Rosetta Code

Farey sequence

Generate Farey sequences of small orders with the classic iterative recurrence.

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Sourcerosettacode/popular/farey_sequence.vibe
def fraction_text(numerator: int, denominator: int) -> string
  "#{numerator}/#{denominator}"
end

def farey_sequence(order: int) -> array<string>
  left_numerator = 0
  left_denominator = 1
  right_numerator = 1
  right_denominator = order
  values = [fraction_text(left_numerator, left_denominator)]

  while right_numerator <= order
    values.push(fraction_text(right_numerator, right_denominator))

    multiplier = (order + left_denominator) // right_denominator
    next_left_numerator = right_numerator
    next_left_denominator = right_denominator
    next_right_numerator = (multiplier * right_numerator) - left_numerator
    next_right_denominator = (multiplier * right_denominator) - left_denominator

    left_numerator = next_left_numerator
    left_denominator = next_left_denominator
    right_numerator = next_right_numerator
    right_denominator = next_right_denominator
  end

  values
end

def run -> { order_five: array<string>, order_seven_count: int }
  {
    order_five: farey_sequence(5),
    order_seven_count: farey_sequence(7).length
  }
end

Output

Click Run example to see the result.

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