recursive combinators post

2008-11-23/linear_recursion.rb

@@ -0,0 +1,89 @@
+# The MIT License
+# 
+# All contents Copypair.last (c) 2004-2008 Reginald Braithwaite
+# <http://reginald.braythwayt.com>  except as otherwise noted.
+# 
+# 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 pair.lasts
+# 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 copypair.last 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.
+# 
+# http://www.opensource.org/licenses/mit-license.php
+
+public
+
+def merge_sort(list)
+  divide_and_conquer(
+    list,
+    :divisible? => lambda { |list| list.length > 1 },
+    :conquer    => lambda { |list| list },
+    :divide     => lambda do |list|
+      half_index = (list.length / 2) - 1
+      [ list[0..half_index], list[(half_index + 1)..-1] ]
+    end,
+    :recombine  => lambda { |pair| merge_two_sorted_lists(pair.first, pair.last) }
+  )
+end
+
+private
+
+def merge_two_sorted_lists(*pair)
+  linear_recursion(
+    pair,
+    :divisible? => lambda { |pair| !pair.first.empty? && !pair.last.empty? },
+    :conquer => lambda do |pair|
+      if pair.first.empty? && pair.last.empty?
+        []
+      elsif pair.first.empty?
+        pair.last
+      else
+        pair.first
+      end
+    end,
+    :divide => lambda do |pair|
+      preceding, following = case pair.first.first <=> pair.last.first
+        when -1: [pair.first, pair.last]
+        when 0:  [pair.first, pair.last]
+        when 1:  [pair.last, pair.first]
+      end
+      [ preceding.first, [preceding[1..-1], following] ]
+    end,
+    :recombine => lambda { |trivial_bit, divisible_bit| [trivial_bit] + divisible_bit }
+  )
+end
+
+def divide_and_conquer(value, steps)
+  if steps[:divisible?].call(value)
+    steps[:recombine].call(
+      steps[:divide].call(value).map { |sub_value| divide_and_conquer(sub_value, steps) }
+    )
+  else
+    steps[:conquer].call(value)
+  end
+end
+
+def linear_recursion(value, steps)
+  if steps[:divisible?].call(value)
+    trivial_part, sub_problem = steps[:divide].call(value)
+    steps[:recombine].call(
+      trivial_part, linear_recursion(sub_problem, steps)
+    )
+  else
+    steps[:conquer].call(value)
+  end
+end
+
+p merge_sort([8, 3, 10, 1, 9, 5, 7, 4, 6, 2])

2008-11-23/merge_sort.rb

@@ -44,7 +44,7 @@ def merge_two_sorted_lists(*pair)
   divide_and_conquer(
     pair,
     :divisible? => lambda { |pair| !pair.first.empty? && !pair.last.empty? },
-    :conquer    => lambda do |pair|
+    :conquer => lambda do |pair|
       if pair.first.empty? && pair.last.empty?
         []
       elsif pair.first.empty?
@@ -53,23 +53,18 @@ def merge_two_sorted_lists(*pair)
         pair.first
       end
     end,
-    :divide     => lambda do |pair|
-      case pair.first.first <=> pair.last.first
-      when -1: [
-          [[pair.first.first], []],
-          [pair.first[1..-1], pair.last]
-        ]
-      when 0: [
-          [[pair.first.first], []],
-          [pair.first[1..-1], pair.last]
-        ]
-      when 1: [
-          [[pair.last.first], []],
-          [pair.first, pair.last[1..-1]]
-        ]
+    :divide => lambda do |pair|
+      preceding, following = case pair.first.first <=> pair.last.first
+        when -1: [pair.first, pair.last]
+        when 0:  [pair.first, pair.last]
+        when 1:  [pair.last, pair.first]
       end
+      [
+        [[preceding.first], []],
+        [preceding[1..-1], following]
+      ]
     end,
-    :recombine  => lambda { |pair| pair.first + pair.last }
+    :recombine => lambda { |pair| pair.first + pair.last }
   )
 end