My favourite algorithm

A lightning talk about my favourite algorithm, the Burrows–Wheeler transform (http://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform).

Given at Brighton Ruby Conference 2014 (http://lanyrd.com/2014/brightonruby/) and BaRuCo 2014 (http://lanyrd.com/2014/baruco/).

Transcript

1. MY
   FAVOURITE
   ALGORITHM
   @tomstuart / BaRuCo / 2014-09-12
   

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2. BURROWS—
   WHEELER
   TRANSFORM
   

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3. B A N A N A
   

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4. B A N A N A
   B
   A N A N A
   B A
   N A N A
   B A N
   A N A
   B A N A
   N A
   B A N A N
   A
   

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5. B A N A N A
   B
   A N A N A
   B A
   N A N A
   B A N
   A N A
   B A N A
   N A
   B A N A N
   A
   

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6. B A N A N A
   B
   A N A N A
   B A
   N A N A
   B A N
   A N A
   B A N A
   N A
   B A N A N
   A
   N
   N
   A
   B
   A
   A
   “NNBAAA”
   

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7. def burrows_wheeler(string)
   chars = string.chars
   !
   chars.each_index.
   map(&chars.method(:rotate)).
   sort.map(&:last).join
   end
   

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8. >> string = 'banana'
   => "banana"
   

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9. >> string = 'banana'
   => "banana"
   !
   >> chars = string.chars
   => ["b", "a", "n", "a", "n", "a"]
   

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10. >> string = 'banana'
    => "banana"
    !
    >> chars = string.chars
    => ["b", "a", "n", "a", "n", "a"]
    !
    >> chars.each_index
    !
    !
    => #"n", "a"]:each_index>
    

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11. >> string = 'banana'
    => "banana"
    !
    >> chars = string.chars
    => ["b", "a", "n", "a", "n", "a"]
    !
    >> chars.each_index.
    map(&chars.method(:rotate))
    !
    => [
    ["b", "a", "n", "a", "n", "a"],
    ["a", "n", "a", "n", "a", "b"],
    ["n", "a", "n", "a", "b", "a"],
    ["a", "n", "a", "b", "a", "n"],
    ["n", "a", "b", "a", "n", "a"],
    ["a", "b", "a", "n", "a", "n"]
    ]
    

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12. >> string = 'banana'
    => "banana"
    !
    >> chars = string.chars
    => ["b", "a", "n", "a", "n", "a"]
    !
    >> chars.each_index.
    map(&chars.method(:rotate)).
    sort
    => [
    ["a", "b", "a", "n", "a", "n"],
    ["a", "n", "a", "b", "a", "n"],
    ["a", "n", "a", "n", "a", "b"],
    ["b", "a", "n", "a", "n", "a"],
    ["n", "a", "b", "a", "n", "a"],
    ["n", "a", "n", "a", "b", "a"]
    ]
    

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13. >> string = 'banana'
    => "banana"
    !
    >> chars = string.chars
    => ["b", "a", "n", "a", "n", "a"]
    !
    >> chars.each_index.
    map(&chars.method(:rotate)).
    sort.map(&:last)
    => ["n", "n", "b", "a", "a", "a"]
    

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14. >> string = 'banana'
    => "banana"
    !
    >> chars = string.chars
    => ["b", "a", "n", "a", "n", "a"]
    !
    >> chars.each_index.
    map(&chars.method(:rotate)).
    sort.map(&:last).join
    => "nnbaaa"
    

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15. >> burrows_wheeler('banana')
    => "nnbaaa"
    >> burrows_wheeler('The rain in Spain
    stays mainly in the plain')
    => "nnyseenn nrplmthhtT aa aapn
    iiiiiiS y s la"
    

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16. !
    

