CSC 172 DATA STRUCTURES

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CSC 172 DATA STRUCTURES
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WORKSHOP LEADERINTEREST MEETINGFRIDAY, APRIL
6th1230pm 601 CSB

• Good grades in CSC171 CSC172
• Good people skills
• Favorable approach to workshops

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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)

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PATHS ON GRAPHS

• Simple
• Euler
• Hamiltonian

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SIMPLE PATH

• Given two vertices is there a simple path that
  connects them?

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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).

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EULER PATH

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

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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?

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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.

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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.