Module: Algorithms::Sort

Defined in:
lib/algorithms/sort.rb

Overview

This module implements sorting algorithms. Documentation is provided for each algorithm.

Class Method Summary collapse

Class Method Details

.bubble_sort(container) ⇒ Object

Bubble sort: A very naive sort that keeps swapping elements until the container is sorted. Requirements: Needs to be able to compare elements with <=>, and the [] []= methods should be implemented for the container. Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.bubble_sort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


16
17
18
19
20
21
22
23
24
25
26
27
28
# File 'lib/algorithms/sort.rb', line 16

def self.bubble_sort(container)
  loop do
    swapped = false
    (container.size-1).times do |i|
      if (container[i] <=> container[i+1]) == 1
        container[i], container[i+1] = container[i+1], container[i] # Swap
        swapped = true
      end
    end
    break unless swapped
  end
  container
end

.comb_sort(container) ⇒ Object

Comb sort: A variation on bubble sort that dramatically improves performance. Source: yagni.com/combsort/ Requirements: Needs to be able to compare elements with <=>, and the [] []= methods should be implemented for the container. Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.comb_sort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
# File 'lib/algorithms/sort.rb', line 39

def self.comb_sort(container)
  container
  gap = container.size
  loop do
    gap = gap * 10/13
    gap = 11 if gap == 9 || gap == 10
    gap = 1 if gap < 1
    swapped = false
    (container.size - gap).times do |i|
      if (container[i] <=> container[i + gap]) == 1
        container[i], container[i+gap] = container[i+gap], container[i] # Swap
        swapped = true
      end
    end
    break if !swapped && gap == 1
  end
  container
end

.heapsort(container) ⇒ Object

Heap sort: Uses a heap (implemented by the Containers module) to sort the collection. Requirements: Needs to be able to compare elements with <=> Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.heapsort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


85
86
87
88
89
90
# File 'lib/algorithms/sort.rb', line 85

def self.heapsort(container)
  heap = Containers::Heap.new(container)
  ary = []
  ary << heap.pop until heap.empty?
  ary
end

.insertion_sort(container) ⇒ Object

Insertion sort: Elements are inserted sequentially into the right position. Requirements: Needs to be able to compare elements with <=>, and the [] []= methods should be implemented for the container. Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.insertion_sort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


100
101
102
103
104
105
106
107
108
109
110
111
112
# File 'lib/algorithms/sort.rb', line 100

def self.insertion_sort(container)
  return container if container.size < 2
  (1..container.size-1).each do |i|
    value = container[i]
    j = i-1
    while j >= 0 and container[j] > value do
      container[j+1] = container[j]
      j = j-1
    end
    container[j+1] = value
  end
  container
end

.merge(left, right) ⇒ Object



230
231
232
233
234
235
236
# File 'lib/algorithms/sort.rb', line 230

def self.merge(left, right)
  sorted = []
  until left.empty? or right.empty?
    left.first <= right.first ? sorted << left.shift : sorted << right.shift
  end
  sorted + left + right
end

.mergesort(container) ⇒ Object

Mergesort: A stable divide-and-conquer sort that sorts small chunks of the container and then merges them together. Returns an array of the sorted elements. Requirements: Container should implement [] Time Complexity: О(n log n) average and worst-case Space Complexity: О(n) auxiliary Stable: Yes

Algorithms::Sort.mergesort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


222
223
224
225
226
227
228
# File 'lib/algorithms/sort.rb', line 222

def self.mergesort(container)
  return container if container.size <= 1
  mid   = container.size / 2
  left  = container[0...mid]
  right = container[mid...container.size]
  merge(mergesort(left), mergesort(right))
end

.partition(data, left, right) ⇒ Object

Quicksort: A divide-and-conquer sort that recursively partitions a container until it is sorted. Requirements: Container should implement #pop and include the Enumerable module. Time Complexity: О(n log n) average, O(n^2) worst-case Space Complexity: О(n) auxiliary Stable: No

Algorithms::Sort.quicksort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]

def self.quicksort(container)

return [] if container.empty?

x, *xs = container

quicksort(xs.select { |i| i <  x }) + [x] + quicksort(xs.select { |i| i >= x })

end



154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
# File 'lib/algorithms/sort.rb', line 154

def self.partition(data, left, right)
  pivot = data[front]
  left += 1

  while left <= right do
    if data[frontUnknown] < pivot
      back += 1
      data[frontUnknown], data[back] = data[back], data[frontUnknown] # Swap
    end

    frontUnknown += 1
  end

  data[front], data[back] = data[back], data[front] # Swap
  back
end

.quicksort(container) ⇒ Object

def self.quicksort(container, left = 0, right = container.size - 1)

if left < right 
  middle = partition(container, left, right)
  quicksort(container, left, middle - 1)
  quicksort(container, middle + 1, right)
end

end



180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
# File 'lib/algorithms/sort.rb', line 180

def self.quicksort(container)
  bottom, top = [], []
  top[0] = 0
  bottom[0] = container.size
  i = 0
  while i >= 0 do
    l = top[i]
    r = bottom[i] - 1;
    if l < r
      pivot = container[l]
      while l < r do
        r -= 1 while (container[r] >= pivot  && l < r)
        if (l < r)
          container[l] = container[r]
          l += 1
        end
        l += 1 while (container[l] <= pivot  && l < r)
        if (l < r)
          container[r] = container[l]
          r -= 1
        end
      end
      container[l] = pivot
      top[i+1] = l + 1
      bottom[i+1] = bottom[i]
      bottom[i] = l
      i += 1
    else
      i -= 1
    end
  end
  container    
end

.selection_sort(container) ⇒ Object

Selection sort: A naive sort that goes through the container and selects the smallest element, putting it at the beginning. Repeat until the end is reached. Requirements: Needs to be able to compare elements with <=>, and the [] []= methods should be implemented for the container. Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.selection_sort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


67
68
69
70
71
72
73
74
75
76
# File 'lib/algorithms/sort.rb', line 67

def self.selection_sort(container)
  0.upto(container.size-1) do |i|
    min = i
    (i+1).upto(container.size-1) do |j|
      min = j if (container[j] <=> container[min]) == -1
    end
    container[i], container[min] = container[min], container[i] # Swap
  end
  container
end

.shell_sort(container) ⇒ Object

Shell sort: Similar approach as insertion sort but slightly better. Requirements: Needs to be able to compare elements with <=>, and the [] []= methods should be implemented for the container. Time Complexity: О(n^2) Space Complexity: О(n) total, O(1) auxiliary Stable: Yes

Algorithms::Sort.shell_sort [5, 4, 3, 1, 2] => [1, 2, 3, 4, 5]


122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
# File 'lib/algorithms/sort.rb', line 122

def self.shell_sort(container)
  increment = container.size/2
  while increment > 0 do
    (increment..container.size-1).each do |i|
      temp = container[i]
      j = i
      while j >= increment && container[j - increment] > temp do
        container[j] = container[j-increment]
        j -= increment
      end
      container[j] = temp
    end
    increment = (increment == 2 ? 1 : (increment / 2.2).round)
  end
  container
end