Add dualpivotquicksort (Dual-Pivot Quicksort)

Dual-Pivot Quicksort is a variation of Quicksort by
Vladimir Yaroslavskiy.

"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

Author: mhutchin

README.markdown

@@ -41,6 +41,7 @@ compare performance in different situations.
       - Shell sort               Algorithms::Sort.shell_sort
       - Quicksort                Algorithms::Sort.quicksort
       - Mergesort                Algorithms::Sort.mergesort
+      - Dual-Pivot Quicksort     Algorithms::Sort.dualpivotquicksort
 
 ## SYNOPSIS:
 

lib/algorithms.rb

@@ -43,6 +43,7 @@
     - Shell sort            - Algorithms::Sort.shell_sort
     - Quicksort             - Algorithms::Sort.quicksort
     - Mergesort             - Algorithms::Sort.mergesort
+    - Dual-Pivot Quicksort  - Algorithms::Sort.dualpivotquicksort
   * String algorithms
     - Levenshtein distance  - Algorithms::String.levenshtein_dist
 =end

lib/algorithms/sort.rb

@@ -235,4 +235,134 @@ def self.merge(left, right)
     sorted + left + right
   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:
+  # 
+  # http://iaroslavski.narod.ru/quicksort/DualPivotQuicksort.pdf
+  # 
+  # Mirror:
+  # http://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:
+  # http://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]
+
+  def self.dualpivotquicksort(container)
+    return container if container.size <= 1
+    dualpivot(container, 0, container.size-1, 3)
+  end
+ 
+  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
+
+  def self.dualpivot_swap(container, i, j)
+    container[i],  container[j] = container[j],  container[i]
+  end
 end
+

spec/sort_spec.rb

@@ -4,7 +4,8 @@
 
 describe "sort algorithms" do
   before(:each) do
-    @sorts = %w(bubble_sort comb_sort selection_sort heapsort insertion_sort shell_sort quicksort mergesort)
+    @sorts = %w(bubble_sort comb_sort selection_sort heapsort insertion_sort 
+      shell_sort quicksort mergesort dualpivotquicksort)
   end
 
   it "should work for empty containers" do