Module: MoreMath::CantorPairingFunction

Defined in:
lib/more_math/cantor_pairing_function.rb

Class Method Summary collapse

Class Method Details

.cantor_pairing(*xs) ⇒ Object 



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# File 'lib/more_math/cantor_pairing_function.rb', line 6

def cantor_pairing(*xs)
  if xs.size == 1 and xs.first.respond_to?(:to_ary)
    xs = xs.first.to_ary
  end
  case xs.size
  when 0, 1
    raise ArgumentError, "at least two arguments are required"
  when 2
    x, y, = *xs
    (x + y) * (x + y + 1) / 2 + y
  else
    cantor_pairing(cantor_pairing(*xs[0..1]), *xs[2..-1])
  end
end

.cantor_pairing_inv(c, n = 2) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/more_math/cantor_pairing_function.rb', line 33

def cantor_pairing_inv(c, n = 2)
  raise ArgumentError, "n is required to be >= 2" unless n >= 2
  result = []
  begin
    q = CantorPairingFunction.cantor_pairing_inv_q(c)
    y = c - CantorPairingFunction.cantor_pairing_inv_f(q)
    x = q - y
    result.unshift y
    c = x
    n -= 1
  end until n <= 1
  result.unshift x
end

.cantor_pairing_inv_f(z) ⇒ Object 



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# File 'lib/more_math/cantor_pairing_function.rb', line 21

def self.cantor_pairing_inv_f(z)
  z * (z + 1) / 2
end

.cantor_pairing_inv_q(z) ⇒ Object 



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# File 'lib/more_math/cantor_pairing_function.rb', line 25

def self.cantor_pairing_inv_q(z)
  v = 0
  while cantor_pairing_inv_f(v) <= z
    v += 1
  end
  v - 1
end