1. CSC 172 DATA STRUCTURES

2. WORKSHOP LEADER INTEREST MEETING FRIDAY, APRIL 6th 12:30pm 601 CSB
Good grades in CSC171 & CSC172
Good people skills
Favorable approach to workshops

3. GRAPHS GRAPH G= (V,E) V: a set of vertices (nodes)
E: a set of edges connecting vertices  V
An edge is a pair of nodes
Example:
V = {a,b,c,d,e,f,g}
E = {(a,b),(a,c),(a,d),(b,e),(c,d) ,(c,e),(d,e),(e,f)} a b d c e f g

4. PATHS ON GRAPHS
Simple
Euler
Hamiltonian

5. SIMPLE PATH
Given two vertices is there a simple path that connects them?

6. HAMILTONIAN PATH
Given a starting vertex is there a path through the graph that visits each (and every) vertex exactly once?
If the path finishes at the starting vertex, it is a Hamiltonian cycle (a.k.a. The Traveling Salesman Problem).

7. EULER PATH
Given a starting vertex is there a path through the graph that traverses each (and every) edge exactly once?

8. SIMPLE PATH
Given two vertices is there a simple path that connects them?
We can find this path in linear O(V + e) time
Sort of, recall that e is O(V2)
Use Depth first search.
How can we modify DFS to print the path?

9. HAMILTONIAN PATH
Given a starting vertex is there a path/cycle/tour through the graph that visits each (and every) vertex exactly once?
In order to do this, we may need to consider every possible path. (How many are there?)
We may need to consider (V-1)! paths in a complete graph.

10. EULER PATH
Given a starting vertex is there a path through the graph that traverses each (and every) edge exactly once?
We can prove that an Euler cycle exists iff the graph is connected and all nodes have even degree.
We can find the path in linear time.