From 990ec8b39e9fd206986337ec7c7b46444c8b7a72 Mon Sep 17 00:00:00 2001
From: Shanthi Pendleton <pendletons@users.noreply.github.com>
Date: Tue, 25 Oct 2016 15:20:56 +0100
Subject: [PATCH] Fast alphametics solver (uses simplified partial equations to
 limit set of viable permutations)

---
 exercises/allergies/allergies_test.rb         |   1 -
 exercises/alphametics/example.rb              | 163 +++++++++++-------
 exercises/atbash-cipher/atbash_cipher_test.rb |   1 -
 exercises/beer-song/beer_song_test.rb         |   3 +-
 .../binary_search_tree_test.rb                |   2 +-
 exercises/binary/example.rb                   |   1 -
 .../circular-buffer/circular_buffer_test.rb   |   2 -
 exercises/clock/example.rb                    |   2 -
 exercises/connect/connect_test.rb             |   1 -
 exercises/custom-set/custom_set_test.rb       |   1 -
 exercises/diamond/diamond_test.rb             |   1 -
 exercises/etl/etl_test.rb                     |   2 +-
 exercises/house/house_test.rb                 |   1 -
 exercises/largest-series-product/example.tt   |   3 -
 .../largest_series_product_test.rb            |   4 -
 exercises/linked-list/linked_list_test.rb     |   2 +-
 exercises/meetup/meetup_test.rb               |   1 -
 exercises/nth-prime/example.tt                |   2 -
 exercises/nth-prime/nth_prime_test.rb         |   2 -
 exercises/ocr-numbers/ocr_numbers_test.rb     |   3 +-
 .../protein_translation_test.rb               |   1 -
 exercises/proverb/proverb_test.rb             |   4 +-
 exercises/queen-attack/queen_attack_test.rb   |   6 +-
 .../robot-simulator/robot_simulator_test.rb   |   2 +-
 exercises/strain/strain_test.rb               |   4 +-
 25 files changed, 111 insertions(+), 104 deletions(-)

diff --git a/exercises/allergies/allergies_test.rb b/exercises/allergies/allergies_test.rb
index e7f6b45aee..9a60b6559a 100755
--- a/exercises/allergies/allergies_test.rb
+++ b/exercises/allergies/allergies_test.rb
@@ -59,7 +59,6 @@ def test_allergic_to_lots_of_stuff
   def test_allergic_to_everything
     skip
     allergies = Allergies.new(255)
-    # rubocop:disable Metrics/LineLength
     expected = %w(eggs peanuts shellfish strawberries tomatoes chocolate pollen cats)
     assert_equal expected, allergies.list
   end
diff --git a/exercises/alphametics/example.rb b/exercises/alphametics/example.rb
index 2a20e14b26..49446d4326 100644
--- a/exercises/alphametics/example.rb
+++ b/exercises/alphametics/example.rb
@@ -1,98 +1,135 @@
 module BookKeeping
-  VERSION = 3
+  VERSION = 4
 end
 
 class Alphametics
-  def solve(puzzle)
-    letters = Hash.new(0)
-    puzzle.scan(/[a-zA-Z]/) { |w| letters[w] += 1 }
 
-    possible_values(letters.keys) do |letters_values|
-      return letters_values if valid?(puzzle, letters_values)
-    end
+  def self.solve(equation)
+    new.solve(equation)
+  end
 
-    nil
+  def solve(equation)
+    @prime_solver = AlphaSolver.new(equation)
+    solve_using_partials
   end
 
   private
 
-  def possible_values(letters)
-    (0..9).to_a.combination(letters.length) do |combined_integers|
-      combined_integers.permutation do |permutated_integers|
-         yield permutated_integers.map.with_index { |integer, index|
-           [letters[index], integer]
-         }.to_h
-      end
+  attr_accessor :prime_solver
+
+  def solve_using_partials
+    prime_solver.partial_solutions.each do |partial_solution|
+      sub_solver = AlphaSolver.new(prime_solver.partial_equation(partial_solution))
+      sub_solution = sub_solver.first_solution
+      return sub_solution.merge(partial_solution) if sub_solution
     end
+    {}
   end
 
