Tower of Hanoi: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Tower of Hanoi - Time.png|1000px]] | [[File:Tower of Hanoi - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Tower of Hanoi - Space.png|1000px]] | [[File:Tower of Hanoi - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Tower of Hanoi - Pareto Frontier.png|1000px]] | [[File:Tower of Hanoi - Pareto Frontier.png|1000px]] | ||
Revision as of 13:05, 15 February 2023
Description
The Tower of Hanoi puzzle consists of $n$ discs, no two of the same size, stacked on $p \geq 3$ vertical pegs, in such a way that no disc lies on top of a smaller disc. A permissible $move$ is to take the top disc from one of the pegs and move it to one of the other pegs, as long as it is not placed on top of a smaller disc. Initially, they are all stacked on the first peg. The goal is to end up with them all stacked on the last peg.
Parameters
n: number of discs
p: number of pegs
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Iteration based | 1883 | $O({2}^n)$ | $O(n)$ auxiliary | Exact | Deterministic | |
| Recursion based | 1940 | $O({2}^n)$ | $O(n*log n)$ auxiliary | Exact | Deterministic | |
| Non-recursion based | 1940 | $O({2}^n)$ | $O(n)$ auxiliary | Exact | Deterministic | |
| Gray-code based | 1940 | $O({2}^n)$ | $O(n)$ auxiliary | Exact | Deterministic | |
| Hanoi graph | 2008 | $O({2}^n)$ | Exact | Deterministic | Time |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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