Cycle Detection

Cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values.

Parameters

  • tft_f: time to perform one evaluation of ff
  • μ\mu: the starting index of the cycle
  • λ\lambda: the period of the cycle
  • MM: number of values stored

Related Problems


Filters

Computational Model

Randomization

Approximation

Algorithms Table

Displaying 5 of 5 algorithms

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Nivasch2004O(μ+λ)O(\mu + \lambda)O(logμ)O(\log\mu)
Sedgewick; Szymanski; and Yao1982(μ+λ)(1+Θ(1/M))(\mu + \lambda)(1+\Theta(1/\sqrt{M}))MM
Gosper's algorithm1978O((λ+μ)log(λ+μ)tf)O((\lambda + \mu) \log(\lambda + \mu) t_f)Θ(log(μ+λ))\Theta(\log(\mu + \lambda))
Brent's algorithm1973O((λ+μ)tf)O((\lambda + \mu) t_f)O(1)O(1)
Floyd's tortoise and hare algorithm1967O((λ+μ)tf)O((\lambda + \mu) t_f)O(1)O(1)

Reductions Table

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Other relevant algorithms

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