-  def valid?(puzzle, letters_values)
-    equation = puzzle.gsub(/[a-zA-Z]/, letters_values)
-    Equation.new(equation).valid?
-  end
 end
 
-class Equation
-  attr_reader :equation
+class AlphaSolver
 
-  def initialize(equation)
-    @equation = equation
+  def initialize(input_equation)
+    @input_equation = input_equation.gsub('^', '**')
+    @puzzle = Puzzle.new(input_equation)
   end
 
-  def valid?
-    return false if has_leading_zeros?
+  def partial_solutions
+    AlphaSolver.new(puzzle.simplified).all_solutions
+  end
 
-    expression, result = equation.split('==')
+  def all_solutions
+    numeric_permutations.map { |values| result_table if solution?(values) }.compact
+  end
 
-    numbers = []
-    operators = []
+  def first_solution
+    numeric_permutations.each { |values| return result_table if solution?(values) }
+    nil
+  end
 
-    expression.scan(/\d+|\+|\-|\*|\/|\^/).each do |token|
-      case token
-      when /^\d+$/
-        numbers.push(token.to_i)
-      when '+', '-', '*', '/', '^'
-        calculate_last(numbers, operators) if has_precedence?(operators, token)
-        operators.push(token)
-      end
-    end
+  def partial_equation(partial_solution)
+    input_equation.tr(partial_solution.keys.join, partial_solution.values.join)
+  end
 
-    until operators.empty?
-      calculate_last(numbers, operators)
-    end
+  private
+
+  attr_reader :input_equation, :puzzle
+  attr_accessor :proposed_values
 
-    numbers.last == result.to_i
+  def solution?(values)
+    self.proposed_values = values.join
+    proposed_equation_qualified? && proposed_equation_evaluates?
   end
 
-  private
+  def proposed_equation
+    input_equation.tr(puzzle_letters, proposed_values)
+  end
 
-  def has_leading_zeros?
-    equation.match(/^0\d+|\D0\d+/)
+  def numeric_permutations
+    puzzle.numeric_permutations
   end
 
-  def has_precedence?(operators, token)
-    return false if operators.empty?
-    prev_operator = operators.last
+  def puzzle_letters
+    puzzle.letters
+  end
 
-    case token
-    when '+', '-'
-      prev_operator == '*' || prev_operator == '/' || prev_operator == '^'
-    when '*', '/'
-      prev_operator == '^'
-    else
-      false
-    end
+  def proposed_equation_qualified?
+    (proposed_equation =~ /\b0\d+/).nil?
   end
 
-  def calculate_last(numbers, operators)
-    right = numbers.pop
-    left = numbers.pop
-    operator = as_ruby_operator(operators.pop)
-    result = left.send(operator, right)
-    numbers.push(result)
+  def proposed_equation_evaluates?
+    eval(proposed_equation)
   end
 
-  def as_ruby_operator(operator)
-    operator == '^' ? '**' : operator
+  def result_table
+    Hash[puzzle_letters.chars.zip(result_numbers)]
   end
+
+  def result_numbers
+    proposed_values.chars.map(&:to_i)
+  end
+
 end
+
+class Puzzle
+
+  PATTERNS = {mod_10: ' % 10',
+              adjacent_letters: /(\b)([A-Z]{1,})([A-Z])/,
+              equation_left_side: /(.*)( == )/}
+
+  def initialize(string_equation)
+    @string_equation = string_equation
+  end
+
+  def letters
+    @letters ||= string_equation.scan(/[A-Z]/).uniq.join
+  end
+
+  def numeric_permutations
+    @numeric_permutations ||= unused_numbers.to_a.permutation(letter_count)
+  end
+
+  def simplified
+    @simplified ||= string_equation
+                        .gsub(PATTERNS[:adjacent_letters], "\\1\\3")
+                        .gsub(PATTERNS[:equation_left_side], "(\\1)#{PATTERNS[:mod_10]}\\2")
+  end
+
+  private
+
+  attr_reader :string_equation
+
+  def letter_count
+    @letter_count ||= letters.length
+  end
+
+  def unused_numbers
+    @unused_numbers ||= (0..9).to_a.map(&:to_s) - used_numbers
+  end
+
+  def used_numbers
+    @used_numbers ||= string_equation.gsub(PATTERNS[:mod_10], '').scan(/\d/).uniq
+  end
+
+end
\ No newline at end of file
diff --git a/exercises/atbash-cipher/atbash_cipher_test.rb b/exercises/atbash-cipher/atbash_cipher_test.rb
index 81cf01b539..d2c0dc5536 100755
--- a/exercises/atbash-cipher/atbash_cipher_test.rb
+++ b/exercises/atbash-cipher/atbash_cipher_test.rb
@@ -3,7 +3,6 @@
 require 'minitest/autorun'
 require_relative 'atbash_cipher'
 
