Algorithms: CLRS in Ruby

One of the most celebrated books in Computer Science academia is "Introduction to Algorithms," also known as "CLRS" after its 4 authors. It's the go-to (pun!) textbook for many intermediate college courses, and this talk will introduce some of its many wonderful algorithms in Ruby form, including: various sorting techniques, dynamic programming, and some fun graph techniques. If you want a theory-heavy lecture, this talk is NOT for you!

Transcript

1. ALGORITHMS
   CLRS IN RUBY
   

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2. rubyconf 2019
   BRAD GRZESIAK
   ‣ 2002 ICPC WORLD FINALS:
   11TH PLACE
   ‣ FORMER AEROSPACE
   ENGINEER
   ‣ FOUNDER/CEO OF
   BENDYWORKS
   ‣ PORTED matrix TO ruby
   @LISTROPHY
   

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3. rubyconf 2019
   SYLLABUS
   ‣ COMPLEXITY
   ‣ INSERTION SORT
   ‣ QUICK SORT
   ‣ BUCKET SORT
   ‣ LONGEST COMMON SUBSEQUENCE
   ‣ MINIMUM SPANNING TREE
   ‣ SHORTEST PATH
   ‣ MAX FLOW
   

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4. rubyconf 2019
   INTRODUCTION TO
   ALGORITHMS
   ‣ CORMEN
   ‣ LEISERSON
   ‣ RIVEST
   ‣ STEIN
   

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5. rubyconf 2019
   COMPLEXITY
   

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6. rubyconf 2019
   COMPLEXITY
   hNoHereComes
   ( _ )
   O
   thing(s)!
   

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7. rubyconf 2019
   COMPLEXITY
   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
   O(1)
   a[4]
   O(n)
   a.map
   O(log n)
   a.bsearch
   V
   D T X
   B F N R U W Y
   P
   H
   L
   J
   A C E G I K M O Q S U V W X Y Z
   

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8. rubyconf 2019
   COMPLEXITY
   O(1)
   O(log n)
   O(n)
   O(n log n)
   O(n²)
   great!
   ok
   hmmm
   uffda
   oh no
   

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9. rubyconf 2019
   SORTING
   

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10. rubyconf 2019
    INSERTION SORT
    

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11. rubyconf 2019
    SORTING
    INSERTION SORT
    (1...length).each do |right|
    subject = self[right]
    left = right - 1
    while left > -1 && self[left] > self[right]
    self[left + 1] = self[left]
    left += 1
    end
    self[left + 1] = subject
    end
    

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12. rubyconf 2019
    INSERTION SORT DEMO
    

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13. rubyconf 2019
    INSERTION SORT
    COMPLEXITY
    O(n²)
    

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14. rubyconf 2019
    QUICK SORT
    

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15. rubyconf 2019
    SORTING
    QUICK SORT
    def quicksort
    qsort_help(0, self.length - 1)
    end
    def qsort_help(p, r)
    return unless p < r
    q = partition(p, r)
    qsort_help(p, q - 1)
    qsort_help( q + 1, r)
    end
    def partition(p, r)
    x = self[r]
    i = p - 1
    (p...r).each do |j|
    if self[j] <= x
    i += 1
    swap(i, j)
    end
    end
    swap(i + 1, r)
    i + 1
    end
    

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16. rubyconf 2019
    QUICK SORT DEMO
    

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17. rubyconf 2019
    QUICK SORT
    COMPLEXITY
    O(n log n)
    

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18. rubyconf 2019
    SORTING
    TWITTER POLL
    

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19. rubyconf 2019
    BUCKET SORT
    

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20. rubyconf 2019
    SORTING
    BUCKET SORT
    def bucket_sort
    b = Array.new(length)
    each_with_index do |val, idx|
    b[val] = val
    end
    replace(b)
    end
    def bucket_sort
    b = Array.new(length)
    mx = max
    (0...length).each do |i|
    idx = length * (self[i] / mx)
    b[idx] ||= []
    b[idx] << self[i]
    end
    b.each(&:insertion_sort!)
    replace(b.flatten.compact)
    end
    

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21. rubyconf 2019
    BUCKET SORT DEMO
    

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22. rubyconf 2019
    BUCKET SORT
    COMPLEXITY
    O(n) ?
    

