Maze generation

Maze generation
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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.

Ada

Works with: Ada 2005

Works with: GNAT

mazes.ads: <lang Ada>generic

  Height : Positive;
  Width : Positive;

package Mazes is

  type Maze_Grid is private;

  procedure Initialize (Maze : in out Maze_Grid);

  procedure Put (Item : Maze_Grid);

private

  type Directions is (North, South, West, East);

  type Cell_Walls is array (Directions) of Boolean;
  type Cells is record
     Walls   : Cell_Walls := (others => True);
     Visited : Boolean    := False;
  end record;

  subtype Height_Type is Positive range 1 .. Height;
  subtype Width_Type is Positive range 1 .. Width;

  type Maze_Grid is array (Height_Type, Width_Type) of Cells;

end Mazes;</lang> mazes.adb: <lang Ada>with Ada.Numerics.Discrete_Random; with Ada.Text_IO;

package body Mazes is

  package RNG is new Ada.Numerics.Discrete_Random (Positive);
  package Random_Direction is new Ada.Numerics.Discrete_Random (Directions);

  Generator     : RNG.Generator;
  Dir_Generator : Random_Direction.Generator;

  function "-" (Dir : Directions) return Directions;

  procedure Depth_First_Algorithm
    (Maze   : in out Maze_Grid;
     Row    : Height_Type;
     Column : Width_Type);

  function Has_Unvisited_Neighbours
    (Maze   : Maze_Grid;
     Row    : Height_Type;
     Column : Width_Type)
     return   Boolean;

  procedure Move
    (Row        : in out Height_Type;
     Column     : in out Width_Type;
     Direction  : Directions;
     Valid_Move : out Boolean);

  function "-" (Dir : Directions) return Directions is
  begin
     case Dir is
        when North =>
           return South;
        when South =>
           return North;
        when East =>
           return West;
        when West =>
           return East;
     end case;
  end "-";

  procedure Depth_First_Algorithm
    (Maze   : in out Maze_Grid;
     Row    : Height_Type;
     Column : Width_Type)
  is
     Next_Row        : Height_Type;
     Next_Column     : Width_Type;
     Next_Direction  : Directions;
     Valid_Direction : Boolean;
  begin
     -- mark as visited
     Maze (Row, Column).Visited := True;
     -- continue as long as there are unvisited neighbours left
     while Has_Unvisited_Neighbours (Maze, Row, Column) loop
        -- use random direction
        Next_Direction := Random_Direction.Random (Dir_Generator);
        Next_Row       := Row;
        Next_Column    := Column;
        Move (Next_Row, Next_Column, Next_Direction, Valid_Direction);
        if Valid_Direction then
           -- connect the two cells
           if not Maze (Next_Row, Next_Column).Visited then
              Maze (Row, Column).Walls (Next_Direction)              :=
                False;
              Maze (Next_Row, Next_Column).Walls (-Next_Direction)   :=
                False;
              Depth_First_Algorithm (Maze, Next_Row, Next_Column);
           end if;
        end if;
     end loop;
  end Depth_First_Algorithm;

  function Has_Unvisited_Neighbours
    (Maze   : Maze_Grid;
     Row    : Height_Type;
     Column : Width_Type)
     return   Boolean
  is
     Neighbour_Row    : Height_Type;
     Neighbour_Column : Width_Type;
     Is_Valid         : Boolean;
  begin
     for Dir in Directions loop
        Neighbour_Row    := Row;
        Neighbour_Column := Column;
        Move
          (Row        => Neighbour_Row,
           Column     => Neighbour_Column,
           Direction  => Dir,
           Valid_Move => Is_Valid);
        if Is_Valid
          and then not Maze (Neighbour_Row, Neighbour_Column).Visited
        then
           return True;
        end if;
     end loop;
     return False;
  end Has_Unvisited_Neighbours;

  procedure Initialize (Maze : in out Maze_Grid) is
     Row, Column : Positive;
  begin
     -- initialize random generators
     RNG.Reset (Generator);
     Random_Direction.Reset (Dir_Generator);
     -- choose starting cell
     Row    := RNG.Random (Generator) mod Height + 1;
     Column := RNG.Random (Generator) mod Width + 1;
     Ada.Text_IO.Put_Line
       ("Starting generation at " &
        Positive'Image (Row) &
        " x" &
        Positive'Image (Column));
     Depth_First_Algorithm (Maze, Row, Column);
  end Initialize;

