A version of the algorithm that permits arbitrary clustering of crossings

kruskal-weave-3.rb

# --------------------------------------------------------------------
# An implementation of a "weave" maze generator. Weave mazes are those
# with passages that pass both over and under other passages. The
# technique used in this program was described to me by Robin Houston,
# and works by first decorating the blank grid with the over/under
# crossings, and then using Kruskal's algorithm to fill out the rest
# of the grid. (Kruskal's is very well-suited to this approach, since
# it treats the cells as separate sets and joins them together.)
# --------------------------------------------------------------------
# NOTE: the display routine used in this script requires a terminal
# that supports ANSI escape sequences. Windows users, sorry. :(
# --------------------------------------------------------------------

# --------------------------------------------------------------------
# 1. Allow the maze to be customized via command-line parameters
# --------------------------------------------------------------------

width   = (ARGV[0] || 10).to_i
height  = (ARGV[1] || width).to_i
density = (ARGV[2] || 50).to_i
seed    = (ARGV[3] || rand(0xFFFF_FFFF)).to_i
delay   = (ARGV[4] || 0.01).to_f

srand(seed)

# --------------------------------------------------------------------
# 2. Set up constants to aid with describing the passage directions
# --------------------------------------------------------------------

N, S, E, W, U = 0x1, 0x2, 0x4, 0x8, 0x10
DX            = { E => 1, W => -1, N =>  0, S => 0 }
DY            = { E => 0, W =>  0, N => -1, S => 1 }
OPPOSITE      = { E => W, W =>  E, N =>  S, S => N }

# --------------------------------------------------------------------
# 3. Data structures and methods to assist the algorithm
# --------------------------------------------------------------------

EW, NS, SE, SW, NE, NW = [0x80, 0x82, 0x8C, 0x90, 0x94, 0x98].map { |v| "\xE2\x94#{v.chr}" }
NSE, NSW, EWS, EWN     = [0x9C, 0xA4, 0xAC, 0xB4].map { |v| "\xE2\x94#{v.chr}" }

TILES = {
  0       => ["\e[47m   \e[m", "\e[47m   \e[m"],
  N       => ["#{NS} #{NS}", "#{NE}#{EW}#{NW}"],
  S       => ["#{SE}#{EW}#{SW}", "#{NS} #{NS}"],
  E       => ["#{SE}#{EW}#{EW}", "#{NE}#{EW}#{EW}"],
  W       => ["#{EW}#{EW}#{SW}", "#{EW}#{EW}#{NW}"],
  N|S     => ["#{NS} #{NS}", "#{NS} #{NS}"],
  N|W     => ["#{NW} #{NS}", "#{EW}#{EW}#{NW}"],
  N|E     => ["#{NS} #{NE}", "#{NE}#{EW}#{EW}"],
  S|W     => ["#{EW}#{EW}#{SW}", "#{SW} #{NS}"],
  S|E     => ["#{SE}#{EW}#{EW}", "#{NS} #{SE}"],
  E|W     => ["#{EW}#{EW}#{EW}", "#{EW}#{EW}#{EW}"],
  N|S|E   => ["#{NS} #{NE}", "#{NS} #{SE}"],
  N|S|W   => ["#{NW} #{NS}", "#{SW} #{NS}"],
  E|W|N   => ["#{NW} #{NE}", "#{EW}#{EW}#{EW}"],
  E|W|S   => ["#{EW}#{EW}#{EW}", "#{SW} #{SE}"],
  N|S|E|W => ["#{NW} #{NE}", "#{SW} #{SE}"],
  N|S|U   => ["#{NSW} #{NSE}", "#{NSW} #{NSE}"],
  E|W|U   => ["#{EWN}#{EW}#{EWN}", "#{EWS}#{EW}#{EWS}"]
}

def display_maze(grid, sets, delay=0, show_sets=false)
  print "\e[H" # move to upper-left
  grid.each_with_index do |row, y|
    2.times do |i|
      row.each { |cell| print TILES[cell][i] } if row

