1. Lecture 11
CSE 331
Sep 21, 2017

2. Mini Project group due Monday!

3. HW 3 is out!

4. Support page is very imp.

5. Solutions to HW 2
Handed out at the end of the lecture

6. Tree
Connected undirected graph with no cycles

7. Today’s agenda Prove that n vertex tree has n-1 edges
Algorithms for checking connectivity

8. Questions?

9. Rest of Today’s agenda Algorithms for checking connectivity
Finish Proving 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