sudoku_guess_and_check.rb

class SudokuBoard

  def initialize(board_str)
    @board = board_str.split("").map { |value| Cell.new(value.to_i) }
    @groups = []
    (generate_rows + generate_cols + generate_grids).each do |group_member_indices_ar|
      group_cell_members = group_member_indices_ar.map { |index| @board[index] }
      @groups << Group.new(group_cell_members)
    end
    puts to_s
  end

  def solve
    if complete?
      return to_s
    else
      @board.select { |cell| !cell.solved? }.each do |cell|
        cell.potential_values.each do |val|
          cell.value = val
          result = SudokuBoard.new(to_s).solve 
          if result.is_a?(String)
            return result
          end
        end
        return false #This is the key error checking step. Reaching this line indicates that we have encountered an unsolved cell that, thanks to previous guessing, has no possible valid values. This line of inquiry is a dead end.
      end
    end
  end

  def to_s
    @board.map { |cell| cell.value }.join
  end

  private

  def complete?
    !to_s.include? '0'
  end

  def generate_rows
    ar = (0..80).to_a
    Array.new(9).map { ar.shift(9) }
  end

  def generate_cols
    cols = Array.new(9,[])
    (0..80).to_a.each { |index| cols[index % 9] += [index] }
    cols
  end

  def generate_grids
    grids = Array.new(9,[])
    (0..80).to_a.each { |index| grids[(index / 9 / 3 * 3) + ((index % 9) / 3)] += [index]}
    grids
  end

end

class Group

  def initialize(cell_members_ar)
    @cells = cell_members_ar
    @cells.each { |cell| cell.add_group(self)}
  end

  def taken_values
    @cells.map {|cell| cell.value}.select { |val| val > 0 }
  end

end

class Cell

  attr_accessor :value

  def initialize(value)
    @value = value
    @groups = []
  end

  def potential_values
    if solved?
      []
    else
      potential_values_ar = (1..9).to_a
      @groups.each { |group| potential_values_ar -= group.taken_values}
      potential_values_ar
    end
  end

  def add_group(group)
    @groups << group
  end

  def solved?
    @value > 0
  end

end


#board = SudokuBoard.new("619030040270061008000047621486302079000014580031009060005720806320106057160400030")
board = SudokuBoard.new("096040001100060004504810390007950043030080000405023018010630059059070830003590007")
#board = SudokuBoard.new("300000000050703008000028070700000043000000000003904105400300800100040000968000200")
puts "final answer #{board.solve}"