From 155dd334dadcd06e712b653474f2737b4e4a1f37 Mon Sep 17 00:00:00 2001
From: Mark Oveson <mark.oveson@gmail.com>
Date: Mon, 31 Oct 2016 13:09:00 -0600
Subject: [PATCH] Fast alphametics solver that uses partials to limit the set
 of viable permutations.

---
 exercises/alphametics/example.rb | 163 +++++++++++++++++++------------
 1 file changed, 100 insertions(+), 63 deletions(-)

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