-# rubocop:disable Style/MethodName
 class AtbashTest < Minitest::Test
   def test_encode_no
     assert_equal 'ml', Atbash.encode('no')
diff --git a/exercises/beer-song/beer_song_test.rb b/exercises/beer-song/beer_song_test.rb
index 11c51c61ef..01fc5614b7 100755
--- a/exercises/beer-song/beer_song_test.rb
+++ b/exercises/beer-song/beer_song_test.rb
@@ -3,7 +3,6 @@
 require 'minitest/autorun'
 require_relative 'beer_song'
 
-# rubocop:disable Metrics/LineLength
 class BeerSongTest < Minitest::Test
   def test_the_first_verse
     expected = "99 bottles of beer on the wall, 99 bottles of beer.\n" \
@@ -62,7 +61,7 @@ def test_a_few_verses
     assert_equal expected, BeerSong.new.verses(2, 0)
   end
 
-  def test_the_whole_song # rubocop:disable Metrics/MethodLength
+  def test_the_whole_song
     skip
     expected = <<-SONG
 99 bottles of beer on the wall, 99 bottles of beer.
diff --git a/exercises/binary-search-tree/binary_search_tree_test.rb b/exercises/binary-search-tree/binary_search_tree_test.rb
index 3ae1496d55..16b6ae9b61 100755
--- a/exercises/binary-search-tree/binary_search_tree_test.rb
+++ b/exercises/binary-search-tree/binary_search_tree_test.rb
@@ -32,7 +32,7 @@ def test_inserting_right
     assert_equal 5, four.right.data
   end
 
-  def test_complex_tree # rubocop:disable Metrics/MethodLength
+  def test_complex_tree
     skip
     four = Bst.new 4
     four.insert 2
diff --git a/exercises/binary/example.rb b/exercises/binary/example.rb
index 80464cd24b..02847622bb 100644
--- a/exercises/binary/example.rb
+++ b/exercises/binary/example.rb
@@ -19,7 +19,6 @@ def to_decimal
 
   private
 
-  # rubocop:disable Style/WordArray
   def valid?(s)
     s.chars.all? { |char| ['0', '1'].include?(char) }
   end
diff --git a/exercises/circular-buffer/circular_buffer_test.rb b/exercises/circular-buffer/circular_buffer_test.rb
index 86bed08721..725daf591b 100755
--- a/exercises/circular-buffer/circular_buffer_test.rb
+++ b/exercises/circular-buffer/circular_buffer_test.rb
@@ -89,7 +89,6 @@ def test_forced_writes_to_non_full_buffer_should_behave_like_writes
     assert_raises(CircularBuffer::BufferEmptyException) { buffer.read }
   end
 
-  # rubocop:disable Metrics/MethodLength
   def test_alternate_read_and_write_into_buffer_overflow
     skip
     buffer = CircularBuffer.new(5)
@@ -108,5 +107,4 @@ def test_alternate_read_and_write_into_buffer_overflow
     assert_equal 'B', buffer.read
     assert_raises(CircularBuffer::BufferEmptyException) { buffer.read }
   end
-  # rubocop:enable Metrics/MethodLength
 end
diff --git a/exercises/clock/example.rb b/exercises/clock/example.rb
index 579b7a8d02..fb26f26421 100644
--- a/exercises/clock/example.rb
+++ b/exercises/clock/example.rb
@@ -12,7 +12,6 @@ def initialize(hours=0, minutes=0)
     @internal = hours * 60 + minutes
   end
 
