数学パズル

q31_1.rb

Square = 6
is_used = Array.new(Square + 1) {Array.new(Square + 1) {[false, false]}}
count = 0

route = lambda do |x, y, is_first_time|
  if x == Square and y == Square
    if is_first_time
      route.call(0, 0, false)
    else
      count += 1
    end
  end
  if x < Square
    unless is_used[x][y][0]
      is_used[x][y][0] = true
      route.call(x + 1, y, is_first_time)
      is_used[x][y][0] = false
    end
  end
  if y < Square
    unless is_used[x][y][1]
      is_used[x][y][1] = true
      route.call(x, y + 1, is_first_time)
      is_used[x][y][1] = false
    end
  end
end

route.call(0, 0, true)
puts count

q31_2.rb

def route(width, height, back_y)
  return (back_y == height) ? back_y : back_y + 2 if width == 1
  return (back_y.zero?) ? 2 : 1 if height == 1
  total = 0
  if back_y.zero?
    height.times {|i| total += 2 * route(width - 1, height, i + 1)}
  else
    back_y.upto(height) {|i| total += route(width - 1, height, i)}
    total += route(width, height - 1, back_y - 1)
  end
  total
end

puts route(6, 6, 0)

q32.rb

width, height = 7, 4
str = ""
tatami = Array.new(height + 2) do |h|
  Array.new(width + 2) do |w|
    (h.zero? or w.zero? or h == height + 1 or w == width + 1) ? -1 : 0
  end
end

print_tatami = lambda do
  1.upto(height) do |i|
    1.upto(width) do |j|
      if tatami[i][j] == tatami[i][j + 1] or tatami[i][j] == tatami[i][j - 1]
        str += "-"
      end
      if tatami[i][j] == tatami[i + 1][j] or tatami[i][j] == tatami[i - 1][j]
        str += "|" 
      end
    end
    str += "\n"
  end
  str += "\n"
end

set_tatami = lambda do |h, w, id|
  if h == height + 1
    print_tatami.call
  elsif w == width + 1
    set_tatami.call(h + 1, 1, id)
  elsif tatami[h][w] > 0
    set_tatami.call(h, w + 1, id)
  else
    if tatami[h - 1][w - 1] == tatami[h - 1][w] or
       tatami[h - 1][w - 1] == tatami[h][w - 1]
      if tatami[h][w + 1].zero?
        tatami[h][w] = tatami[h][w + 1] = id
        set_tatami.call(h, w + 2, id + 1)
        tatami[h][w] = tatami[h][w + 1] = 0
      end
      if tatami[h + 1][w].zero?
        tatami[h][w] = tatami[h + 1][w] = id
        set_tatami.call(h, w + 1, id + 1)
        tatami[h][w] = tatami[h + 1][w] = 0
      end
    end
  end
end

set_tatami.call(1, 1, 1)
puts str