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23. rubyconf 2019
    DYNAMIC
    PROGRAMMING
    

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24. rubyconf 2019
    LONGEST COMMON
    SUBSEQUENCE
    

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25. rubyconf 2019
    DYNAMIC PROGRAMMING
    LONGEST COMMON SUBSEQUENCE
    ATCGG G
    C TTTGC
    ACCAC G
    C TAACA
    

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26. rubyconf 2019
    DYNAMIC PROGRAMMING
    LONGEST COMMON SUBSEQUENCE
    def command
    return @command if @command
    @command = Message::Command...
    @command ||= Message::Command...
    ...
    end
    def subject
    @subject ||= sentence
    .nouns
    .reject...
    end
    def command
    @command = Message::Command...
    @command ||= Message::Command...
    ...
    end
    def subject
    @subject ||= sentence.nouns.reject...
    end
    github.com/CoralineAda/alice
    

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27. rubyconf 2019
    DYNAMIC PROGRAMMING
    LONGEST COMMON SUBSEQUENCE ( ABCDEF 㱻 BDF )
    A B C D E F
    B
    D
    F
    0 1 1 1 1 1
    0 1 1 2 2 2
    0 1 1 2 2 3
    if match?(top, left)
    1 + ⬉
    else
    [‐, ‏].max
    end
    O(n∙m)
    

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28. rubyconf 2019
    LONGEST COMMON SUBSEQUENCE
    def lcs
    setup
    compute_matrix
    @matrix.last.last
    end
    def setup
    @matrix = Array.new(@a.length + 1) do
    Array.new(@b.length + 1, 0)
    end
    end
    def compute_matrix
    (1..(@a.length)).each do |i|
    (1..(@b.length)).each do |j|
    compute_cell(i, j)
    end
    end
    end
    def compute_cell(i, j)
    @matrix[i][j] =
    if @a[i - 1] == @b[j - 1]
    matches(i, j)
    else
    does_not_match(i, j)
    end
    end
    def matches(i, j)
    @matrix[i - 1][j - 1] + 1
    end
    def does_not_match(i, j)
    [ @matrix[i - 1][j],
    @matrix[i][j - 1]
    ].max
    end
    

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29. rubyconf 2019
    GRAPHS
    

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30. rubyconf 2019
    MINIMUM SPANNING
    TREE
    

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31. rubyconf 2019
    GRAPHS
    MINIMUM SPANNING TREE
    A
    H G F
    E
    I
    B C D
    8
    4
    11
    7
    1
    2
    4
    8 7
    14
    10
    9
    2
    

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32. rubyconf 2019
    GRAPHS
    MINIMUM SPANNING TREE (PRIM'S ALGORITHM)
    A
    H G F
    E
    I
    B C D
    8
    4
    11
    7
    1
    2
    4
    8 7
    14
    10
    9
    2
    vertices.map { |u| u.key = ∞ }
    queue = PQueue.new(vertices)
    until queue.empty?
    u = queue.extract
    u.neighbors.each do |v, w|
    if queue.has?(v) && w < v.key
    v.parent = u
    v.key = w
    end
    end
    end
    A B H G F C I D E
    O(E+V log V)
    

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33. rubyconf 2019
    SHORTEST PATH
    

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34. rubyconf 2019
    GRAPHS
    SHORTEST PATH (DIJKSTRA'S ALGORITHM)
    A
    H G F
    E
    I
    B C D
    8
    4
    11
    7
    1
    2
    4
    8 7
    14
    10
    9
    2
    queue = PQueue.new(nodes)
    until queue.empty?
    u = queue.extract_first
    adj[u.name].each_pair do |v, w|
    u.relax(v, w)
    end
    end
    class Node
    # ...
    def relax(other, w)
    if other.d > (d + w)
    other.d = d + w
    other.parent = self
    end
    end
    end
    A B H G F C I D E
    0
    8
    4
    12
    15
    9 11
    25
    21
    14
    19
    O(E+V log V)
    

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35. rubyconf 2019
    MAX FLOW
    

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36. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    loop do
    # find any path from s to t
    p = find_path(s, t,
    edges.reject {|_names, e| e.capacity == 0 })
    break if p.empty?
    # find the segement with least remaining capacity
    segs = segments(p)
    residual_capacity_p = segs.map do |uv|
    edges[uv].residual_capacity
    end.min
    segs.each do |(u, v)|
    # add that capacity to each edge
    edges[[u, v]].flow += residual_capacity_p
    # if we need to reverse the flow in the future:
    edges[[v, u]].flow = -edges[[u, v]].flow
    end
    end
    

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37. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    

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38. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    4
    4
    4
    

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39. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    12
    4
    4
    12
    4
    12
    

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40. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    12
    4
    4
    12
    7
    4
    12
    

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41. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    12
    11
    11
    12
    7
    4
    19
    

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42. rubyconf 2019
    GRAPHS
    MAX FLOW (FORD-FULKERSON ALGORITHM)
    S
    D
    C
    B
    A
    T
    16
    13
    4
    10
    12
    9
    14
    7
    20
    4
    12
    0
    0
    11
    11
    0
    12
    7
    4
    19
    O(E |f *|)
    

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43. rubyconf 2019
    THANK YOU
    @listrophy
    @bendyworks
    COMPLEXITY
    INSERTION SORT
    QUICK SORT
    BUCKET SORT
    LONGEST COMMON SUBSEQUENCE
    MINIMUM SPANNING TREE
    SHORTEST PATH
    MAX FLOW
    gitlab.com/listrophy/clrs-algorithms/
    

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