67 lines
1.9 KiB
Plaintext
67 lines
1.9 KiB
Plaintext
defmodule Rational do
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import Kernel, except: [div: 2]
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defstruct numerator: 0, denominator: 1
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def new(numerator), do: %Rational{numerator: numerator, denominator: 1}
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def new(numerator, denominator) do
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sign = if numerator * denominator < 0, do: -1, else: 1
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{numerator, denominator} = {abs(numerator), abs(denominator)}
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gcd = gcd(numerator, denominator)
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%Rational{numerator: sign * Kernel.div(numerator, gcd),
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denominator: Kernel.div(denominator, gcd)}
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end
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def add(a, b) do
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{a, b} = convert(a, b)
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new(a.numerator * b.denominator + b.numerator * a.denominator,
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a.denominator * b.denominator)
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end
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def sub(a, b) do
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{a, b} = convert(a, b)
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new(a.numerator * b.denominator - b.numerator * a.denominator,
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a.denominator * b.denominator)
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end
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def mult(a, b) do
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{a, b} = convert(a, b)
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new(a.numerator * b.numerator, a.denominator * b.denominator)
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end
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def div(a, b) do
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{a, b} = convert(a, b)
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new(a.numerator * b.denominator, a.denominator * b.numerator)
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end
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defp convert(a), do: if is_integer(a), do: new(a), else: a
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defp convert(a, b), do: {convert(a), convert(b)}
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defp gcd(a, 0), do: a
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defp gcd(a, b), do: gcd(b, rem(a, b))
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end
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defimpl Inspect, for: Rational do
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def inspect(r, _opts) do
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"%Rational<#{r.numerator}/#{r.denominator}>"
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end
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end
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Enum.each(2..trunc(:math.pow(2,19)), fn candidate ->
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sum = 2 .. round(:math.sqrt(candidate))
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|> Enum.reduce(Rational.new(1, candidate), fn factor,sum ->
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if rem(candidate, factor) == 0 do
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Rational.add(sum, Rational.new(1, factor))
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|> Rational.add(Rational.new(1, div(candidate, factor)))
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else
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sum
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end
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end)
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if sum.denominator == 1 do
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:io.format "Sum of recipr. factors of ~6w = ~w exactly ~s~n",
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[candidate, sum.numerator, (if sum.numerator == 1, do: "perfect!", else: "")]
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end
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end)
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