-  # rubocop:disable Style/OpMethod
   def +(hours=0, minutes)
     @internal += hours * 60 + minutes
     self
@@ -21,7 +20,6 @@ def +(hours=0, minutes)
   def -(*args)
     self.+(*args.map(&:-@))
   end
-  # rubocop:enable Style/OpMethod
 
   def ==(other)
     to_s == other.to_s
diff --git a/exercises/connect/connect_test.rb b/exercises/connect/connect_test.rb
index 82b65c5b41..a517fe948f 100755
--- a/exercises/connect/connect_test.rb
+++ b/exercises/connect/connect_test.rb
@@ -95,7 +95,6 @@ def test_x_wins_using_a_convoluted_path
     assert_equal 'X', game.winner, 'X wins using a convoluted path'
   end
 
-  # rubocop:disable MethodLength
   def test_x_wins_using_a_spiral_path
     skip
     board = [
diff --git a/exercises/custom-set/custom_set_test.rb b/exercises/custom-set/custom_set_test.rb
index ba89640a1b..7a06d402a5 100755
--- a/exercises/custom-set/custom_set_test.rb
+++ b/exercises/custom-set/custom_set_test.rb
@@ -204,7 +204,6 @@ def test_intersection_of_two_sets_with_no_shared_elements_is_an_empty_set
     assert_equal expected, set2.intersection(set1)
   end
 
-  # rubocop:disable Metrics/LineLength
   def test_intersection_of_two_sets_with_shared_elements_is_a_set_of_the_shared_elements
     skip
     set1 = CustomSet.new [1, 2, 3, 4]
diff --git a/exercises/diamond/diamond_test.rb b/exercises/diamond/diamond_test.rb
index ab2a1ada2e..9649200075 100755
--- a/exercises/diamond/diamond_test.rb
+++ b/exercises/diamond/diamond_test.rb
@@ -1,4 +1,3 @@
-# rubocop:disable Metrics/MethodLength
 # !/usr/bin/env ruby
 gem 'minitest', '>= 5.0.0'
 require 'minitest/autorun'
diff --git a/exercises/etl/etl_test.rb b/exercises/etl/etl_test.rb
index a53c50caef..2a8b81d02c 100755
--- a/exercises/etl/etl_test.rb
+++ b/exercises/etl/etl_test.rb
@@ -32,7 +32,7 @@ def test_more_keys
     assert_equal expected, ETL.transform(old)
   end
 
-  def test_full_dataset # rubocop:disable Metrics/MethodLength
+  def test_full_dataset
     skip
     old = {
       1 => %w(A E I O U L N R S T),
diff --git a/exercises/house/house_test.rb b/exercises/house/house_test.rb
index 42c35836fa..871724cc73 100755
--- a/exercises/house/house_test.rb
+++ b/exercises/house/house_test.rb
@@ -3,7 +3,6 @@
 require 'minitest/autorun'
 require_relative 'house'
 
-# rubocop:disable Metrics/MethodLength
 class HouseTest < Minitest::Test
   def test_rhyme
     expected = <<-RHYME
diff --git a/exercises/largest-series-product/example.tt b/exercises/largest-series-product/example.tt
index 4f923f201f..e3d54438c2 100644
--- a/exercises/largest-series-product/example.tt
+++ b/exercises/largest-series-product/example.tt
@@ -5,9 +5,6 @@ require_relative 'largest_series_product'
 
 # Test data version:
 # <%= sha1 %>
-# Rubocop directives
-# rubocop:disable Style/NumericLiterals
-# rubocop:disable Metrics/LineLength
 #
 class Seriestest < Minitest::Test<% test_cases.each do |test_case| %>
   def <%= test_case.name %><% if test_case.skipped? %>
diff --git a/exercises/largest-series-product/largest_series_product_test.rb b/exercises/largest-series-product/largest_series_product_test.rb
index 2f0ac920ef..de1d9dff2e 100755
--- a/exercises/largest-series-product/largest_series_product_test.rb
+++ b/exercises/largest-series-product/largest_series_product_test.rb
@@ -6,10 +6,6 @@
 # Test data version:
 # deb225e Implement canonical dataset for scrabble-score problem (#255)
 
