Four-8 Puzzle

foureights.rb

#!/usr/bin/env ruby

# foureights.rb : "8-((8+8)/8)" Puzzle
#   by takehikom
#   see also: https://takehikom.hateblo.jp/entry/2020/01/11/062120

# 環境変数LANGの値がja_JP.UTF-8などのときは，
# 日本語文字で出力する（実行時オプションで変更可能）
$option_zenkaku = /jp/i === ENV["LANG"]

class String
  TO_J_PATTERN1 = "-+*/()=0123456789"
  TO_J_PATTERN2 = "－＋×÷（）＝０１２３４５６７８９"
  TO_J_PATTERN3 = "－＋×／（）＝０１２３４５６７８９"
  def to_j(option_slash = false)
    return self if !$option_zenkaku
    tr(TO_J_PATTERN1, option_slash ? TO_J_PATTERN3 : TO_J_PATTERN2)
  end
end

class FourNumberPuzzleSolver
  def initialize(opt)
    @num = opt[:num] || [8, 8, 8, 8]
    raise if !(Array === @num) || @num.length < 4
    @num = @num[0, 4].map { |item| item.to_i }
    @result_only = opt[:res]
    @result_h = {} # "number" => [expr, ...]
  end
  attr_reader :num, :result_h

  def start
    setup_result(!@result_only)
    if !@result_only
      puts; puts "=" * 64; puts
      print_result_all
      puts; puts "=" * 64; puts
    end
    print_result((0..10).to_a)
  end

  def op_sym(o)
    ["+", "-", "*", "/"][o]
  end

  def op(o, x, y)
    return nil if x.nil? || y.nil?
    case o
    when 0
      x + y
    when 1
      x - y
    when 2
      x * y
    when 3
      if y == 0
        return nil
      end
      Rational(x, y)
    end
  end

  def expr(v1, v2, v3, v4, o1, o2, o3, d = 0, opt_j = $option_zenkaku)
    case d
    when 0
      # d == 0: ((8 o1 8) o2 8) o3 8
      pat = "((%d%s%d)%s%d)%s%d"
    when 1
      # d == 1: (8 o1 8) o2 (8 o3 8)
      pat = "(%d%s%d)%s(%d%s%d)"
    when 2
      # d == 2: (8 o1 (8 o2 8)) o3 8
      pat = "(%d%s(%d%s%d))%s%d"
    when 3
      # d == 3: 8 o1 ((8 o2 8) o3 8)
      pat = "%d%s((%d%s%d)%s%d)"
    when 4
      # d == 4: 8 o1 (8 o2 (8 o3 8))
      pat = "%d%s(%d%s(%d%s%d))"
    else
      raise
    end

    pat % [v1, op_sym(o1), v2, op_sym(o2), v3, op_sym(o3), v4]
  end

  def eval(v1, v2, v3, v4, o1, o2, o3, d = 0)
    case d
    when 0
      # d == 0: ((8 o1 8) o2 8) o3 8
      v = op(o3, op(o2, op(o1, v1, v2), v3), v4)
    when 1
      # d == 1: (8 o1 8) o2 (8 o3 8)
      v = op(o2, op(o1, v1, v2), op(o3, v3, v4))
    when 2
      # d == 2: (8 o1 (8 o2 8)) o3 8
      v = op(o3, op(o1, v1, op(o2, v2, v3)), v4)
    when 3
      # d == 3: 8 o1 ((8 o2 8) o3 8)
      v = op(o1, v1, op(o3, op(o2, v2, v3), v4))
    when 4
      # d == 4: 8 o1 (8 o2 (8 o3 8))
      v = op(o1, v1, op(o2, v2, op(o3, v3, v4)))
    else
      raise
    end

    (Rational === v && v.denominator == 1) ? v.numerator : v
  end

  def setup_result(option_print = false)
    (0..4).each do |d|
      (0..3).each do |o1|
        (0..3).each do |o2|
          (0..3).each do |o3|
            s = expr(*@num, o1, o2, o3, d)
            v = eval(*@num, o1, o2, o3, d)
            vs = v.to_s
            vs = "NaN" if v.nil?
            puts [s.to_j, "=".to_j, vs.to_j(true)].join if option_print

            if !@result_h.key?(vs)
              @result_h[vs] = []
            end
            @result_h[vs] << s
          end
        end
      end
    end
  end

  def print_result(output_numbers)
    output_numbers.each do |v|
      vs = v.to_s
      if result_h.key?(vs)
        print_freq(vs, result_h[vs].length)
        #puts "#{vs} ... #{result_h[vs].length}#{$option_zenkaku ? '通り' : ' expression(s)'}"
        puts result_h[vs].map { |s| "    " + s.to_j }
      else
        print_freq(vs, 0)
        #puts "#{vs} ... #{$option_zenkaku ? 'なし' : 'nothing'}"
      end
    end
  end

  def print_result_all
    @result_h.keys.sort.each do |vs|
      print_freq(vs, result_h[vs].length)
      #puts "#{vs} ... #{result_h[vs].length}#{$option_zenkaku ? '通り' : ' expression(s)'}"
      puts @result_h[vs].map { |s| "    " + s.to_j }
    end
  end

  def print_freq(vs, freq)
    if freq == 0
      puts "#{vs} ... #{$option_zenkaku ? 'なし' : 'nothing'}"
    else
      puts "#{vs} ... #{freq}#{$option_zenkaku ? '通り' : ' expression(s)'}"
    end
  end
end

if __FILE__ == $0
  opt = {}
  while /^-/ =~ ARGV.first
    case ARGV.shift
    when /^-R/
      opt[:res] = true
    when /^-j/
      $option_zenkaku = true
    when /^-J/
      $option_zenkaku = false
    when /-h/ # -h or --help
      puts "Usage: #{$0} [-j][-J][-R] number..."
      exit
    end
  end
  opt[:num] = ARGV.dup if ARGV.length >= 4
  FourNumberPuzzleSolver.new(opt).start
end

__END__
# ruby foureights.rb -J -R
0 ... 44 expression(s)
    ((8+8)-8)-8
    ((8-8)+8)-8
    ((8-8)-8)+8
    ((8-8)*8)*8
(snip)
1 ... 32 expression(s)
    ((8+8)-8)/8
    ((8-8)+8)/8
    ((8*8)/8)/8
    ((8/8)+8)-8
(snip)
2 ... 1 expression(s)
    (8/8)+(8/8)
3 ... 2 expression(s)
    ((8+8)+8)/8
    (8+(8+8))/8
4 ... 4 expression(s)
    (8*8)/(8+8)
    (8/(8+8))*8
    8/((8+8)/8)
    8*(8/(8+8))
5 ... nothing
6 ... 1 expression(s)
    8-((8+8)/8)
7 ... 1 expression(s)
    ((8*8)-8)/8
8 ... 9 expression(s)
    ((8-8)*8)+8
    ((8-8)/8)+8
    (8*(8-8))+8
    8+((8-8)*8)
(snip)
9 ... 2 expression(s)
    ((8*8)+8)/8
    (8+(8*8))/8
10 ... 2 expression(s)
    ((8+8)/8)+8
    8+((8+8)/8)