Going The Distance

Levenshtein Distance and the beauty of algorithms

Transcript

1. Going
   The
   Distance
   @schneems
   

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2. They
   Call me
   @Schneems
   

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3. Ruby
   Schneems
   

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4. Ruby
   Python
   

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5. View Slide

6. Code
   Triage
   .com
   

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7. Challenge:
   Comment on
   an issue
   

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8. Docs
   Doctor
   .org
   

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9. View Slide

10. Top 50
    Rails
    Contrib
    

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11. Cats
    

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13. Can you keep
    Ruby weird?
    

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14. %CP%CP
    

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15. 'XGT[QPG%CP%CP
    

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16. Thank
    You!
    

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17. Algorithms:
    

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18. I went to
    Georgia Tech
    for…
    

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19. Mechanical 

    Engineering
    

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20. Self taught
    Programmer
    ~8 years
    

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21. CS is boring
    to me
    

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22. Programming
    is interesting
    

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23. Building
    programs that
    accomplish
    tasks
    

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24. But…
    

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25. Those CS
    students are
    on to
    something
    

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26. Algorithms
    

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27. Are
    

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28. Beautiful
    

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29. <3
    

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30. Algorithms
    solve
    problems
    

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31. Introducting
    A
    Problem…
    

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32. Spelling
    

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33. When you are
    tired, or
    distracted
    spelling
    becomes harder
    

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34. $ git commmit -m first
    WARNING: You called a Git command named 'commmit',
    which does not exist.
    Continuing under the assumption that you meant 'commit'
    in 0.1 seconds automatically...
    

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35. How does Git
    know?
    

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36. Introducing:

    Edge
    Distance
    

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37. The “cost”
    to change one
    word to
    another
    

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38. Less “cost”
    means less
    more likely
    match
    

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39. Cost of?
    zat => bat
    

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40. Cost of?
    zat => bat
    1
    

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41. Cost of?
    zzat => bat
    

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42. Cost of?
    bat
    2
    zzat =>
    

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43. How do we
    code it
    though?
    

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44. My First
    Attempt
    

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45. def distance(str1, str2)
    cost = 0
    str1.each_char.with_index do |char, index|
    cost += 1 if str2[index] != char
    end
    cost
    end zat bat
    =>
    

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46. def distance(str1, str2)
    cost = 0
    str1.each_char.with_index do |char, index|
    cost += 1 if str2[index] != char
    end
    cost
    end zat bat
    =>
    Cost = 1
    

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47. Perfect?
    

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48. saturday
    sunday
    Cost = ?
    

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49. saturday
    sunday
    Cost = 7
    

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50. Wat?
    

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51. Turns out I
    almost
    recreated
    

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52. Hamming
    Distance
    

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53. Hamming
    AKA: Signal
    Distance
    

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54. Measures: the
    errors
    introduced in a
    string
    Hamming
    

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55. Only valid for
    strings of
    same length
    Hamming
    

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56. Good for: Detecting
    and correcting
    errors in binary and
    telecommunications
    Hamming
    

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57. Bad for: mis-
    spelled words
    Hamming
    

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58. Does not
    include:
    Insertion

    Deletion
    Hamming
    

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59. Introducing:

    An
    Algorithm!
    

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60. Introducing:

    Levenshtein
    Distance
    

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61. How do we
    calculate
    deletion?
    

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62. distance("schneems", "zschneems")
    

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63. distance("schneems", "zschneems")
    Match!
    deletion
    

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64. str1 = “schneems”
    str2 = “zschneems”
    str1 == str2[1..-1]
    deletion
    

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65. How do we
    calculate
    insertion?
    

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66. distance("schneems", "chneems")
    

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67. distance("schneems", "chneems")
    Match!
    insertion
    

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68. str1 = “schneems”
    str2 = “chneems”
    str1[1..-1] == str2
    insertion
    

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69. substitution?
    

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70. distance("zchneems", "schneems")
    Substitution
    

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71. str1 = “zchneems”
    str2 = “schneems”
    str1[1..-1] == str2[1..-1]
    Substitution
    

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72. How do we
    calculate
    Distance?
    

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73. Pretend we
    have a
    distance()
    method
    

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74. Strings of
    different
    lengths
    

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75. distance(“”, “foo”) # => 3
    distance(“foo”, “”) # => 3
    

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76. return str2.length if str1.empty?
    return str1.length if str2.empty?
    Different
    Lengths
    

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77. Calculate
    distance
    between every
    substring
    

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78. l1 = distance(str1, str2[1..-1]) # deletion
    l2 = distance(str1[1..-1], str2) # insertion
    l3 = distance(str1[1..-1], str2[1..-1]) # substitution
    Calculate
    costs
    

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79. l1 = distance(str1, str2[1..-1]) # deletion
    l2 = distance(str1[1..-1], str2) # insertion
    l3 = distance(str1[1..-1], str2[1..-1]) # substitution
    cost = 1 + [l1,l2,l3].min
    Take
    minimum
    

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80. l1 = distance(str1, str2[1..-1]) # deletion
    l2 = distance(str1[1..-1], str2) # insertion
    l3 = distance(str1[1..-1], str2[1..-1]) # substitution
    cost = 1 + [l1,l2,l3].min
    Why did we
    add one?
    

