Lecture 13
CSE 331
Oct 2, 2009
Announcements
Please turn in your HW 3
Graded HW2, solutions to HW 3, HW 4 at the END of the class
Maybe extra lectures next week on proofs– check the blog!
Connected Component
Connected component (of s) is the set of all nodes connected to s
Computing Connected Component
Start with R = {s}
While exists (u,v) edge v not in R and u in R
Add v to R
Output R
R is the connected component of s
Claim 1: All vertices in R are connected to s
Base Case
Induction on number of iterations
I.H.: u is connected to s
Start with R = {s}
While exists (u,v) edge v not in R and u in R
Add v to R
Output R
Today’s agenda
If w is not in R then w is not connected to s
Depth First Search
Computing all connected components
Run-time analysis of DFS and BFS
A DFS run
1
1
7
2
2
3
8
4
4
Every nontree edge is
between a
node and its
ancestor
5
5
6
DFS tree
6
3
8
7
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
Read Sec 3.2