The Towers of Hanoi Problem in Graph Form

1 / 8

# The Towers of Hanoi Problem in Graph Form - PowerPoint PPT Presentation

The Towers of Hanoi Problem in Graph Form. Finding bounds for the number of moves. Presented by: Shibo Fang 9 July 2010 Mentor: Dr. Ernst Leiss. Background. Towers of Hanoi: a classic problem Three poles to move disks on Goal is to move all disks to third pole

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'The Towers of Hanoi Problem in Graph Form' - aquila-hicks

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### The Towers of Hanoi Problem in Graph Form

Finding bounds for the number of moves

• Presented by:
• Shibo Fang
• 9 July 2010
• Mentor:
• Dr. Ernst Leiss
Background
• Towers of Hanoi: a classic problem
• Three poles to move disks on
• Goal is to move all disks to third pole
• Certain rules apply in movement of disks
• Can be represented as a direct graph
• S = start node, A = auxiliary node (between S and D nodes), D = destination node
• Two edges between every two nodes
Solvable and Finite Graphs
• A graph is solvable when:
• There exist vertices S, D, and A
• There exist paths from S to A, from A to D, and from D to S
• Solvable means any number of disks can be moved from the S to the D node
• Any graph that is not solvable is a finite graph
Hanoi Graphs
• Original Hanoi problem with three nodes requires 2d – 1 moves (d = number of disks)
• Modified Hanoi problem (there are no edges between S and D) requires 3d – 1 moves
Special Hanoi Graphs
• First special Hanoi graph (k graph)
• Has k+3 nodes, S0 through Sk, A, D
• Requires k*d + 3d – 1 moves
Special Hanoi Graphs (Cont.)
• Second special Hanoi graph (cycle graph)
• An edge between each two nodes
• First edge from S node to first A node
• Last edge from D node to S node
Findings
• Needed to find algorithm and formula for number of moves for cycle graph
• Found for d ≤ n – 1 (n = number of nodes)
• Need to find for d ≥ n
• K graph thought to be upper bound
• Requires most moves out of all Hanoi graphs
• Cycle graph worse than K graph
• When d ≤ n – 1, small d and large n
Questions

Thank you. Any questions?