1. Lecture 12
CSE 331
Sep 28, 2012

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

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

5. Tree
Connected undirected graph with no cycles

6. Rooted Tree

7. A rooted tree AC’s child=SG Pick any vertex as root SG’s parent=AC
Let the rest of the tree hang under “gravity”

8. 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

9. Rest of Today’s agenda Prove n vertex tree has n-1 edges
Algorithms for checking connectivity

10. Checking by inspection

11. What about large graphs?
Are s and t connected?

12. Brute-force algorithm?
List all possible vertex sequences between s and t
nn such sequences
Check if any is a path between s and t

13. Algorithm motivation
all

14. Distance between u and v
Length of the shortest length path between u and v
Distance between RM and BO? 1

15. Questions?

16. Breadth First Search (BFS)
Is s connected to t?
Build layers of vertices connected to s
Lj : all nodes at distance j from s
L0 = {s}
Assume L0,..,Lj have been constructed
Lj+1 set of vertices not chosen yet but are connected to Lj
Stop when new layer is empty

17. Exercise for you
Prove that Lj has all nodes at distance j from s

18. BFS Tree BFS naturally defines a tree rooted at s Add non-tree edges
Lj forms the jth “level” in the tree
u in Lj+1 is child of v in Lj from which it was “discovered” 1 7 1 L0 2 3 L1 2 3 8 4 5 4 5 7 8 L2 6 6 L3