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81. Pick the
    cheapest
    operation,
    then add one
    

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82. What about
    when
    characters
    match?
    

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83. distance(str1[1..-1], str2[1..-1]) if str1[0] == str2[0]
    Match
    str1 = “saturday”
    str2 = “sunday”
    

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84. Our powers
    combined, we
    form!
    

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86. `
    

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87. Recursive
    Levenshtein
    Distance!
    

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88. def distance(str1, str2)
    # Different lengths
    return str2.length if str1.empty?
    return str1.length if str2.empty?
    !
    return distance(str1[1..-1], str2[1..-1]) if str1[0] == str2[0] # match
    l1 = distance(str1, str2[1..-1]) # deletion
    l2 = distance(str1[1..-1], str2) # insertion
    l3 = distance(str1[1..-1], str2[1..-1]) # substitution
    return 1 + [l1,l2,l3].min # increment cost
    end
    Recursive
    

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89. distance(“saturday”, “sunday”)
    # => 3
    Recursive
    Levenshtein
    

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90. Much better
    

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91. What does
    that look
    like?
    

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93. github.com/
    schneems/
    going_the_distance
    

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94. Hmm…
    

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95. “Dirty
    Distance”
    took 8
    comparisons
    

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96. “Recursive”
    took 1647
    comparisons
    

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97. No trophy, no
    flowers, no
    flashbulbs,
    no wine,
    

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98. Ouch
    

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99. Can we do
    better?
    

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100. If you watch the
     recursive
     algorithm
     closely, you
     notice repeats
     

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101. Maybe we can
     store substring
     distance and
     use to calculate
     total distance
     

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102. I want you to
     join the
     club
     

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103. A
     members only
     club
     

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104. Matrix:

     Levenshtein
     Distance
     

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105. Matrix:

     Levenshtein
     Distance
     

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106. “” => “saturday”
     Cost?
     

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107. +---+---+
     | | S |
     +---+---+
     | | 1 |
     +---+---+
     Matrix
     

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108. +---+---+---+
     | | S | A |
     +---+---+---+
     | | 1 | 2 |
     +---+---+---+
     Matrix
     

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109. +---+---+---+---+
     | | S | A | T |
     +---+---+---+---+
     | | 1 | 2 | 3 |
     +---+---+---+---+
     Matrix
     

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110. +---+---+---+---+---+
     | | S | A | T | U |
     +---+---+---+---+---+
     | | 1 | 2 | 3 | 4 |
     +---+---+---+---+---+
     Matrix
     

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111. +---+---+---+---+---+---+
     | | S | A | T | U | R |
     +---+---+---+---+---+---+
     | | 1 | 2 | 3 | 4 | 5 |
     +---+---+---+---+---+---+
     Matrix
     

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112. +---+---+---+---+---+---+---+
     | | S | A | T | U | R | D |
     +---+---+---+---+---+---+---+
     | | 1 | 2 | 3 | 4 | 5 | 6 |
     +---+---+---+---+---+---+---+
     Matrix
     

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113. +---+---+---+---+---+---+---+---+
     | | S | A | T | U | R | D | A |
     +---+---+---+---+---+---+---+---+
     | | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
     +---+---+---+---+---+---+---+---+
     Matrix
     

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114. +---+---+---+---+---+---+---+---+---+
     | | S | A | T | U | R | D | A | Y |
     +---+---+---+---+---+---+---+---+---+
     | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
     +---+---+---+---+---+---+---+---+---+
     Matrix
     

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115. “sunday” => “”
     Cost?
     

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116. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     Matrix
     

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117. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     Matrix
     

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118. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     | N | 3 |
     +---+---+
     Matrix
     

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119. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     | N | 3 |
     +---+---+
     | D | 4 |
     +---+---+
     Matrix
     

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120. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     | N | 3 |
     +---+---+
     | D | 4 |
     +---+---+
     | A | 5 |
     +---+---+
     Matrix
     

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121. +---+---+
     | | |
     +---+---+
     | | 0 |
     +---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     | N | 3 |
     +---+---+
     | D | 4 |
     +---+---+
     | A | 5 |
     +---+---+
     | Y | 6 |
     +---+---+
     Matrix
     

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122. Now, fill in
     the matrix
     

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123. +---+---+---+---+---+---+---+---+---+---+
     | | | S | A | T | U | R | D | A | Y |
     +---+---+---+---+---+---+---+---+---+---+
     | | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
     +---+---+---+---+---+---+---+---+---+---+
     | S | 1 |
     +---+---+
     | U | 2 |
     +---+---+
     | N | 3 |
     +---+---+
     | D | 4 |
     +---+---+
     | A | 5 |
     +---+---+
     | Y | 6 |
     +---+---+
     Matrix
     

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124. Break it down
     

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125. How much
     does it cost to
     change “s”
     into “s”?
     