  procedure Move
    (Row        : in out Height_Type;
     Column     : in out Width_Type;
     Direction  : Directions;
     Valid_Move : out Boolean)
  is
  begin
     Valid_Move := False;
     case Direction is
        when North =>
           if Row > Height_Type'First then
              Valid_Move := True;
              Row        := Row - 1;
           end if;
        when East =>
           if Column < Width_Type'Last then
              Valid_Move := True;
              Column     := Column + 1;
           end if;
        when West =>
           if Column > Width_Type'First then
              Valid_Move := True;
              Column     := Column - 1;
           end if;
        when South =>
           if Row < Height_Type'Last then
              Valid_Move := True;
              Row        := Row + 1;
           end if;
     end case;
  end Move;

  procedure Put (Item : Maze_Grid) is
  begin
     for Row in Item'Range (1) loop
        if Row = Item'First (1) then
           for Col in Item'Range (2) loop
              if Col = Item'First (2) then
                 Ada.Text_IO.Put ('+');
              end if;
              if Item (Row, Col).Walls (North) then
                 Ada.Text_IO.Put ("---");
              else
                 Ada.Text_IO.Put ("   ");
              end if;
              Ada.Text_IO.Put ('+');
           end loop;
           Ada.Text_IO.New_Line;
        end if;
        for Col in Item'Range (2) loop
           if Col = Item'First (2) then
              if Item (Row, Col).Walls (West) then
                 Ada.Text_IO.Put ('|');
              else
                 Ada.Text_IO.Put (' ');
              end if;
           elsif Item (Row, Col).Walls (West)
             and then Item (Row, Col - 1).Walls (East)
           then
              Ada.Text_IO.Put ('|');
           elsif Item (Row, Col).Walls (West)
             or else Item (Row, Col - 1).Walls (East)
           then
              Ada.Text_IO.Put ('>');
           else
              Ada.Text_IO.Put (' ');
           end if;
           if Item (Row, Col).Visited then
              Ada.Text_IO.Put ("   ");
           else
              Ada.Text_IO.Put ("???");
           end if;
           if Col = Item'Last (2) then
              if Item (Row, Col).Walls (East) then
                 Ada.Text_IO.Put ('|');
              else
                 Ada.Text_IO.Put (' ');
              end if;
           end if;
        end loop;
        Ada.Text_IO.New_Line;
        for Col in Item'Range (2) loop
           --for Col in Item'Range (2) loop
           if Col = Item'First (2) then
              Ada.Text_IO.Put ('+');
           end if;
           if Item (Row, Col).Walls (South) then
              Ada.Text_IO.Put ("---");
           else
              Ada.Text_IO.Put ("   ");
           end if;
           Ada.Text_IO.Put ('+');
           --end loop;
        end loop;
        Ada.Text_IO.New_Line;
     end loop;
  end Put;

end Mazes;</lang> Example main.adb: <lang Ada>with Mazes; procedure Main is

  package Small_Mazes is new Mazes (Height => 8, Width => 11);
  My_Maze : Small_Mazes.Maze_Grid;

begin

  Small_Mazes.Initialize (My_Maze);
  Small_Mazes.Put (My_Maze);

end Main;</lang>

Output:

Starting generation at  3 x 7
+---+---+---+---+---+---+---+---+---+---+---+
|   |               |   |                   |
+   +   +   +---+   +   +   +---+---+---+   +
|       |       |       |   |       |       |
+   +---+---+   +---+---+   +   +   +   +---+
|           |           |   |   |   |   |   |
+   +---+---+---+---+   +---+   +   +   +   +
|   |           |       |       |       |   |
+   +   +---+   +   +   +   +---+---+---+   +
|   |   |           |   |       |           |
+   +   +---+---+---+---+---+   +---+   +   +
|   |   |                   |           |   |
+---+   +   +---+---+---+   +---+---+---+   +
|       |   |           |                   |
+   +---+   +---+---+   +---+---+---+---+---+
|                                           |
+---+---+---+---+---+---+---+---+---+---+---+

Aime

<lang aime>void grid_maze(data b, integer N) {

   data d;
   integer i, j;

   j = N;
   while (j) {

b_suffix(d, "+---"); j -= 1;

