Maze generation

Maze generation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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Generate and show a maze, using using the simple Depth-first search algorithm.

J

This algorithm allows almost no parallelism. So, while it might be "simple", it will not be necessarily efficient to implement on future (highly parallel) systems.

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
 ' ' (0 1;0 2; 0 3;(2 1-~$text);(1 4&+&.> hdoor),,vdoor+&.>"0/2 1;2 2;2 3)} text

)</lang>

Example use (with ascii box drawing enabled):

<lang j> display 12 maze 16 + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | + +---+---+---+---+ + + +---+---+ +---+ +---+---+ + | | | | | | | | | +---+---+ + +---+---+ + + +---+---+ +---+---+ + + | | | | | | | | | + +---+ +---+---+ + + + + +---+---+ + +---+ + | | | | | | | | | | + +---+---+---+ + +---+---+ + + + +---+---+---+---+ | | | | | | | | | | + + + +---+---+ +---+ +---+ + +---+---+---+ + + | | | | | | | + + +---+---+---+---+---+---+ +---+---+ + +---+---+ + | | | | | | | | | + +---+---+---+---+ + + + + + + + + +---+---+ | | | | | | | | | | + + +---+ + + + +---+---+ +---+---+---+---+ +---+ | | | | | | | | | + + + +---+ +---+ + +---+ +---+---+---+---+---+ + | | | | | | | | | | + +---+ + + + +---+ +---+---+ +---+ + + +---+ | | | | | | | | | | | | +---+ + + + + +---+---+ + +---+ +---+---+---+ + | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+</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)) ) ) ) )
           (=: west)
           (=: east)
           (=: south)
           (=: north) ) )
     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