@Dave
Cycle finding algo (Floyd's, Brent's) can be applied only for the iterated 
function values.
This means: f(x0) = x1; f(x1) = x2 and etc.
Suppose we have the following array: 1 2 3 2 4. Value 2 have two different 
transitions.

Clarify your proposed method if it needs additional observations.

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