This module implements sorting algorithms. Documentation is provided for each algorithm.
Methods
Public Class
Public Class methods
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]
# 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: 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]
# 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
# File lib/algorithms/sort.rb, line 278 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
# File lib/algorithms/sort.rb, line 364 def self.dualpivot_swap(container, i, j) container[i], container[j] = container[j], container[i] end
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]
# File lib/algorithms/sort.rb, line 273 def self.dualpivotquicksort(container) return container if container.size <= 1 dualpivot(container, 0, container.size-1, 3) end
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]
# 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: 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]
# 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
# 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: 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]
# 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
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
# 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
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
# 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: 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]
# 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: 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]
# 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