Created
September 29, 2021 12:14
Ruby implementation of the Cantor pairing function to uniquely encode two natural numbers into a single natural number while being order sensitive.
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# 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] |
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