   }
   {

b_suffix(d, "+\n");

   }

   j = N;
   while (j) {

b_suffix(d, "| * "); j -= 1;

   }
   {

b_suffix(d, "|\n");

   }

   i = N;
   while (i) {

b_extend(b, d);

i -= 1;

   }

   b_size(d, N * 4 + 2);

   {

b_extend(b, d);

   }

}

void walk_cell(data b, integer N, integer line_size, integer x, integer y, list x_offsets, list y_offsets) {

   integer i, r;

   b_replace(b, y + x, ' ');

   r = drand(3);

   i = 0;
   while (i < 4) {

integer p, q;

p = x + l_q_integer(x_offsets, (r + i) & 3); q = y + l_q_integer(y_offsets, (r + i) & 3);

if (-1 < p && p < line_size && -1 < q && q < line_size * (N * 2 + 1)) { if (b_text(b, q + p) == '*') { walk_cell(b, N, line_size, p, q, x_offsets, y_offsets); b_replace(b, (q + y) / 2 + (p + x) / 2, ' '); if (p == x) { b_replace(b, (q + y) / 2 + p - 1, ' '); b_replace(b, (q + y) / 2 + p + 1, ' '); } } }

i += 1;

   }

}

void walk_maze(data b, integer N) {

   integer line_size, x, y;
   list x_offsets, y_offsets;

   line_size = N * 4 + 1 + 1;

   lb_p_integer(x_offsets, 4);
   lb_p_integer(y_offsets, 0);
   lb_p_integer(x_offsets, 0);
   lb_p_integer(y_offsets, line_size * 2);
   lb_p_integer(x_offsets, -4);
   lb_p_integer(y_offsets, 0);
   lb_p_integer(x_offsets, 0);
   lb_p_integer(y_offsets, line_size * -2);

   x = drand(N - 1) * 4 + 2;
   y = line_size * (drand(N - 1) * 2 + 1);

   walk_cell(b, N, line_size, x, y, x_offsets, y_offsets);

}

integer main(void) {

   data b;
   integer N;

   N = 10;

   grid_maze(b, N);

   walk_maze(b, N);

   o_text(b_string(b));

   return 0;

}</lang>

Output:

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

AutoHotkey

For a challenge, this maze generation is entirely string based. That is to say, all operations including the wall removal and retrieval of cell states are done on the output string. <lang AHK>; Initially build the board Width := 11 Height := 8 Loop % height*2+1 { Outer := A_Index Loop % Width maze .= Outer & 1 ? "+-" : "|0" maze .= (Outer & 1 ? "+" : "|") "`n" } StringTrimRight, maze, maze, 1 ; removes trailing newline Clipboard := Walk(maze)

Walk(S, x=0, y=0){ If !x{ ; --Start at a random cell... StringReplace, junk, S, `n,,UseErrorLevel ; Calculate rows Random, y, 1, ErrorLevel//2 Random, x, 1, InStr(S, "`n")//2-1  ; Calculate height }

; --Obtain a list of its neighbors... neighbors := x "," y+1 "`n" x "," y-1 "`n" x+1 "," y "`n" x-1 "," y ; --Randomize the list... Sort neighbors, random

; --Then for each neighbor... Loop Parse, neighbors, `n { pC := InStr(A_LoopField, ","), x2 := SubStr(A_LoopField, 1, pC-1), y2 := SubStr(A_LoopField, pC+1) ; If it has not been visited... If GetChar(S, 2*x2, 2*y2) = "0"{ ; Mark it as visited... S := ChangeChar(s, 2*x2, 2*y2, " ") ; Remove the wall between this cell and the neighbor... S := ChangeChar(S, x+x2, y+y2, " ") ; Then recurse with the neighbor as the current cell S := Walk(S, x2, y2) } } return S }

Change a character in a string using x and y coordinates

ChangeChar(s, x, y, c){ Loop Parse, s, `n { If (A_Index = Y) Loop Parse, A_LoopField If (A_Index = x) out .= c Else out .= A_LoopField Else out .= A_LoopField out .= "`n" } StringTrimRight, out, out, 1 return out }

retrieve a character in a string using x and y coordinates

GetChar(s, x, y, n=1){ x*=n, y*=n Loop Parse, s, `n If (A_Index = Y) return SubStr(A_LoopField, x, 1) }</lang>

