magicsquare.rb

#!/usr/bin/env ruby

# ruby magicsquare.rb
# ruby magicsquare.rb -c
# ruby magicsquare.rb 2
# ruby magicsquare.rb 3

module MagicSquare
  class Table
    def initialize(t = nil)
      @numbers = t || [nil, nil, 6, 3, nil, nil, 0, nil, nil]
    end
    attr_accessor :numbers

    def to_s
      s = ""

      3.times do |row|
        3.times do |col|
          s += "[#{@numbers[3 * row + col] || ' '}]"
        end
        s += "\n"
      end

      s.strip
    end

    def print
      puts to_s
    end

    def fill(ary)
      i = 0
      ary.each do |item|
        until @numbers[i].nil?
          i += 1
          if i == @numbers.length
            return self
          end
        end
        @numbers[i] = item
      end

      self
    end

    def answer?(opt_msg = false)
      if @numbers.compact.length != @numbers.length
        return opt_msg ? "not filled" : false
      end

      if @numbers.uniq.length != @numbers.length
        return opt_msg ? "same numbers found" : false
      end

      if @numbers[2] != 6 || @numbers[3] != 3 || @numbers[6] != 0
        return opt_msg ? "initial state changed" : false
      end

      [@numbers[1], @numbers[3], @numbers[5], @numbers[7]].each do |num|
        if num.even?
          return opt_msg ? "odd number condition violated" : false
        end
      end

      sums = []
      sums << @numbers[0] + @numbers[1] + @numbers[2]
      sums << @numbers[3] + @numbers[4] + @numbers[5]
      sums << @numbers[6] + @numbers[7] + @numbers[8]
      sums << @numbers[0] + @numbers[3] + @numbers[6]
      sums << @numbers[1] + @numbers[4] + @numbers[7]
      sums << @numbers[2] + @numbers[5] + @numbers[8]
      sums << @numbers[0] + @numbers[4] + @numbers[8]
      sums << @numbers[2] + @numbers[4] + @numbers[6]
      if sums.uniq.length != sums.length
        return opt_msg ? "same sums found" : false
      end

      opt_msg ? "OK" : true
    end
  end

  class Solver
    def initialize(opt_c = false)
      @table_init = Table.new
      @opt_correct_answer_only = opt_c
      @trial_count = 0
    end

    def fill_table(t, ary)
      t.fill(ary)
    end

    def valid_table(t = @table_init, opt_msg = false)
      t.answer?(opt_msg)
    end

    def check_and_print_result(t)
      @trial_count += 1

      if @opt_correct_answer_only
        if t.answer?
          t.print
          puts
        end
      else
        puts "Trial \##{@trial_count} / Result: #{valid_table(t, true)}"
        t.print
        puts
      end
    end

    def solve(param = nil)
      case param
      when "2"
        solve_evenodd
      when "3"
        solve_perm9
      else
        solve_perm6
      end
    end

    def solve_evenodd
      if !@opt_correct_answer_only
        Table.new.print
        puts
      end

      ary_odd = "157".split(//).map {|item| item.to_i}
      ary_even = "248".split(//).map {|item| item.to_i}
      ary_odd.permutation do |perm_odd|
        ary_even.permutation do |perm_even|
          t = Table.new
          t.numbers[1], t.numbers[5], t.numbers[7] = perm_odd
          t.numbers[0], t.numbers[4], t.numbers[8] = perm_even
          check_and_print_result(t)
        end
      end
    end

    def solve_perm9
      ary = (0..8).to_a
      ary.permutation do |perm|
        check_and_print_result(Table.new(perm))
      end
    end

    def solve_perm6
      if !@opt_correct_answer_only
        Table.new.print
        puts
      end

      ary = "124578".split(//).map {|item| item.to_i}
      ary.permutation do |perm|
        check_and_print_result(Table.new.fill(perm))
      end
    end
  end
end

if __FILE__ == $0
  opt_c = false
  if /^-c/ =~ ARGV.first
    ARGV.shift
    opt_c = true
  end
  MagicSquare::Solver.new(opt_c).solve(ARGV.first)
end

=begin
http://www.juen.ac.jp/math/journal/files/vol29/29-tsukada.pdf

【問題1】
[ ][_][6]
[3][ ][_]
[0][_][ ]
たて，横，ななめの3つのマス内の数字の和がすべてことなるように0～8を各1個ずつ入れます．灰色の4つのマスには奇数の数字を入れます．いま，0，3，6が図上のように入っています．このとき，残りの1，2，4，5，7，8を入れなさい．
（灰色：[_]および[3]）
=end