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17. ?
    ?
    ?
    ?
    ?
    ?
    ? ? ? ? ?
    ? ? ? ? ?
    ?
    ? ? ? ?
    ? ?
    ? ? ?
    ? ? ?
    ? ?
    ? ? ? ?
    ?
    “NNBAAA”
    

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18. A
    B
    A
    N
    A
    N
    ? ? ? ? ?
    ? ? ? ? ?
    ?
    ? ? ? ?
    ? ?
    ? ? ?
    ? ? ?
    ? ?
    ? ? ? ?
    ?
    “NNBAAA”
    

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19. ?
    A ? ? ? ?
    ?
    B ? ? ? ?
    ?
    ?
    A ? ? ?
    ?
    ? ?
    N ? ?
    ?
    ? ? ?
    A ?
    ?
    ? ? ? ?
    N
    “NNBAAA”
    

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20. ?
    A ? ? ? ?
    ?
    B ? ? ? ?
    ?
    ?
    A ? ? ?
    ?
    ? ?
    N ? ?
    ?
    ? ? ?
    A ?
    ?
    ? ? ? ?
    N
    “NNBAAA”
    

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21. A
    B
    A
    N
    A
    N
    B ? ? ? ?
    A ? ? ? ?
    ?
    N ? ? ?
    ? ?
    A ? ?
    ? ? ?
    N ?
    ? ? ? ?
    A
    “NNBAAA”
    

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22. ?
    A B ? ? ?
    ?
    B A ? ? ?
    ?
    ?
    A N ? ?
    ?
    ? ?
    N A ?
    ?
    ? ? ?
    A N
    ?
    A ? ? ?
    N
    “NNBAAA”
    

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23. ?
    A B ? ? ?
    ?
    B A ? ? ?
    ?
    ?
    A N ? ?
    ?
    ? ?
    N A ?
    ?
    ? ? ?
    A N
    ?
    A ? ? ?
    N
    “NNBAAA”
    

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24. A
    B
    A
    N
    A
    N
    B A ? ? ?
    A N ? ? ?
    ?
    N A ? ?
    ? ?
    A N ?
    ? ? ?
    N A
    B ? ? ?
    A
    “NNBAAA”
    

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25. ?
    A B A ? ?
    ?
    B A N ? ?
    ?
    ?
    A N A ?
    ?
    ? ?
    N A N
    ?
    A ? ?
    A N
    ?
    A B ? ?
    N
    “NNBAAA”
    

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26. ?
    A B A ? ?
    ?
    B A N ? ?
    ?
    ?
    A N A ?
    ?
    ? ?
    N A N
    ?
    A ? ?
    A N
    ?
    A B ? ?
    N
    “NNBAAA”
    

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27. A
    B
    A
    N
    A
    N
    B A N ? ?
    A N A ? ?
    ?
    N A N ?
    ? ?
    A N A
    B ? ?
    N A
    B A ? ?
    A
    “NNBAAA”
    

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28. ?
    A B A N ?
    ?
    B A N A ?
    ?
    ?
    A N A N
    ?
    A ?
    N A N
    ?
    A B ?
    A N
    ?
    A B A ?
    N
    “NNBAAA”
    

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29. ?
    A B A N ?
    ?
    B A N A ?
    ?
    ?
    A N A N
    ?
    A ?
    N A N
    ?
    A B ?
    A N
    ?
    A B A ?
    N
    “NNBAAA”
    

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30. A
    B
    A
    N
    A
    N
    B A N A ?
    A N A N ?
    ?
    N A N A
    B ?
    A N A
    B A ?
    N A
    B A N ?
    A
    “NNBAAA”
    

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31. ?
    A B A N A
    ?
    B A N A N
    ?
    A
    A N A N
    ?
    A B
    N A N
    ?
    A B A
    A N
    ?
    A B A N
    N
    “NNBAAA”
    

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32. ?
    A B A N A
    ?
    B A N A N
    ?
    A
    A N A N
    ?
    A B
    N A N
    ?
    A B A
    A N
    ?
    A B A N
    N
    “NNBAAA”
    

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33. A
    A
    N
    N
    B A N A N
    B
    N A N A
    B A
    A N A
    B A N A
    A
    “NNBAAA”
    B
    A
    A N A N A
    B A N
    N A
    