-# Rubocop directives
-# rubocop:disable Style/NumericLiterals
-# rubocop:disable Metrics/LineLength
-#
 class Seriestest < Minitest::Test
   def test_can_find_the_largest_product_of_2_with_numbers_in_order
     assert_equal 72, Series.new('0123456789').largest_product(2)
diff --git a/exercises/linked-list/linked_list_test.rb b/exercises/linked-list/linked_list_test.rb
index baf8814b8c..1dbe46d07c 100755
--- a/exercises/linked-list/linked_list_test.rb
+++ b/exercises/linked-list/linked_list_test.rb
@@ -39,7 +39,7 @@ def test_unshift_pop
     assert_equal 20, deque.pop
   end
 
-  def test_example # rubocop:disable Metrics/MethodLength
+  def test_example
     skip
     deque = Deque.new
     deque.push(10)
diff --git a/exercises/meetup/meetup_test.rb b/exercises/meetup/meetup_test.rb
index 3595e1d3d5..304feb73f4 100755
--- a/exercises/meetup/meetup_test.rb
+++ b/exercises/meetup/meetup_test.rb
@@ -8,7 +8,6 @@
 # and a method day(weekday, schedule)
 # where weekday is one of :monday, :tuesday, etc
 # and schedule is :first, :second, :third, :fourth, :last or :teenth.
-# rubocop:disable Style/AlignParameters
 class MeetupTest < Minitest::Test
   def test_monteenth_of_may_2013
     assert_equal Date.new(2013, 5, 13),
diff --git a/exercises/nth-prime/example.tt b/exercises/nth-prime/example.tt
index 822d6c5d49..8b4a62595f 100644
--- a/exercises/nth-prime/example.tt
+++ b/exercises/nth-prime/example.tt
@@ -5,8 +5,6 @@ require_relative 'nth_prime'
 
 # Test data version:
 # <%= sha1 %>
-# Rubocop directives
-# rubocop:disable Style/NumericLiterals
 #
 class NthPrimeTest < Minitest::Test<% test_cases.each do |test_case| %>
   def <%= test_case.name %><% if test_case.skipped? %>
diff --git a/exercises/nth-prime/nth_prime_test.rb b/exercises/nth-prime/nth_prime_test.rb
index 8ae9b56b62..f13f1ecc29 100755
--- a/exercises/nth-prime/nth_prime_test.rb
+++ b/exercises/nth-prime/nth_prime_test.rb
@@ -5,8 +5,6 @@
 
 # Test data version:
 # bb79e10
-# Rubocop directives
-# rubocop:disable Style/NumericLiterals
 #
 class NthPrimeTest < Minitest::Test
   def test_first_prime
diff --git a/exercises/ocr-numbers/ocr_numbers_test.rb b/exercises/ocr-numbers/ocr_numbers_test.rb
index cb093cc359..4211a1157c 100755
--- a/exercises/ocr-numbers/ocr_numbers_test.rb
+++ b/exercises/ocr-numbers/ocr_numbers_test.rb
@@ -4,7 +4,6 @@
 require_relative 'ocr_numbers'
 
 class OCRTest < Minitest::Test
-  # rubocop:disable  Style/TrailingWhitespace
   def test_recognize_zero
     text = <<-NUMBER.chomp
  _ 
@@ -169,7 +168,7 @@ def test_identify_1234567890
     assert_equal '1234567890', OCR.new(text).convert
   end
 
-  def test_identify_123_456_789 # rubocop:disable Metrics/MethodLength
+  def test_identify_123_456_789
     skip
     text = <<-NUMBER.chomp
     _  _ 
diff --git a/exercises/protein-translation/protein_translation_test.rb b/exercises/protein-translation/protein_translation_test.rb
index 6810f43737..68209f551d 100755
--- a/exercises/protein-translation/protein_translation_test.rb
+++ b/exercises/protein-translation/protein_translation_test.rb
@@ -3,7 +3,6 @@
 require 'minitest/autorun'
 require_relative 'protein_translation'
 
-# rubocop:disable Style/MethodName
 class TranslationTest < Minitest::Test
   def test_AUG_translates_to_methionine
     assert_equal 'Methionine', Translation.of_codon('AUG')
diff --git a/exercises/proverb/proverb_test.rb b/exercises/proverb/proverb_test.rb
index 1414fead6f..992c1d1c41 100755
--- a/exercises/proverb/proverb_test.rb
+++ b/exercises/proverb/proverb_test.rb
@@ -38,7 +38,7 @@ def test_proverb_does_not_hard_code_the_rhyme_dictionary
     assert_equal expected, proverb.to_s
   end
 
