Maze generation: Difference between revisions

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# <code>line</code> -- characters of current line
# <code>line</code> -- characters of current line


Note that this implementation relies on javascript arrays being treatable as infinite in size with false (empty) values springing into existence as needed, to support referenced array locations. (This significantly reduces the bulk of the necessary initialization code.)
Note that this implementation relies on javascript arrays being treatable as infinite in size with false (null) values springing into existence as needed, to support referenced array locations. (This significantly reduces the bulk of the necessary initialization code.)


Example use:
Example use:

Revision as of 15:49, 22 December 2010

Task
Maze generation
You are encouraged to solve this task according to the task description, using any language you may know.
This page uses content from Wikipedia. The original article was at Maze generation algorithm. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

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

  1. Start at a random cell.
  2. 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.

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 millions of cells are not very likely to be needed to be generated quickly.

Anyways, based on the picolisp implementation, except without any relevant grid support:

<lang j>maze=:4 :0 

 assert.0<:n=.<:x*y
 horiz=. 0$~x,y-1
 verti=. 0$~(x-1),y
 path=.,:here=. ?x,y
 unvisited=.0 (<here+1)} 0,0,~|:0,0,~1$~y,x
 while.n do.
   neighbors=. here+"1 (,-)=0 1
   neighbors=. neighbors #~ (<"1 neighbors+1) {unvisited
   if.#neighbors do.
     n=.n-1
     next=. ({~ ?@#) neighbors
     unvisited=.0 (<next+1)} unvisited
     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>

JavaScript

Translation of: J

<lang javascript>function maze(x,y) { var n=x*y-1; if (n<0) {alert("illegal maze dimensions");return;} var horiz=[]; for (var j= 0; j<x+1; j++) horiz[j]= []; var verti=[]; for (var j= 0; j<x+1; j++) verti[j]= []; var here= [Math.floor(Math.random()*x), Math.floor(Math.random()*y)]; var path= [here]; var unvisited= []; for (var j= 0; j<x+2; j++) { unvisited[j]= []; for (var k= 0; k<y+1; k++) unvisited[j].push(j>0 && j<x+1 && k>0 && (j != here[0]+1 || k != here[1]+1)); } while (0<n) { var potential= [[here[0]+1, here[1]], [here[0],here[1]+1], [here[0]-1, here[1]], [here[0],here[1]-1]]; var neighbors= []; for (var j= 0; j < 4; j++) if (unvisited[potential[j][0]+1][potential[j][1]+1]) neighbors.push(potential[j]); if (neighbors.length) { n= n-1; next= neighbors[Math.floor(Math.random()*neighbors.length)]; unvisited[next[0]+1][next[1]+1]= false; if (next[0] == here[0]) horiz[next[0]][(next[1]+here[1]-1)/2]= true; else verti[(next[0]+here[0]-1)/2][next[1]]= true; path.push(here= next); } else here= path.pop(); } return ({x: x, y: y, horiz: horiz, verti: verti}); }


function display(m) { var text= []; for (var j= 0; j<m.x*2+1; j++) { var line= []; if (0 == j%2) for (var k=0; k<m.y*4+1; k++) if (0 == k%4) line[k]= '+'; else if (j>0 && m.verti[j/2-1][Math.floor(k/4)]) line[k]= ' '; else line[k]= '-'; else for (var k=0; k<m.y*4+1; k++) if (0 == k%4) if (k>0 && m.horiz[(j-1)/2][k/4-1]) line[k]= ' '; else line[k]= '|'; else line[k]= ' '; if (0 == j) line[1]= line[2]= line[3]= ' '; if (m.x*2-1 == j) line[4*m.y]= ' '; text.push(line.join()+'\r\n'); } return text.join(); }</lang>

Variable meanings in function maze:

  1. x,y -- dimensions of maze
  2. n -- number of openings to be generated
  3. horiz -- two dimensional array of locations of horizontal openings (true means wall is open)
  4. verti -- two dimensional array of locations of vertical openings (true means wall is open)
  5. here -- current location under consideration
  6. path -- history (stack) of locations that might need to be revisited
  7. unvisited -- two dimensional array of locations that have not been visited, padded to avoid need for boundary tests (true means location needs to be visited)
  8. potential -- locations adjacent to here
  9. neighbors -- unvisited locations adjacent to here

Variable meanings in function display:

  1. m -- maze to be drawn
  2. text -- lines of text representing maze
  3. line -- characters of current line

Note that this implementation relies on javascript arrays being treatable as infinite in size with false (null) values springing into existence as needed, to support referenced array locations. (This significantly reduces the bulk of the necessary initialization code.)

