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・ Cyclic pump
・ Cyclic pyranopterin monophosphate
・ Cyclic pyranopterin monophosphate synthase
・ Cyclic quadrilateral
・ Cyclic reduction
・ Cyclic redundancy check
・ Cycle basis
・ Cycle button
・ Cycle chic
・ Cycle Collstrop
・ Cycle Computing
・ Cycle count
・ Cycle cover
・ Cycle decomposition
・ Cycle decomposition (graph theory)
Cycle detection
・ Cycle double cover
・ Cycle for Declamation
・ Cycle for Survival
・ Cycle Force Group
・ Cycle Friendly Awards
・ Cycle Gear
・ Cycle Glacier
・ Cycle graph
・ Cycle graph (algebra)
・ Cycle index
・ Cycle Messenger World Championships
・ Cycle News
・ Cycle of abuse
・ Cycle of erosion


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Cycle detection : ウィキペディア英語版
Cycle detection

In computer science, cycle detection is the algorithmic problem of finding a cycle in a sequence of iterated function values.
For any function ''ƒ'' that maps a finite set ''S'' to itself, and any initial value ''x''0 in ''S'', the sequence of iterated function values
: x_0,\ x_1=f(x_0),\ x_2=f(x_1),\ \dots,\ x_i=f(x_),\ \dots
must eventually use the same value twice: there must be some ''i'' ≠ ''j'' such that ''xi'' = ''xj''. Once this happens, the sequence must continue periodically, by repeating the same sequence of values from ''xi'' to ''xj''−1. Cycle detection is the problem of finding ''i'' and ''j'', given ''ƒ'' and ''x''0.
==Example==

The figure shows a function ƒ that maps the set ''S'' = to itself. If one starts from ''x''0 = 2 and repeatedly applies ƒ, one sees the sequence of values
:2, 0, 6, 3, 1, 6, 3, 1, 6, 3, 1, ....
The cycle in this value sequence is 6, 3, 1.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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