Sample output:

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

AWK

<lang awk>#!/usr/bin/awk -f

1. Remember: AWK is 1-based, for better or worse.

BEGIN {

   # The maze dimensions.
   width = 20;  # Global
   height = 20; # Global
   resetMaze();

   # Some constants.
   top = 1;
   bottom = 2;
   left = 3;
   right = 4;

   # Randomize the PRNG.
   randomize();

   # Visit all the cells starting at a random point.
   visitCell(getRandX(), getRandY());
   
   # Show the result.
   printMaze();

}

1. Wander through the maze removing walls as we go.

function visitCell(x, y, dirList, dir, nx, ny, ndir, pi) {

   setVisited(x, y);   # This cell has been visited.

   # Visit neighbors in a random order.
   dirList = getRandDirList();
   for (dir = 1; dir <= 4; dir++) {
       # Get coordinates of a random neighbor (next in random direction list).
       ndir = substr(dirList, dir, 1);
       nx = getNextX(x, ndir);
       ny = getNextY(y, ndir);
       
       # Visit an unvisited neighbor, removing the separating walls.
       if (wasVisited(nx, ny) == 0) {
           rmWall(x, y, ndir);
           rmWall(nx, ny, getOppositeDir(ndir));
           visitCell(nx, ny)
       } 
   }

}

1. Display the text-mode maze.

function printMaze( x, y, r, w) {

   for (y = 1; y <= height; y++) {
       for (pass = 1; pass <= 2; pass++) { # Go over each row twice: top, middle
           for (x = 1; x <= width; x++) {
               if (pass == 1) { # top
                   printf("+");
                   printf(hasWall(x, y, top) == 1 ? "---" : "   ");
                   if (x == width) printf("+");
               }
               else if (pass == 2) { # left, right
                   printf(hasWall(x, y, left) == 1 ? "|" : " ");
                   printf("   ");
                   if (x == width) printf(hasWall(x, y, right) == 1 ? "|" : " ");
               }
           }
           print;
       }
   }
   for (x = 1; x <= width; x++) printf("+---"); # bottom row
   print("+"); # bottom right corner

}

1. Given a direction, get its opposite.

function getOppositeDir(d) {

   if (d == top) return bottom;
   if (d == bottom) return top;
   if (d == left) return right;
   if (d == right) return left;

}

1. Build a list (string) of the four directions in random order.

function getRandDirList( dirList, randDir, nx, ny, idx) {

   dirList = "";
   while (length(dirList) < 4) {
       randDir = getRandDir();
       if (!index(dirList, randDir)) {
           dirList = dirList randDir;
       }
   }
   return dirList;

}

1. Get x coordinate of the neighbor in a given a direction.

function getNextX(x, dir) {

   if (dir == left) x = x - 1;
   if (dir == right) x = x + 1;
   if (!isGoodXY(x, 1)) return -1; # Off the edge.
   return x;

}

1. Get y coordinate of the neighbor in a given a direction.

function getNextY(y, dir) {

   if (dir == top) y = y - 1;
   if (dir == bottom) y = y + 1;
   if (!isGoodXY(1, y)) return -1; # Off the edge.
   return y;

}

1. Mark a cell as visited.

function setVisited(x, y, cell) {

   cell = getCell(x, y);
   if (cell == -1) return;
   cell = substr(cell, 1, 4) "1"; # walls plus visited
   setCell(x, y, cell);

}

1. Get the visited state of a cell.

function wasVisited(x, y, cell) {

   cell = getCell(x, y);
   if (cell == -1) return 1; # Off edges already visited.
   return substr(getCell(x,y), 5, 1);

}

1. Remove a cell's wall in a given direction.

function rmWall(x, y, d, i, oldCell, newCell) {

   oldCell = getCell(x, y);
   if (oldCell == -1) return;
   newCell = "";
   for (i = 1; i <= 4; i++) { # Ugly as concat of two substrings and a constant?.
       newCell = newCell (i == d ? "0" : substr(oldCell, i, 1));
   }
   newCell = newCell wasVisited(x, y);
   setCell(x, y, newCell);

}

1. Determine if a cell has a wall in a given direction.

function hasWall(x, y, d, cell) {

   cell = getCell(x, y);
   if (cell == -1) return 1; # Cells off edge always have all walls.
   return substr(getCell(x, y), d, 1);