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126. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     Match!
     Cost = 0
     

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127. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     Insertion!
     Cost = ?
     

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128. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     Insertion!
     Cost = 1
     

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129. How do we
     calculate insertion
     programmatically?
     

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130. str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     Insertion!
     

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131. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1]
     Insertion!
     

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132. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     Insertion!
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1]
     

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133. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     Insertion!
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1]
     

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134. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     Insertion!
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1]
     

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135. + cost of
     change
     (+1)
     

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136. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | |
     +---+---+---+---+
     Insertion!
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1] + 1
     

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137. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     Insertion!
     Cost = 1
     str1 = “schneems”
     str2 = “chneems”
     str1[1..-1] == str2
     matrix[row_index][column_index - 1] + 1
     

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138. Keep Going
     

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139. +---+---+---+---+---+---+---+---+---+---+
     | | | S | A | T | U | R | D | A | Y |
     +---+---+---+---+---+---+---+---+---+---+
     | | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
     +---+---+---+---+---+---+---+---+---+---+
     | S | 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
     +---+---+---+---+---+---+---+---+---+---+
     Insertion(s)
     

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140. Next Char
     “su” => “s”
     

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141. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | |
     +---+---+---+
     Action?
     

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142. Change “su” to
     “s” is a deletion.
     How do we
     calculate?
     

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143. Deletion
     

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144. str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     deletion
     

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145. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | |
     +---+---+---+
     Deletion
     str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     matrix[row_index - 1][column_index]
     

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146. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | |
     +---+---+---+
     Deletion
     str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     matrix[row_index - 1][column_index]
     

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147. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | |
     +---+---+---+
     Deletion
     str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     matrix[row_index - 1][column_index]
     

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148. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | |
     +---+---+---+
     Deletion
     str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     matrix[row_index - 1][column_index] + 1
     

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149. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     | U | 2 | 1 |
     +---+---+---+
     Deletion
     Cost = 1
     str1 = “schneems”
     str2 = “zschneems”
     str1 == str2[1..-1]
     matrix[row_index - 1][column_index] + 1
     

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150. - Insertion
     - Deletion
     - Substitution
     

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151. - Insertion
     - Deletion
     - Substitution
     

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152. Substitution
     

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153. str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     Substitution!
     

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154. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | |
     +---+---+---+---+
     Substitution
     str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     

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155. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | |
     +---+---+---+---+
     Substitution
     str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     

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156. str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | |
     +---+---+---+---+
     Substitution
     

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157. str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | |
     +---+---+---+---+
     Substitution
     

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158. str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | |
     +---+---+---+---+
     Substitution
     

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159. +---+---+---+---+
     | | | S | A |
     +---+---+---+---+
     | | 0 | 1 | 2 |
     +---+---+---+---+
     | S | 1 | 0 | 1 |
     +---+---+---+---+
     | U | 2 | 1 | 1 |
     +---+---+---+---+
     Substitution
     Cost = 1
     str1 = “zchneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     + 1
     

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160. - Insertion
     - Deletion
     - Substitution
     

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161. What about
     match?
     

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162. +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     Match!
     str1 = “schneems”
     str2 = “schneems”
     str1[1..-1] == str2[1..-1]
     matrix[row_index - 1][column_index- 1]
     

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163. Why?
     

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164. If the current
     character matches,
     cost is to change
     previous character
     to previous sub
     string
     

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165. i.e. changing
     “” to “”
     +---+---+---+
     | | | S |
     +---+---+---+
     | | 0 | 1 |
     +---+---+---+
     | S | 1 | 0 |
     +---+---+---+
     

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166. Now What?
     

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167. Algorithm
     str2.each_char.each_with_index do |char1,i|
     str1.each_char.each_with_index do |char2, j|
     if char1 == char2
     puts [:skip, matrix[i][j]].inspect
     matrix[i + 1 ][j + 1 ] = matrix[i][j]
     else
     actions = {
     deletion: matrix[i][j + 1] + 1,
     insert: matrix[i + 1][j] + 1,
     substitution: matrix[i][j] + 1
     }
     action = actions.sort {|(k,v), (k2, v2)| v <=> v2 }.first
     puts action.inspect
     matrix[i + 1 ][j + 1 ] = action.last
     end
     each_step.call(matrix) if each_step
     end
     end
     

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168. Iterate!
     

