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I was recently working on solving problem 64 for project Euler and one of the needed algorithms was a detection of cycles in a list. This routine works for detecting cycles in lists of cardinality greater than 2.
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def get_cycle_len(N):
  i = k = 0
  for j in range(2, len(N)):
    if N[i] == N[j]:
      if k == 0:
        k = j
        i = 1
      else:
        if i == k:
          return k
        i += 1
    else:
      i = 0
      k = 0
  return -1

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