Maze generation
Generate and show a maze, using using the simple Depth-first search algorithm.
- Start at a random cell.
- Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor:
- If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell.
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See also Maze solving.
J
This algorithm allows almost no parallelism. So, while it might be "simple", generating very large mazes this way will not be necessarily efficient to implement on future (highly parallel) systems. That said, perhaps mazes with hundreds of thousands of cells are not very likely to be needed by anyone.
Anyways, based on the picolisp implementation, except without any relevant grid support:
<lang j>maze=:4 :0
horiz=. 0$~x,y-1 verti=. 0$~(x-1),y unvisited=. 0,0,~|:0,0,~1$~y,x path=.,:here=. ?x,y while. 1 e.,unvisited do. unvisited=.0 (<here+1)} unvisited neighbors=. here+"1 (,-)=0 1 neighbors=. neighbors #~ (<"1 neighbors+1) {unvisited if.#neighbors do. next=. ({~ ?@#) neighbors if.{.next=here do. horiz=.1 (<-:here+next-0 1)} horiz else. verti=. 1 (<-:here+next-1 0)} verti end. path=.path,here=.next else. here=.{:path path=.}:path end. end. horiz;verti
)
display=:3 :0
size=. >.&$&>/y text=. (}:1 3$~2*1+{:size)#"1":size$<' ' 'hdoor vdoor'=. 2 4&*&.>&.> (#&,{@;&i./@$)&.> y ' ' (a:-.~0 1;0 2; 0 3;(2 1-~$text);(1 4&+&.> hdoor),,vdoor+&.>"0/2 1;2 2;2 3)} text
)</lang>
The result of maze
is a pair of arrays: one for open "doors" in the horizontal direction and the other for open "doors" in the vertical direction. The entry and exit doors are not represented by maze
-- they are implicitly defined and are implemented in display
.
Example use (with ascii box drawing enabled):
<lang j> display 8 maze 11 + +---+---+---+---+---+---+---+---+---+---+ | | | | | + + + + +---+ + +---+---+ + + | | | | | | | | + +---+---+ + +---+---+---+ + + + | | | | | | | +---+ +---+ + + +---+ + +---+---+ | | | | | | | + + +---+---+ +---+ + +---+---+ + | | | | | | | | | + +---+ + + + + +---+---+ + + | | | | | + +---+---+---+---+---+---+---+ +---+ + | | | | | | | | | + + + + + + + + +---+ + + | | | | | +---+---+---+---+---+---+---+---+---+---+---+</lang>
PicoLisp
This solution uses 'grid' from "lib/simul.l" to generate the two-dimensional structure. <lang PicoLisp>(load "@lib/simul.l")
(de maze (DX DY)
(let Maze (grid DX DY) (let Fld (get Maze (rand 1 DX) (rand 1 DY)) (recur (Fld) (for Dir (shuffle '((west . east) (east . west) (south . north) (north . south))) (with ((car Dir) Fld) (unless (or (: west) (: east) (: south) (: north)) (put Fld (car Dir) This) (put This (cdr Dir) Fld) (recurse This) ) ) ) ) ) (for (X . Col) Maze (for (Y . This) Col (set This (cons (cons (: west) (or (: east) (and (= Y 1) (= X DX)) ) ) (cons (: south) (or (: north) (and (= X 1) (= Y DY)) ) ) ) ) ) ) Maze ) )
(de display (Maze)
(disp Maze 0 '((This) " ")) )</lang>
Output:
: (display (maze 16 12)) + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 12 | | | | | | + + + + + +---+ + +---+---+ + +---+ +---+ + 11 | | | | | | | | | | | + +---+ +---+---+ +---+---+ + +---+---+ +---+ +---+ 10 | | | | | | | | | | + + + +---+ + + + + +---+---+ +---+ +---+ + 9 | | | | | | | | | | | + +---+---+ + +---+ +---+---+ + + + +---+ + + 8 | | | | | | | | | | + + + + + +---+---+ +---+ +---+---+ +---+ + + 7 | | | | | | | | | | +---+ +---+---+---+---+ +---+ +---+ + +---+ +---+ + 6 | | | | | | | | | | | + +---+ +---+ +---+ + +---+ + +---+---+---+ + + 5 | | | | | | | | +---+ +---+ +---+ +---+ +---+---+ + +---+ +---+ + 4 | | | | | | | | | | | + +---+ +---+ +---+ +---+ + + +---+---+ + +---+ 3 | | | | | | | | | | + +---+---+ + + +---+---+---+ +---+ + + +---+ + 2 | | | | | | | | | | + + + +---+ + + +---+ +---+ +---+ + +---+---+ 1 | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ a b c d e f g h i j k l m n o p