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Another approach to generating weave mazes, described by Robin Houston. Scatter the over/under passages randomly across the blank maze, and then generate the maze around them. Kruskal's algorithm is particularly well-suited to this approach.
# --------------------------------------------------------------------
# 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)
print "\e[H" # move to upper-left
grid.each do |row|
2.times do |i|
row.each { |cell| print TILES[cell][i] }
puts
end
end
end
class Tree
attr_accessor :parent
def initialize
@parent = nil
end
def root
@parent ? @parent.root : self
end
def connected?(tree)
root == tree.root
end
def connect(tree)
tree.root.parent = self
end
end
grid = Array.new(height) { Array.new(width, 0) }
sets = Array.new(height) { Array.new(width) { Tree.new } }
# build the list of edges
edges = []
height.times do |y|
width.times do |x|
edges << [x, y, N] if y > 0
edges << [x, y, W] if x > 0
end
end
edges = edges.sort_by{rand}
# --------------------------------------------------------------------
# 4. Build the over/under locations
# --------------------------------------------------------------------
print "\e[2J" # clear the screen
1.upto(height-2) do |cy|
1.upto(width-2) do |cx|
next unless rand(100) < density
nx, ny = cx, cy-1
wx, wy = cx-1, cy
ex, ey = cx+1, cy
sx, sy = cx, cy+1
next if grid[cy][cx] != 0 ||
sets[ny][nx].connected?(sets[sy][sx]) ||
sets[ey][ex].connected?(sets[wy][wx])
sets[ny][nx].connect(sets[sy][sx])
sets[ey][ex].connect(sets[wy][wx])
if rand(2) == 0
grid[cy][cx] = E|W|U
else
grid[cy][cx] = N|S|U
end
grid[ny][nx] |= S
grid[wy][wx] |= E
grid[ey][ex] |= W
grid[sy][sx] |= N
edges.delete_if do |x, y, dir|
(x == cx && y == cy) ||
(x == ex && y == ey && dir == W) ||
(x == sx && y == sy && dir == N)
end
display_maze(grid)
sleep(delay)
end
end
puts
puts "--- PRESS ENTER TO BEGIN ---"
STDIN.gets
print "\e[2J" # clear the screen
# --------------------------------------------------------------------
# 5. Kruskal's algorithm
# --------------------------------------------------------------------
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)
display_maze(grid)
sleep(delay)
set1.connect(set2)
grid[y][x] |= direction
grid[ny][nx] |= OPPOSITE[direction]
end
end
display_maze(grid)
# --------------------------------------------------------------------
# 6. Show the parameters used to build this maze, for repeatability
# --------------------------------------------------------------------
puts "#{$0} #{width} #{height} #{density} #{seed}"
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