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Pyth, 8 bytes qu/Red._ Try it online! A list is in a loop if and only if it is the first list seen twice as f is applied repeatedly. qu/Red._ u Apply the following function, ...
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# [Pyth], 8 bytes qu/Red._ [Try it online!][TIO-ltauip7o] A list is in a loop if and only if it is the first list seen twice as f is applied repeatedly. qu/Red._ u Apply the following function, until a list is seen twice. ._ Take all prefixes of the list /R Count the number of appearance of ed The last element of the prefix q Check if the first repeated is the input [Pyth]: https://github.com/isaacg1/pyth [TIO-ltauip7o]: https://tio.run/##K6gsyfj/v7BUPyg1RS/@//9oQx1DHSMgNNYxjgUA "Pyth – Try It Online"