Tower Of Hanoi
- 1. Tower of Hanoi (Application Of Stacks) -Vinit Dantkale
- 2. The Tower of Hanoi puzzle was invented by the French mathematician Edouard Lucas in 1883. Tower Of Hanoi is a Puzzle involving the usage of Stacks. Shifting of discs from source tower to target tower. Rules for solving puzzle: 1. One disc can be shifted at once. 2. Only top disc can be shifted. 3. Large disc cannot be placed on smaller disc. 4. Only 3 stacks can be used for solving the puzzle. Source Tower having N discs can be solved using (2^N)-1 moves. Introduction
- 3. Usage of Stacks in Tower of Hanoi: Real life analogy of Stack ie. Access single disc, Single Access location. Steps: 1. Move 1 from A to C 2. Move 2 from A to B 3. Move 1 from C to B 4. Move 3 from A to C 5. Move 1 from B to A 6. Move 2 from B to C 7. Move 1 from A to C
- 4. Use of Recursion for algorithm:
- 5. Explanation: • The recursion used before "movedisk" is to move all but the bottom disk on the initial tower to an intermediate pole. • The next line simply moves the bottom disk to its final resting place. • Then on line we move the tower from the intermediate pole to the top of the largest disk. • The base case is detected when the tower height is 0 and the base of the tower is moved Use of recursion is again use of stack
- 6. Application: Used as Backup rotation Scheme (Backups of Computers having multiple tapes/media) A backup rotation scheme is a system for managing your backup storage media (tapes/DVDs/HDDs). Used by neuropsychologists trying to evaluate frontal lobe deficits. Used to Solve mathematical problems related to Hamilton Cycle.
- 7. Other possible data structures: Puzzles are connected with graphs, it means can be modeled by using graphs. Other possible data structure used for this puzzle is Undirected Graph. Vertices of the graph represent configuration and graph edges define possible moves of the puzzle. For Tower with Height as 2