-  def test_the_whole_proverb # rubocop:disable Metrics/MethodLength
+  def test_the_whole_proverb
     skip
     chain = %w(nail shoe horse rider message battle kingdom)
     proverb = Proverb.new(*chain)
@@ -52,7 +52,6 @@ def test_the_whole_proverb # rubocop:disable Metrics/MethodLength
     assert_equal expected, proverb.to_s
   end
 
-  # rubocop:disable Metrics/MethodLength
   def test_an_optional_qualifier_in_the_final_consequence
     skip
     chain = %w(nail shoe horse rider message battle kingdom)
@@ -66,7 +65,6 @@ def test_an_optional_qualifier_in_the_final_consequence
       'And all for the want of a horseshoe nail.'
     assert_equal expected, proverb.to_s
   end
-  # rubocop:enable Metrics/MethodLength
 
   def test_proverb_is_same_each_time
     skip
diff --git a/exercises/queen-attack/queen_attack_test.rb b/exercises/queen-attack/queen_attack_test.rb
index 3bf71ed36b..2fe1c0d37c 100755
--- a/exercises/queen-attack/queen_attack_test.rb
+++ b/exercises/queen-attack/queen_attack_test.rb
@@ -34,7 +34,7 @@ def test_cannot_occupy_same_space
     end
   end
 
-  def test_string_representation # rubocop:disable Metrics/MethodLength
+  def test_string_representation
     skip
     queens = Queens.new(white: [2, 4], black: [6, 6])
     board = <<-BOARD.chomp
@@ -50,7 +50,7 @@ def test_string_representation # rubocop:disable Metrics/MethodLength
     assert_equal board, queens.to_s
   end
 
-  def test_another_string_representation # rubocop:disable Metrics/MethodLength
+  def test_another_string_representation
     skip
     queens = Queens.new(white: [7, 1], black: [0, 0])
     board = <<-BOARD.chomp
@@ -66,7 +66,6 @@ def test_another_string_representation # rubocop:disable Metrics/MethodLength
     assert_equal board, queens.to_s
   end
 
-  # rubocop:disable Metrics/MethodLength
   def test_yet_another_string_representation
     skip
     queens = Queens.new(white: [4, 3], black: [3, 4])
@@ -88,7 +87,6 @@ def test_cannot_attack
     queens = Queens.new(white: [2, 3], black: [4, 7])
     assert !queens.attack?
   end
-  # rubocop:enable Metrics/MethodLength
 
   def test_can_attack_on_same_row
     skip
diff --git a/exercises/robot-simulator/robot_simulator_test.rb b/exercises/robot-simulator/robot_simulator_test.rb
index 6857793a93..8498ddec50 100755
--- a/exercises/robot-simulator/robot_simulator_test.rb
+++ b/exercises/robot-simulator/robot_simulator_test.rb
@@ -160,7 +160,7 @@ def test_instruct_robot
     assert_equal :west, robot.bearing
   end
 
-  def test_instruct_many_robots # rubocop:disable Metrics/MethodLength
+  def test_instruct_many_robots
     skip
     robot1 = Robot.new
     robot2 = Robot.new
diff --git a/exercises/strain/strain_test.rb b/exercises/strain/strain_test.rb
index 57dedad921..334f9d28e8 100755
--- a/exercises/strain/strain_test.rb
+++ b/exercises/strain/strain_test.rb
@@ -30,7 +30,7 @@ def test_keep_strings
     assert_equal %w(zebra zombies zelot), result
   end
 
-  def test_keep_arrays # rubocop:disable Metrics/MethodLength
+  def test_keep_arrays
     skip
     rows = [
       [1, 2, 3],
@@ -72,7 +72,7 @@ def test_discard_strings
     assert_equal %w(apple banana cherimoya), result
   end
 
-  def test_discard_arrays # rubocop:disable Metrics/MethodLength
+  def test_discard_arrays
     skip
     rows = [
       [1, 2, 3],