}

1. Plunk a cell into the maze.

function setCell(x, y, cell, idx) {

   if (!isGoodXY(x, y)) return;
   maze[x, y] = cell

}

1. Get a cell from the maze.

function getCell(x, y, idx) {

   if (!isGoodXY(x, y)) return -1; # Bad cell marker.
   return maze[x, y];

}

1. Are the given coordinates in the maze?

function isGoodXY(x, y) {

   if (x < 1 || x > width) return 0;
   if (y < 1 || y > height) return 0;
   return 1;

}

1. Build the empty maze.

function resetMaze( x, y) {

   delete maze;
   for (y = 1; y <= height; y++) {
       for (x = 1; x <= width; x++) {
           maze[x, y] = "11110"; # walls (up, down, left, right) and visited state.
       }
   }

}

1. Random things properly scaled.

function getRandX() {

   return 1 + int(rand() * width);

}

function getRandY() {

   return 1 +int(rand() * height);

}

function getRandDir() {

   return 1 + int(rand() * 4);

}

function randomize() {

   "echo $RANDOM" | getline t;
   srand(t);

} </lang>

Example output:

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

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> MazeWidth% = 11

     MazeHeight% = 9
     MazeCell% = 50
     
     VDU 23,22,MazeWidth%*MazeCell%/2+3;MazeHeight%*MazeCell%/2+3;8,16,16,128
     VDU 23,23,3;0;0;0; : REM Line thickness
     PROCgeneratemaze(Maze&(), MazeWidth%, MazeHeight%, MazeCell%)
     END
     
     DEF PROCgeneratemaze(RETURN m&(), w%, h%, s%)
     LOCAL x%, y%
     DIM m&(w%, h%)
     FOR y% = 0 TO h%
       LINE 0,y%*s%,w%*s%,y%*s%
     NEXT
     FOR x% = 0 TO w%
       LINE x%*s%,0,x%*s%,h%*s%
     NEXT
     GCOL 15
     PROCcell(m&(), RND(w%)-1, y% = RND(h%)-1, w%, h%, s%)
     ENDPROC
     
     DEF PROCcell(m&(), x%, y%, w%, h%, s%)
     LOCAL i%, p%, q%, r%
     m&(x%,y%) OR= &40 : REM Mark visited
     r% = RND(4)
     FOR i% = r% TO r%+3
       CASE i% MOD 4 OF
         WHEN 0: p% = x%-1 : q% = y%
         WHEN 1: p% = x%+1 : q% = y%
         WHEN 2: p% = x% : q% = y%-1
         WHEN 3: p% = x% : q% = y%+1
       ENDCASE
       IF p% >= 0 IF p% < w% IF q% >= 0 IF q% < h% IF m&(p%,q%) < &40 THEN
         IF p% > x% m&(p%,q%) OR= 1 : LINE p%*s%,y%*s%+4,p%*s%,(y%+1)*s%-4
         IF q% > y% m&(p%,q%) OR= 2 : LINE x%*s%+4,q%*s%,(x%+1)*s%-4,q%*s%
         IF x% > p% m&(x%,y%) OR= 1 : LINE x%*s%,y%*s%+4,x%*s%,(y%+1)*s%-4
         IF y% > q% m&(x%,y%) OR= 2 : LINE x%*s%+4,y%*s%,(x%+1)*s%-4,y%*s%
         PROCcell(m&(), p%, q%, w%, h%, s%)
       ENDIF
     NEXT
     ENDPROC</lang>

Sample output:

C

Generation/solver in one. Requires UTF8 locale and unicode capable console. If your console font line-drawing chars are single width, define DOUBLE_SPACE to 0. <lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <string.h>
3. include <locale.h>

1. define DOUBLE_SPACE 1

1. if DOUBLE_SPACE
2. define SPC "　"
3. else
4. define SPC " "
5. endif

wchar_t glyph[] = L""SPC"│││─┘┐┤─└┌├─┴┬┼"SPC"┆┆┆┄╯╮ ┄╰╭ ┄";

typedef unsigned char byte; enum { N = 1, S = 2, W = 4, E = 8, V = 16 };

byte **cell; int w, h, avail;