      if show_sets && i == 1
        print "  "
        sets[y].each { |set| print " %2s" % set.root.id.to_s(36) }
      end

      puts
    end
  end
  sleep(delay)
end

class Tree
  attr_accessor :parent
  attr_reader :id

  @@__next_id = -1
  def self.next_id
    @@__next_id += 1
  end

  def initialize
    @parent = nil
    @id = self.class.next_id
  end

  def root
    @parent ? @parent.root : self
  end

  def connected?(tree)
    root == tree.root
  end

  def connect(tree)
    tree.root.parent = self if not self.connected?(tree)
  end
end

grid = Array.new(height)
grid[0] = Array.new(width, 0)
grid[height-1] = Array.new(width, 0)

# --------------------------------------------------------------------
# 4. Build the over/under locations
# --------------------------------------------------------------------

print "\e[2J" # clear the screen

sets = Array.new(height) { Array.new(width) { Tree.new } }

1.upto(height-2) do |cy|
  
  # Generate a candidate row of random crossings
  grid[cy] = row = Array.new(width, 0)
  segment_lengths = Hash.new(0)
  segment_start = 0
  
  1.upto(width-2) do |cx|
    if rand(100) < density
      row[cx] = [E|W|U, N|S|U][rand(2)]
      if segment_start == 0
        segment_start = cx
      end
      segment_lengths[segment_start] += 1
      
      display_maze(grid, sets, delay)
    else
      segment_start = 0
    end
  end
  
  # Now check whether it would create a loop, and try again if so
  has_loop = false
  segment_lengths.each do |x, len|
    if sets[cy][x - 1].connected?(sets[cy][x + len])
      has_loop = true
      break
    end
    if segment_lengths.has_key?(x + len + 1)
      len += 1 + segment_lengths[x + len + 1]
      redo
    end
  end
  redo if has_loop
  
  # Update the connections and the grid
  segment_lengths.each do |x, len|
    grid[cy][x - 1] |= E
    grid[cy][x + len] |= W
    display_maze(grid, sets, delay)
    sets[cy][x - 1].connect(sets[cy][x + len])
  end
  width.times do |x|
    if (row[x] & U) != 0
      if (grid[cy - 1][x] & U) == 0
        grid[cy - 1][x] |= S
        display_maze(grid, sets, delay)
        sets[cy+1][x].connect(sets[cy-1][x])
      else
        sets[cy+1][x].connect(sets[cy][x])
      end
    elsif (grid[cy-1][x] & U) != 0
      grid[cy][x] |= N
      display_maze(grid, sets, delay)
    end
  end
end

width.times do |x|
  if (grid[height-2][x] & U) != 0
    grid[height-1][x] |= N 
    display_maze(grid, sets, delay)
  end
end

puts
puts "--- PHASE 1 DONE; PRESS ENTER TO START PHASE 2 ---"
STDIN.gets

print "\e[2J" # clear the screen

# --------------------------------------------------------------------
# 5. Kruskal's algorithm
# --------------------------------------------------------------------

# build the list of edges
edges = []
height.times do |y|
  width.times do |x|
    edges << [x, y, N] if y > 0 and (grid[y][x] & (N|U)) == 0
    edges << [x, y, W] if x > 0 and (grid[y][x] & (W|U)) == 0
  end
end

edges = edges.sort_by{rand}

# Add edges at random until there are none left
until edges.empty?
  x, y, direction = edges.pop
  nx, ny = x + DX[direction], y + DY[direction]

  set1, set2 = sets[y][x], sets[ny][nx]

  unless set1.connected?(set2)
    set1.connect(set2)
    grid[y][x] |= direction
    grid[ny][nx] |= OPPOSITE[direction]
    
    display_maze(grid, sets, delay)
  end
end

# --------------------------------------------------------------------
# 6. Show the parameters used to build this maze, for repeatability
# --------------------------------------------------------------------

puts "#{$0} #{width} #{height} #{density} #{seed}"