Ruby implementation of the Cantor pairing function to uniquely encode two natural numbers into a single natural number while being order sensitive.

cantor_functions.rb

# LINK: https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function
# LINK: https://www.cantorsparadise.com/cantor-pairing-function-e213a8a89c2b

def inv_cantor(z)
  w = ((Math.sqrt(8.0*z.to_f + 1.0) - 1.0) / 2.0).floor
  t = (w**2 + w) / 2
  y = (z - t)
  x = (w - y)
  [x, y]
end

def cantor(x, y)
  (x + y) * (x + y + 1) / 2 + y
end

def test(n = 25)
  assert_equal = ->(a, b, msg) {
    raise "TEST FAILED!\n#{msg}" unless a == b
  }
  assert_not_equal = ->(a, b, msg) {
    raise "TEST FAILED!\n#{msg}" if a == b
  }

  assert_not_equal.(cantor(2, 1), cantor(1, 2), 'Pairing function should be order sensitive')

  n.times do |i|
    randx = rand(0...10**rand(1..8)).to_i
    randy = rand(0...10**rand(1..8)).to_i
    cantorxy = cantor(randx, randy)
    
    expected = [randx, randy]
    actual = inv_cantor(cantorxy)

    assert_equal.(expected, actual, "CHECK cantor(#{randx}, #{randy}) = #{cantorxy} BUT inv_cantor(#{cantorxy}) = #{actual.join(', ')}")
    puts "#{(i+1).to_s.rjust(n.to_s.size)}: cantor(#{randx.to_s.rjust(8)}, #{randy.to_s.rjust(8)}) => #{cantorxy.to_s.rjust(17)} => inv_cantor(_) => [#{actual.join(', ')}]"
  end
end

test

# Example test output:
# --------------------
# 1: cantor(      56,        6) =>              1959 => inv_cantor(_) => [56, 6]
# 2: cantor(27137933,   304794) =>   376551646624422 => inv_cantor(_) => [27137933, 304794]
# 3: cantor(  282455,   310234) =>      175640731939 => inv_cantor(_) => [282455, 310234]
# 4: cantor(       7,    45625) =>        1041208153 => inv_cantor(_) => [7, 45625]
# 5: cantor(    4437,       95) =>          10271873 => inv_cantor(_) => [4437, 95]
# 6: cantor(      22,   339478) =>       57630634228 => inv_cantor(_) => [22, 339478]
# 7: cantor(     903,      201) =>            610161 => inv_cantor(_) => [903, 201]
# 8: cantor(  740444,     5706) =>      278370290031 => inv_cantor(_) => [740444, 5706]
# 9: cantor(      60,   449042) =>      100846976795 => inv_cantor(_) => [60, 449042]
# 10: cantor(   79247,       89) =>        3147140205 => inv_cantor(_) => [79247, 89]
# 11: cantor(    2832,   244406) =>       30563682347 => inv_cantor(_) => [2832, 244406]
# 12: cantor(   71620,   935068) =>      506711803084 => inv_cantor(_) => [71620, 935068]
# 13: cantor(  858819,       34) =>      368814667265 => inv_cantor(_) => [858819, 34]
# 14: cantor(83665641,    28021) =>  3502314571359974 => inv_cantor(_) => [83665641, 28021]
# 15: cantor(  360425,   778875) =>      649003593525 => inv_cantor(_) => [360425, 778875]
# 16: cantor(     252,     6841) =>          25165712 => inv_cantor(_) => [252, 6841]
# 17: cantor( 2260581,   503158) =>     3819128515088 => inv_cantor(_) => [2260581, 503158]
# 18: cantor(20701431, 40089741) =>  1847783367052119 => inv_cantor(_) => [20701431, 40089741]
# 19: cantor(   56097,    23942) =>        3203184722 => inv_cantor(_) => [56097, 23942]
# 20: cantor(  151949,       97) =>       11559069178 => inv_cantor(_) => [151949, 97]
# 21: cantor(      51,      269) =>             51629 => inv_cantor(_) => [51, 269]
# 22: cantor(     429,   974484) =>      475229140725 => inv_cantor(_) => [429, 974484]
# 23: cantor(     786, 37944927) =>   719938624456968 => inv_cantor(_) => [786, 37944927]
# 24: cantor(     211,    71199) =>        2549800954 => inv_cantor(_) => [211, 71199]
# 25: cantor( 2867234,    56484) =>     4274064990105 => inv_cantor(_) => [2867234, 56484]