Lecture Notes on 19 Apr 2013

For the graph given in class

Depth First Search (DFS)
Event		Stack
A		A
B		AB
F		ABF
H		ABFH
Pop H		ABF
Pop F		AB
Pop B		A
C		AC
Pop C		A
D		AD
G		ADG
I		ADGI
Pop I		ADG
Pop G		AD
Pop D		A
E		AE
Pop E		A
Pop A		-
DFS starting at A: ABFHCDGIE

Breadth First Search (BFS):
Event		Queue
A
B		B
C		BC
D		BCD
E		BCDE
Deq B		CDE
F		CDEF
Deq C		DEF
Deq D		EF
G		EFG
Deq E		FG
Def F		G
H		GH
Deq G		H
I		HI
Deq H		I
Deg I		- 
BFS starting at A: ABCDEFGHI

Topological Sort in a Directed Graph
Step 0: Create an empty sequence list.
Step 1: Find a vertex that has no successors.
Step 2: Delete this vertex from the graph and insert this vertex
        to the beginning of the sequence list.
Step 3: Repeat Steps 1 and 2 till there are no more vertices.
The sequence list has the vertices in topological order.

Minimum Cost Spanning Tree - Kruskal's Algorithm
Step 1: Create a list of edges.
Step 2: Sort that list in order of increasing weight (cost).
Step 3: Keep adding the edges from the sorted list to the
minimum cost spanning tree as long as the edge does not form
a cycle.
When there are no more edges to add, you have the minimum cost
spanning tree.