Going The Distance

1.

Going The Distance @schneems

2.

They Call me @Schneems

3.

Ruby Schneems

4.

Ruby Python

5.

None

6.

Code Triage .com

7.

Challenge: Comment on an issue

8.

Docs Doctor .org

9.

None

10.

Top 50 Rails Contrib

11.

Cats

12.

None

13.

Can you keep Ruby weird?

14.

%CP%CP

15.

'XGT[QPG%CP%CP

16.

Thank You!

17.

Algorithms:

18.

I went to Georgia Tech for…

19.

Mechanical   Engineering

20.

Self taught Programmer ~8 years

21.

CS is boring to me

22.

Programming is interesting

23.

Building programs that accomplish tasks

24.

But…

25.

Those CS students are on to something

26.

Algorithms

27.

Are

28.

Beautiful

29.

<3

30.

Algorithms solve problems

31.

Introducting A Problem…

32.

Spelling

33.

When you are tired, or distracted spelling becomes harder

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...

35.

How does Git know?

36.

Introducing:  Edge Distance

37.

The “cost” to change one word to another

38.

Less “cost” means less more likely match

39.

Cost of? zat => bat

40.

Cost of? zat => bat 1

41.

Cost of? zzat => bat

42.

Cost of? bat 2 zzat =>

43.

How do we code it though?

44.

My First Attempt

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 =>

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

47.

Perfect?

48.

saturday sunday Cost = ?

49.

saturday sunday Cost = 7

50.

Wat?

51.

Turns out I almost recreated

52.

Hamming Distance

53.

Hamming AKA: Signal Distance

54.

Measures: the errors introduced in a string Hamming

55.

Only valid for strings of same length Hamming

56.

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

57.

Bad for: mis- spelled words Hamming

58.

Does not include: Insertion  Deletion Hamming

59.

Introducing:  An Algorithm!

60.

Introducing:  Levenshtein Distance

61.

How do we calculate deletion?

62.

distance("schneems", "zschneems")

63.

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

64.

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

65.

How do we calculate insertion?

66.

distance("schneems", "chneems")

67.

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

68.

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

69.

substitution?

70.

distance("zchneems", "schneems") Substitution

71.

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

72.

How do we calculate Distance?

73.

Pretend we have a distance() method

74.

Strings of different lengths

75.

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

76.

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

77.

Calculate distance between every substring

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

79.

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

80.

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

81.

Pick the cheapest operation, then add one

82.

What about when characters match?

83.

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

84.

Our powers combined, we form!

85.

None

86.

`

87.

Recursive Levenshtein Distance!

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

89.

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

90.

Much better

91.

What does that look like?

92.

None

93.

github.com/ schneems/ going_the_distance

94.

Hmm…

95.

“Dirty Distance” took 8 comparisons

96.

“Recursive” took 1647 comparisons

97.

No trophy, no flowers, no flashbulbs, no wine,

98.

Ouch

99.

Can we do better?

100.

If you watch the recursive algorithm closely, you notice repeats

101.

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

102.

I want you to join the club

103.

A members only club

104.

Matrix:  Levenshtein Distance

105.

Matrix:  Levenshtein Distance

106.

“” => “saturday” Cost?

107.

+---+---+ | | S | +---+---+ | | 1 |
+---+---+ Matrix

108.

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

109.

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

110.

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

111.

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

112.

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

113.

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

114.

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

115.

“sunday” => “” Cost?

116.

+---+---+ | | | +---+---+ | | 0 | +---+---+
| S | 1 | +---+---+ Matrix

117.

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

118.

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

119.

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

120.

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

121.

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

122.

Now, fill in the matrix

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

124.

Break it down

125.

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

126.

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

127.

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

128.

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

129.

How do we calculate insertion programmatically?

130.

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

131.

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

132.

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

133.

+---+---+---+---+ | | | S | A | +---+---+---+---+ |

134.

+---+---+---+---+ | | | S | A | +---+---+---+---+ |

135.

+ cost of change (+1)

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

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

138.

Keep Going

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)

140.

Next Char “su” => “s”

141.

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

142.

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

143.

Deletion

144.

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

145.

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

146.

+---+---+---+ | | | S | +---+---+---+ | | 0

147.

+---+---+---+ | | | S | +---+---+---+ | | 0

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

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

150.

- Insertion - Deletion - Substitution

151.


152.

Substitution

153.

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

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]

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]

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

157.


158.


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

160.


161.

What about match?

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]

163.

Why?

164.

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

165.

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

166.

Now What?

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

168.

Iterate!

169.

None

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

171.

We can also get cost of sub strings

172.

“sun” => “sat”

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

174.

Better than Recursive?

175.

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

176.

48 iterations

177.

Wayyyyyy better than 1647

178.

bit.ly/ going_the_distance

179.

My Problem

180.

I am human

181.

I get tired

182.

Machines don’t understand tired

183.

One day I tried typing

184.

$ rails generate migration

185.

But accidentally typed

186.

$ rails generate migratoon

187.

ERROR

188.

None

189.

Stress is increased when we fail at simple tasks

190.

Why? It’s not hard

191.

Why can’t my software be more like git?

192.

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

193.

None

194.

When you have ERROR

195.

Compare given command to possible commands

196.

Recommend smallest distance.

197.

Google:

198.

Google:

199.

Read A lot of words from real books

200.

~1+ million words

201.

Count Each word

202.

Higher count, higher probability

203.

Get edit distance between input and dictionary

204.

Lower edit, higher probability

205.

Show Suggestion

206.

None

207.

Cache correct spelling suggestions

208.

did_you_mean gem

209.

None

210.

More distance measurements

211.

Levenshtein Distance

212.

Hamming Distance

213.

longest common subsequence Distance

214.

Manhattan Distance

215.

Tree Distance

216.

Jaro-Winkler Distance

217.

Many Many More

218.

Algorithms are Awesome

219.

Where to go next?

220.

I want to learn more about algorithms?

221.

Wikipedia!

222.

Rosetta code

223.

Give an algorithm talk

224.

Everyone suggests a new Algorithm!

225.

Algorithms are a way of sharing knowledge

226.

Expand your knowledge Explore Algorithms

227.

Antepenultimate Slide

228.

YAY!

229.

Questions @schneems

230.

Going The Distance

Going The Distance

Going The Distance

Want more?

Transcript