Module: Algorithms::Sort

Defined in:
lib/algorithms/sort.rb

Overview

rdoc

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

MIT License

Copyright (c) 2009 Kanwei Li

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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]



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# File 'lib/algorithms/sort.rb', line 37

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]



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# File 'lib/algorithms/sort.rb', line 60

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

.dualpivot(container, left = 0, right = container.size-1, div = 3) ⇒ Object 



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# File 'lib/algorithms/sort.rb', line 299

def self.dualpivot(container, left=0, right=container.size-1, div=3)
  length = right - left
  if length < 27 # insertion sort for tiny array
    container.each_with_index do |data,i|
      j = i - 1
      while j >= 0
        break if container[j] <= data
        container[j + 1] = container[j]
        j = j - 1
      end
      container[j + 1] = data
    end
  else # full dual-pivot quicksort
    third = length / div
    # medians
    m1 = left + third
    m2 = right - third
    if m1 <= left
      m1 = left + 1
    end
    if m2 >= right
      m2 = right - 1
    end
    if container[m1] < container[m2]
      dualpivot_swap(container, m1, left)
      dualpivot_swap(container, m2, right)
    else
      dualpivot_swap(container, m1, right)
      dualpivot_swap(container, m2, left)
    end
    # pivots
    pivot1 = container[left]
    pivot2 = container[right]
    # pointers
    less = left + 1
    great = right - 1
    # sorting
    k = less
    while k <= great
      if container[k] < pivot1
        dualpivot_swap(container, k, less += 1)
      elsif container[k] > pivot2
        while k < great && container[great] > pivot2
          great -= 1
        end
        dualpivot_swap(container, k, great -= 1)
        if container[k] < pivot1
          dualpivot_swap(container, k, less += 1)
        end
      end
      k += 1
    end
    # swaps
    dist = great - less
    if dist < 13
      div += 1
    end
    dualpivot_swap(container, less-1, left)
    dualpivot_swap(container, great+1, right)
    # subarrays
    dualpivot(container, left, less-2, div)
    dualpivot(container, great+2, right, div)
    # equal elements
    if dist > length - 13 && pivot1 != pivot2
      for k in less..great do
        if container[k] == pivot1
          dualpivot_swap(container, k, less)
          less += 1
        elsif container[k] == pivot2
          dualpivot_swap(container, k, great)
          great -= 1
          if container[k] == pivot1
            dualpivot_swap(container, k, less)
            less += 1
          end
        end
      end
    end
    # subarray
    if pivot1 < pivot2
      dualpivot(container, less, great, div)
    end
    container
  end
end

.dualpivot_swap(container, i, j) ⇒ Object 



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# File 'lib/algorithms/sort.rb', line 385

def self.dualpivot_swap(container, i, j)
  container[i],  container[j] = container[j],  container[i]
end

.dualpivotquicksort(container) ⇒ Object

Dual-Pivot Quicksort is a variation of Quicksort by Vladimir Yaroslavskiy. This is an implementation of the algorithm as it was found in the original research paper:

iaroslavski.narod.ru/quicksort/DualPivotQuicksort.pdf

Mirror: codeblab.com/wp-content/uploads/2009/09/DualPivotQuicksort.pdf

“This algorithm offers O(n log(n)) performance on many data sets that cause other quicksorts to degrade to quadratic performance, and is typically faster than traditional (one-pivot) Quicksort implementations.”

-- http://download.oracle.com/javase/7/docs/api/java/util/Arrays.html

The algorithm was improved by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch, and was implemented as the default sort algorithm for primatives in Java 7.

Implementation in the Java JDK as of November, 2011: www.docjar.com/html/api/java/util/DualPivotQuicksort.java.html

It is proved that for the Dual-Pivot Quicksort the average number of comparisons is 2*n*ln(n), the average number of swaps is 0.8*n*ln(n), whereas classical Quicksort algorithm has 2*n*ln(n) and 1*n*ln(n) respectively. This has been fully examined mathematically and experimentally.

Requirements: Container should implement #pop and include the Enumerable module. Time Complexity: О(n log n) average, О(n log n) worst-case Space Complexity: О(n) auxiliary

Stable: No

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



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# File 'lib/algorithms/sort.rb', line 294

def self.dualpivotquicksort(container)
  return container if container.size <= 1
  dualpivot(container, 0, container.size-1, 3)
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]



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# File 'lib/algorithms/sort.rb', line 106

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]



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# File 'lib/algorithms/sort.rb', line 121

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 



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# File 'lib/algorithms/sort.rb', line 251

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]



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# File 'lib/algorithms/sort.rb', line 243

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



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# File 'lib/algorithms/sort.rb', line 175

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



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# File 'lib/algorithms/sort.rb', line 201

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]



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# File 'lib/algorithms/sort.rb', line 88

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]



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# File 'lib/algorithms/sort.rb', line 143

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