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Floyd's cycle detection on a numeric function f(x) = (2x + 5) mod 17.
Three phases:
Phase 1: advance slow/fast until collision inside the cycle
(fast double-steps, slow single-steps)
Phase 2: restart slow from x0; advance both by 1 until they
meet — count is mu (length of tail before cycle)
Phase 3: advance fast around cycle once until it meets slow
— count is lam (cycle length)
For x0 = 1, the orbit visits 1, 7, 2, 9, 6, 0, 5, 15 then returns
to 1 — pure cycle of length 8, mu = 0, lam = 8. Encoded as
mu*100 + lam = 8.
Tests three sequential while loops sharing ref state,
double-step `fast := f (f !fast)`, meeting-condition flag.
185 baseline programs total.
30 lines
518 B
OCaml
30 lines
518 B
OCaml
let f x = (x * 2 + 5) mod 17
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let floyd_cycle x0 =
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let slow = ref x0 in
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let fast = ref x0 in
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let meet = ref false in
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while not !meet do
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slow := f !slow;
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fast := f (f !fast);
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if !slow = !fast then meet := true
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done;
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slow := x0;
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let mu = ref 0 in
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while !slow <> !fast do
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slow := f !slow;
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fast := f !fast;
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mu := !mu + 1
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done;
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let lam = ref 1 in
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fast := f !slow;
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while !slow <> !fast do
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fast := f !fast;
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lam := !lam + 1
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done;
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!mu * 100 + !lam
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;;
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floyd_cycle 1
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