Maze generation
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Generate and show a maze, using using the simple Depth-first search algorithm.
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)) ) ) ) )
(=: 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 | | | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
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