evil.sud

# http://www.websudoku.com/?level=4&set_id=470872047
..53.694.
.3.1....6
.......3.
7..9.....
.1..3..2.
.....2..7
.6.......
8....7.5.
.436.81..

medium.sud

# http://www.websudoku.com/?level=2&set_id=3350218628
.4...7.3.
..85..1..
.15.3..9.
5...7.21.
..6...8..
.81.6...9
.2..4.57.
..7..29..
.5.7...8.

sudoku.rb

#!/usr/bin/env ruby

require 'set'

class Cell
  attr_reader :number

  OneThruNine = Set[*1..9]

  def initialize(name="unamed")
    @name = name
    @groups = []
  end

  def number=(value)
    @number = value.nonzero?
  end

  def available_numbers
    if number
      Set[]
    else
      @groups.inject(OneThruNine) { |res, group|
        res - group.numbers
      }
    end
  end

  def join(group)
    @groups << group
  end

  def to_s
    @name
  end

  def inspect
    to_s
  end
end

class Group
  def initialize
    @cells = []
  end

  def <<(cell)
    cell.join(self)
    @cells << cell
    self
  end

  def numbers
    Set[*@cells.map { |c| c.number }.compact]
  end
end

class Board
  include Enumerable

  def initialize(verbose=nil)
    @verbose = verbose
    @cells = (0...81).map { |i|
      Cell.new("C#{(i/9)+1}#{(i%9)+1}")
    }
    define_groups
  end

  def parse(string)
    numbers = string.gsub(/^#.*$/, '').gsub(/\n/, '').
      split(//).map { |n| n.to_i }
    each do |cell|
      cell.number = numbers.shift
    end
    self
  end

  def each
    @cells.each do |cell|
      yield cell
    end
  end

  def solved?
    all? { |cell| cell.number }
  end

  def stuck?
    any? { |cell| cell.number.nil? && cell.available_numbers.size == 0 }
  end
  
  def to_s
    encoding.
      gsub(/.../, "\\0 ").
      gsub(/.{12}/, "\\0\n").
      gsub(/.{39}/m, "\\0\n").
      gsub(/[\d.]/, "\\0 ")
  end

  def inspect
    "<Board #{encoding}>"
  end

  def encoding
    map { |cell| cell.number || "." }.join
  end

  def solve
    alternatives = []
    while true
      solve_easy_squares
      break if solved?
      if stuck?
        fail "No Solution Found" if alternatives.empty?
        puts "Backtracking (#{alternatives.size})" if @verbose
        guess(alternatives)
      else
        cell = find_candidate_for_guessing
        remember_alternatives(cell, alternatives)
        guess(alternatives)
      end
    end
  end

  private

  def solve_easy_squares
    while solve_one_easy_square
    end
  end
  
  def solve_one_easy_square
    each do |cell|
      an = cell.available_numbers
      if an.size == 1
        puts "Put #{an.to_a.first} at (#{cell})" if @verbose
        cell.number = an.to_a.first
        return true
      end
    end
    return false
  end
  
  def find_candidate_for_guessing
    cells_without_numbers.sort_by { |cell| 
      [cell.available_numbers.size, to_s]
    }.first
  end

  def cells_without_numbers
    to_a.reject { |cell| cell.number }
  end

  def remember_alternatives(cell, alternatives)
    cell.available_numbers.each do |n|
      alternatives.push([encoding, cell, n])
    end
  end
  
  def guess(alternatives)
    state, cell, number = alternatives.pop
    parse(state)
    puts "Guessing #{number} at #{cell}" if @verbose
    cell.number = number        
  end

  def define_groups
    define_columns
    define_rows
    define_blocks
  end

  def define_rows
    (0..8).each do |r|
      define_group(r..r, 0..8)
    end
  end

  def define_columns
    (0..8).each do |c|
      define_group(0..8, c..c)
    end
  end

  def define_blocks
    [(0..2), (3..5), (6..8)].each do |rrange|
      [(0..2), (3..5), (6..8)].each do |crange|
        define_group(rrange, crange)
      end
    end
  end

  def define_group(row_range, col_range)
    g = Group.new
    row_range.each do |r|
      col_range.each do |c|
        g << @cells[r*9 + c]
      end
    end
  end
  
end

if __FILE__ == $0 then
  def solve(string)
      board = Board.new(true).parse(string)
      puts board
      
      board.solve
      puts
      puts board
      puts
  end

  if ARGV.empty?
    puts "Usage: ruby sudoku.rb sud-files..."
    exit 
  end

  ARGV.each do |fn|
    puts "Solving #{fn} ----------------------------------------------"
    open(fn) do |f|
      solve(f.read)
    end
  end
end

