Editing Cycle detection (section)

====Complexity====

Upon the <math>i</math>-th evaluation of the generator function, the algorithm compares the generated value with <math>\log_2 i</math> previous values; observe that <math>i</math> goes up to at least <math>\mu + \lambda</math> and at most <math>\mu + 2\lambda</math>. Therefore, the time complexity of this algorithm is <math>O((\mu + \lambda) \cdot \log (\mu + \lambda))</math>. Since it stores <math>\log_2 (\mu + 2\lambda)</math> values, its space complexity is <math>\Theta(\log (\mu + \lambda))</math>. This is under the usual [[transdichotomous model]], assumed throughout this article, in which the size of the function values is constant. Without this assumption, we know it requires <math>\Omega(\log (\mu + \lambda))</math> space to store <math>\mu + \lambda</math> distinct values, so the overall space complexity is <math>\Omega(\log^2 (\mu + \lambda)).</math>