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34. A
    A
    N
    N
    B A N A N
    B
    N A N A
    B A
    A N A
    B A N A
    A
    “NNBAAA”
    B A N A N A
    B
    A
    A N A N A
    B A N
    N A
    

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35. def inverse_burrows_wheeler(string)
    chars = string.chars
    !
    chars.
    inject([]) { |table| chars.zip(table).sort }.
    map(&:join)
    end
    

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36. >> inverse_burrows_wheeler('nnbaaa')
    => ["abanan", "anaban", "ananab",
    "banana", "nabana", "nanaba"]
    

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37. >> inverse_burrows_wheeler('nnyseenn nrplmthhtT aa aapn iiiiiiS y s la')

    => [" Spain stays mainly in the plainThe rain in", " in Spain stays mainly in
    the plainThe rain", " in the plainThe rain in Spain stays mainly", " mainly in
    the plainThe rain in Spain stays", " plainThe rain in Spain stays mainly in
    the", " rain in Spain stays mainly in the plainThe", " stays mainly in the
    plainThe rain in Spain", " the plainThe rain in Spain stays mainly in", "Spain
    stays mainly in the plainThe rain in ", "The rain in Spain stays mainly in the
    plain", "ain in Spain stays mainly in the plainThe r", "ain stays mainly in the
    plainThe rain in Sp", "ainThe rain in Spain stays mainly in the pl", "ainly in
    the plainThe rain in Spain stays m", "ays mainly in the plainThe rain in Spain
    st", "e plainThe rain in Spain stays mainly in th", "e rain in Spain stays
    mainly in the plainTh", "he plainThe rain in Spain stays mainly in t", "he rain
    in Spain stays mainly in the plainT", "in Spain stays mainly in the plainThe
    rain ", "in in Spain stays mainly in the plainThe ra", "in stays mainly in the
    plainThe rain in Spa", "in the plainThe rain in Spain stays mainly ", "inThe
    rain in Spain stays mainly in the pla", "inly in the plainThe rain in Spain
    stays ma", "lainThe rain in Spain stays mainly in the p", "ly in the plainThe
    rain in Spain stays main", "mainly in the plainThe rain in Spain stays ", "n
    Spain stays mainly in the plainThe rain i", "n in Spain stays mainly in the
    plainThe rai", "n stays mainly in the plainThe rain in Spai", "n the plainThe
    rain in Spain stays mainly i", "nThe rain in Spain stays mainly in the plai",
    "nly in the plainThe rain in Spain stays mai", "pain stays mainly in the
    plainThe rain in S", "plainThe rain in Spain stays mainly in the ", "rain in
    Spain stays mainly in the plainThe ", "s mainly in the plainThe rain in Spain
    stay", "stays mainly in the plainThe rain in Spain ", "tays mainly in the
    plainThe rain in Spain s", "the plainThe rain in Spain stays mainly in ", "y in
    the plainThe rain in Spain stays mainl", "ys mainly in the plainThe rain in
    Spain sta"]
    

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38. def burrows_wheeler(string)
    chars = string.chars + ['$']
    !
    chars.each_index.
    map(&chars.method(:rotate)).
    sort.map(&:last).join
    end
    !
    def inverse_burrows_wheeler(string)
    chars = string.chars
    !
    chars.
    inject([]) { |table| chars.zip(table).sort }.
    map(&:join).detect { |s| s.end_with?('$') }.chop
    end
    

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39. >> burrows_wheeler('banana')

    => "annb$aa"
    !
    >> inverse_burrows_wheeler('annb$aa')

    => "banana"
    !
    >> burrows_wheeler('The rain in Spain stays mainly
    in the plain')

    => "nnyseennn $rplmthhtT aa aapn iiiiiiS y s la"
    !
    >> inverse_burrows_wheeler('nnyseennn $rplmthhtT
    aa aapn iiiiiiS y s la')

    => "The rain in Spain stays mainly in the plain"
    

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40. thanks!
    @tomstuart / tom@codon.com
    

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