sudoku_test.rb

require 'rubygems'
require 'test/unit'
require 'shoulda'

require 'sudoku'

class CellTest < Test::Unit::TestCase
  def create_group_with(cell, *numbers)
    g = Group.new
    g << cell
    numbers.each do |n|
      c = Cell.new
      c.number = n
      g << c
    end
    g
  end

  context 'a cell' do
    setup do
      @cell = Cell.new("C25")
    end

    should 'know its name' do
      assert_equal "C25", @cell.to_s
    end

    should 'initially have no number' do
      assert_nil @cell.number
    end

    should 'be able to set number' do
      @cell.number = 4
      assert_equal 4, @cell.number
    end

    should 'accept a zero as no number' do
      @cell.number = 0
      assert_nil @cell.number
    end

    should 'report all numbers are available' do
      assert_equal( Set[*(1..9)], @cell.available_numbers )
    end

    context 'within a group' do
      setup do
        @group = create_group_with(@cell, 3, 4, 5)
      end

      should 'report available numbers not in the group' do
        assert_equal Set[1, 2, 6, 7, 8, 9], @cell.available_numbers
      end

      should 'report no available numbers if a number has been assigned' do
        @cell.number = 6
        assert_equal Set[], @cell.available_numbers
      end

    end
  end
end


class GroupTest < Test::Unit::TestCase
  context 'a group of cells' do
    setup do
      @group = Group.new
    end
    
    should 'exist' do
      assert_not_nil @group
    end

    context 'with cells' do
      setup do
        @cells = (1..10).map { |i| Cell.new("C#{i}") }
        @cells.each do |c| @group << c end
      end

      should 'give a list of numbers' do
        assert_equal Set[], @group.numbers
      end

      context 'with some numbers' do
        setup do
          @cells[0].number = 3
          @cells[3].number = 6
        end

        should 'give a list of the remaining missing numbers' do
          assert_equal [3, 6], @group.numbers.sort
        end
      end

    end

  end
end

class BoardTest < Test::Unit::TestCase
  Wiki =
    "53  7    " +
    "6  195   " +
    " 98    6 " +
    "8   6   3" +
    "4  8 3  1" +
    "7   2   6" +
    " 6    28 " +
    "   419  5" +
    "    8  79"

  Medium =
    " 4   7 3 " +
    "  85  1  " +
    " 15 3  9 " +
    "5   7 21 " +
    "  6   8  " +
    " 81 6   9" +
    " 2  4 57 " +
    "  7  29  " +
    " 5 7   8 "
  
  Evil =
    "  53 694 " +
    " 3 1    6" +
    "       3 " +
    "7  9     " +
    " 1  3  2 " +
    "     2  7" +
    " 6       " +
    "8    7 5 " +
    " 436 81  "
  
  context 'a board' do
    setup do
      @board = Board.new
    end

    should 'initially give all 9 numbers for all cells' do
      @board.each do |cell|
        assert_equal((1..9).to_a, cell.available_numbers.sort)
      end
    end

    should 'parse a string representation of the puzzle' do
      @board.parse(Wiki)
      assert_equal "5 3 .  . 7 .  . . .  \n" +
        "6 . .  1 9 5  . . .  \n" +
        ". 9 8  . . .  . 6 .  \n\n" +
        "8 . .  . 6 .  . . 3  \n" +
        "4 . .  8 . 3  . . 1  \n" +
        "7 . .  . 2 .  . . 6  \n\n" +
        ". 6 .  . . .  2 8 .  \n" +
        ". . .  4 1 9  . . 5  \n" +
        ". . .  . 8 .  . 7 9  \n\n",
        @board.to_s
    end

    should 'solve the Wikipedia Puzzle' do
      board = Board.new.parse(Wiki)
      board.solve

      assert board.solved?
      assert_equal "534678912672195348198342567" +
        "859761423426853791713924856" +
        "961537284287419635345286179",
        board.encoding      
    end

    should 'solve the Medium Puzzle' do
      board = Board.new.parse(Medium)
      board.solve

      assert board.solved?
      assert_equal "942187635368594127715236498" +
        "593478216476921853281365749" +
        "829643571137852964654719382",
        board.encoding      
    end

    should 'solve the Evil Puzzle' do
      board = Board.new.parse(Evil)
      board.solve

      assert board.solved?
      assert_equal "285376941439125786176849235" +
        "752981364618734529394562817" +
        "567213498821497653943658172",
        board.encoding      
    end

  end
end

wiki.sud

# http://en.wikipedia.org/wiki/Sudoku
53..7....
6..195...
.98....6.
8...6...3
4..8.3..1
7...2...6
.6....28.
...419..5
....8..79