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169. View Slide

170. Final Cost
     +---+---+---+---+---+---+---+---+---+---+
     | | | S | A | T | U | R | D | A | Y |
     +---+---+---+---+---+---+---+---+---+---+
     | | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
     +---+---+---+---+---+---+---+---+---+---+
     | S | 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
     +---+---+---+---+---+---+---+---+---+---+
     | U | 2 | 1 | 1 | 2 | 2 | 3 | 4 | 5 | 6 |
     +---+---+---+---+---+---+---+---+---+---+
     | N | 3 | 2 | 2 | 2 | 3 | 3 | 4 | 5 | 6 |
     +---+---+---+---+---+---+---+---+---+---+
     | D | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 4 | 5 |
     +---+---+---+---+---+---+---+---+---+---+
     | A | 5 | 4 | 3 | 4 | 4 | 4 | 4 | 3 | 4 |
     +---+---+---+---+---+---+---+---+---+---+
     | Y | 6 | 5 | 4 | 4 | 5 | 5 | 5 | 4 | 3 |
     +---+---+---+---+---+---+---+---+---+---+
     3
     

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171. We can also
     get cost of
     sub strings
     

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172. “sun” => “sat”
     

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173. Final Cost
     +---+---+---+---+---+---+---+---+---+---+
     | | | S | A | T | U | R | D | A | Y |
     +---+---+---+---+---+---+---+---+---+---+
     | | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
     +---+---+---+---+---+---+---+---+---+---+
     | S | 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
     +---+---+---+---+---+---+---+---+---+---+
     | U | 2 | 1 | 1 | 2 | 2 | 3 | 4 | 5 | 6 |
     +---+---+---+---+---+---+---+---+---+---+
     | N | 3 | 2 | 2 | 2 | 3 | 3 | 4 | 5 | 6 |
     +---+---+---+---+---+---+---+---+---+---+
     | D | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 4 | 5 |
     +---+---+---+---+---+---+---+---+---+---+
     | A | 5 | 4 | 3 | 4 | 4 | 4 | 4 | 3 | 4 |
     +---+---+---+---+---+---+---+---+---+---+
     | Y | 6 | 5 | 4 | 4 | 5 | 5 | 5 | 4 | 3 |
     +---+---+---+---+---+---+---+---+---+---+
     2
     

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174. Better than
     Recursive?
     

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175. As they speed
     through the
     finish, the
     flags go down.
     

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176. 48 iterations
     

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177. Wayyyyyy
     better than
     1647
     

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178. bit.ly/
     going_the_distance
     

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179. My Problem
     

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180. I am human
     

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181. I get tired
     

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182. Machines
     don’t
     understand
     tired
     

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183. One day I
     tried typing
     

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184. $ rails generate
     migration
     

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185. But
     accidentally
     typed
     

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186. $ rails generate
     migratoon
     

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187. ERROR
     

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188. View Slide

189. Stress is
     increased
     when we fail
     at simple tasks
     

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190. Why?
     It’s not hard
     

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191. Why
     can’t my
     software be
     more like git?
     

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192. We know what
     you’re trying to
     accomplish.
     Let’s help you
     out
     

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193. View Slide

194. When you
     have ERROR
     

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195. Compare given
     command to
     possible
     commands
     

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196. Recommend
     smallest
     distance.
     

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197. Google:
     

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198. Google:
     

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199. Read A lot of
     words from
     real books
     

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200. ~1+ million
     words
     

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201. Count Each
     word
     

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202. Higher count,
     higher
     probability
     

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203. Get edit
     distance
     between input
     and dictionary
     

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204. Lower edit,
     higher
     probability
     

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205. Show
     Suggestion
     

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206. View Slide

207. Cache
     correct
     spelling
     suggestions
     

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208. did_you_mean
     gem
     

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209. View Slide

210. More distance
     measurements
     

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211. Levenshtein
     Distance
     

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212. Hamming
     Distance
     

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213. longest
     common
     subsequence
     Distance
     

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214. Manhattan
     Distance
     

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215. Tree
     Distance
     

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216. Jaro-Winkler
     Distance
     

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217. Many
     Many
     More
     

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218. Algorithms
     are
     Awesome
     

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219. Where to go
     next?
     

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220. I want to
     learn more
     about
     algorithms?
     

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221. Wikipedia!
     

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222. Rosetta code
     

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223. Give an
     algorithm
     talk
     

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224. Everyone
     suggests
     a new
     Algorithm!
     

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225. Algorithms
     are a
     way of sharing
     knowledge
     

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226. Expand your
     knowledge
     Explore
     Algorithms
     

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227. Antepenultimate
     Slide
     

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228. YAY!
     

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229. Questions
     @schneems
     

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230. Going
     The
     Distance
     

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