors
2m = Σ u in V nu
Rest of the graph
Give 2 pennies to each edge
Total # of pennies = 2m
nv=3 u
nu=4 v
Each edges gives one penny to its end points
# of pennies u receives = nu

8. Today’s agenda
Run-time analysis of BFS

9. Breadth First Search (BFS)
Build layers of vertices connected to s
L0 = {s}
Assume L0,..,Lj have been constructed
Lj+1 set of vertices not chosen yet but are connected to Lj
Use CC[v] array
Stop when new layer is empty
Use linked lists

10. An illustration 1 2 3 4 5 7 8 6 1 7 2 3 8 4 5 6

11. Implementing DFS in O(m+n) time
Same as BFS except stack instead of a queue

12. A DFS run using an explicit stack7 8 1 7 7 6 3 2 3 5 8 4 4 5 5 3 6 2 3 1

13. Reading Assignment
Sec 3.3, 3.4 and 3.5 of [KT]