Example use:

<lang html><html><head><title></title></head><body>

</body></html>

<script type="text/javascript">
/* ABOVE CODE GOES HERE */
document.getElementById('out').innerHTML= display(maze(8,11)); 
</script></lang>

produced:

<lang>+   +---+---+---+---+---+---+---+---+---+---+
|                   |                   |   |
+---+---+   +   +---+   +   +---+---+   +   +
|       |   |   |       |   |           |   |
+   +   +   +---+   +---+   +---+---+   +   +
|   |   |               |           |   |   |
+   +---+   +---+---+---+---+---+   +   +   +
|       |   |               |       |       |
+---+   +---+   +---+---+   +   +---+---+   +
|   |   |       |               |       |   |
+   +   +   +---+---+---+---+---+   +   +   +
|       |                   |       |   |   |
+   +---+---+   +---+---+   +   +---+---+   +
|   |       |   |           |       |       |
+   +   +   +---+   +---+---+   +   +   +---+
|       |           |           |            
+---+---+---+---+---+---+---+---+---+---+---+</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 11 8))
   +   +---+---+---+---+---+---+---+---+---+---+
 8 |           |       |                       |
   +   +   +   +   +   +   +---+   +---+---+   +
 7 |   |   |       |   |   |       |       |   |
   +---+   +---+---+   +   +   +---+   +   +   +
 6 |   |       |       |   |           |   |   |
   +   +---+   +---+   +---+---+---+   +   +---+
 5 |       |       |               |   |       |
   +---+   +---+   +---+---+---+   +---+---+   +
 4 |   |       |       |       |   |           |
   +   +---+   +---+   +---+   +   +   +---+   +
 3 |       |       |   |       |   |       |   |
   +   +---+---+   +   +   +   +   +---+   +   +
 2 |       |       |   |   |   |   |       |   |
   +   +   +   +---+   +   +---+   +   +---+   +
 1 |   |               |               |
   +---+---+---+---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h   i   j   k


Tcl


Translation of: Javascript


<lang tcl>package require TclOO; # Or Tcl 8.6



  1. Helper to pick a random number


proc rand n {expr {int(rand() * $n)}}



  1. Helper to pick a random element of a list


proc pick list {lindex $list [rand [llength $list]]}



  1. Helper _function_ to index into a list of lists


proc tcl::mathfunc::idx {v x y} {lindex $v $x $y}

oo::class create maze {



   variable x y horiz verti
   constructor {width height} {



	set y $width
	set x $height

	set n [expr {$x * $y - 1}]
	if {$n < 0} {error "illegal maze dimensions"}
	set horiz [set verti [lrepeat [expr {$x+1}] [lrepeat [expr {$y+1}] 0]]]
	set unvisited [lrepeat [expr {$x+2}] [lrepeat [expr {$y+2}] 0]]
	# Helper to write into a list of lists (with offsets)
	proc unvisited= {x y value} {
	    upvar 1 unvisited u
	    lset u [expr {$x+1}] [expr {$y+1}] $value
	}

	lappend stack [set here [list [rand $x] [rand $y]]]
	for {set j 0} {$j < $x} {incr j} {
	    for {set k 0} {$k < $y} {incr k} {
		unvisited= $j $k [expr {$here ne [list $j $k]}]
	    }
	}

	while {0 < $n} {
	    lassign $here hx hy
	    set neighbours {}
	    foreach {dx dy} {1 0  0 1  -1 0	 0 -1} {
		if {idx($unvisited, $hx+$dx+1, $hy+$dy+1)} {
		    lappend neighbours [list [expr {$hx+$dx}] [expr {$hy+$dy}]]
		}
	    }
	    if {[llength $neighbours]} {
		lassign [set here [pick $neighbours]] nx ny
		unvisited= $nx $ny 0
		if {$nx == $hx} {
		    lset horiz $nx [expr {min($ny, $hy)}] 1
		} else {
		    lset verti [expr {min($nx, $hx)}] $ny 1
		}
		lappend stack $here
		incr n -1
	    } else {
		set here [lindex $stack end]
		set stack [lrange $stack 0 end-1]
	    }
	}



   }



   # Maze displayer; takes a maze dictionary, returns a string
   method view {} {



	set text {}
	for {set j 0} {$j < $x*2+1} {incr j} {
	    set line {}
	    for {set k 0} {$k < $y*4+1} {incr k} {
		if {$j%2 && ($k%4 || $k && idx($horiz, ($j-1)/2, $k/4-1))} {
		    append line " "
		} elseif {$j%2} {
		    append line "|"
		} elseif {0 == $k%4} {
		    append line "+"
		} elseif {$j && idx($verti, $j/2-1, $k/4)} {
		    append line " "
		} else {
		    append line "-"
		}
	    }
	    if {!$j} {
		lappend text [string replace $line 1 3 "   "]
	    } elseif {$x*2-1 == $j} {
		lappend text [string replace $line end end " "]
	    } else {
		lappend text $line
	    }
	}
	return [join $text \n]



   }



}



  1. Demonstration


maze create m 11 8
puts [m view]</lang>
Output:



+   +---+---+---+---+---+---+---+---+---+---+
|                   |               |       |
+---+---+   +---+---+   +   +---+   +---+   +
|           |           |   |       |       |
+   +   +---+   +---+---+   +---+   +   +   +
|   |   |               |       |   |   |   |
+   +---+   +---+---+---+   +   +   +   +   +
|       |   |           |   |   |       |   |
+   +   +   +   +---+---+   +   +---+---+   +
|   |       |       |       |   |   |       |
+---+---+---+---+   +   +---+   +   +   +---+
|               |   |   |   |   |   |       |
+   +---+---+   +   +   +   +   +   +---+   +
|       |   |       |       |   |       |   |
+---+   +   +---+---+---+---+   +   +---+   +
|                               |            
+---+---+---+---+---+---+---+---+---+---+---+



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