1. define each(i, x, y) for (i = x; i <= y; i++)

int irand(int n) { int r, rmax = n * (RAND_MAX / n); while ((r = rand()) >= rmax); return r / (RAND_MAX/n); }

void show() { int i, j, c; each(i, 0, 2 * h) { each(j, 0, 2 * w) { c = cell[i][j]; if (c > V) printf("\033[31m"); printf("%lc", glyph[c]); if (c > V) printf("\033[m"); } putchar('\n'); } }

inline int max(int a, int b) { return a >= b ? a : b; } inline int min(int a, int b) { return b >= a ? a : b; }

static int dirs[4][2] = {{-2, 0}, {0, 2}, {2, 0}, {0, -2}}; void walk(int x, int y) { int i, t, x1, y1, d[4] = { 0, 1, 2, 3 };

cell[y][x] |= V; avail--;

for (x1 = 3; x1; x1--) if (x1 != (y1 = irand(x1 + 1))) i = d[x1], d[x1] = d[y1], d[y1] = i;

for (i = 0; avail && i < 4; i++) { x1 = x + dirs[ d[i] ][0], y1 = y + dirs[ d[i] ][1];

if (cell[y1][x1] & V) continue;

/* break walls */ if (x1 == x) { t = (y + y1) / 2; cell[t][x+1] &= ~W, cell[t][x] &= ~(E|W), cell[t][x-1] &= ~E; } else if (y1 == y) { t = (x + x1)/2; cell[y-1][t] &= ~S, cell[y][t] &= ~(N|S), cell[y+1][t] &= ~N; } walk(x1, y1); } }

int solve(int x, int y, int tox, int toy) { int i, t, x1, y1;

cell[y][x] |= V; if (x == tox && y == toy) return 1;

each(i, 0, 3) { x1 = x + dirs[i][0], y1 = y + dirs[i][1]; if (cell[y1][x1]) continue;

/* mark path */ if (x1 == x) { t = (y + y1)/2; if (cell[t][x] || !solve(x1, y1, tox, toy)) continue;

cell[t-1][x] |= S, cell[t][x] |= V|N|S, cell[t+1][x] |= N; } else if (y1 == y) { t = (x + x1)/2; if (cell[y][t] || !solve(x1, y1, tox, toy)) continue;

cell[y][t-1] |= E, cell[y][t] |= V|E|W, cell[y][t+1] |= W; } return 1; }

/* backtrack */ cell[y][x] &= ~V; return 0; }

void make_maze() { int i, j; int h2 = 2 * h + 2, w2 = 2 * w + 2; byte **p;

p = calloc(sizeof(byte*) * (h2 + 2) + w2 * h2 + 1, 1);

p[1] = (byte*)(p + h2 + 2) + 1; each(i, 2, h2) p[i] = p[i-1] + w2; p[0] = p[h2]; cell = &p[1];

each(i, -1, 2 * h + 1) cell[i][-1] = cell[i][w2 - 1] = V; each(j, 0, 2 * w) cell[-1][j] = cell[h2 - 1][j] = V; each(i, 0, h) each(j, 0, 2 * w) cell[2*i][j] |= E|W; each(i, 0, 2 * h) each(j, 0, w) cell[i][2*j] |= N|S; each(j, 0, 2 * w) cell[0][j] &= ~N, cell[2*h][j] &= ~S; each(i, 0, 2 * h) cell[i][0] &= ~W, cell[i][2*w] &= ~E;

avail = w * h; walk(irand(2) * 2 + 1, irand(h) * 2 + 1);

/* reset visited marker (it's also used by path finder) */ each(i, 0, 2 * h) each(j, 0, 2 * w) cell[i][j] &= ~V; solve(1, 1, 2 * w - 1, 2 * h - 1);

show(); }

int main(int c, char **v) { setlocale(LC_ALL, ""); if (c < 2 || (w = atoi(v[1])) <= 0) w = 16; if (c < 3 || (h = atoi(v[2])) <= 0) h = 8;

make_maze();

return 0; }</lang>

Sample output:

┌───┬─────┬─────────┬───────┬───┐
│┄┄╮│╭┄┄┄╮│　　╭┄┄┄┄┄╮│　　╭┄┄┄╮│╭┄╮│
│　│┆│┆──┐┆│　│┆──┬─┐┆└──┆┌─┐┆│┆│┆│
│　│┆│╰┄╮│┆│　│╰┄╮│　│╰┄┄┄╯│　│╰┄╯│┆│
│　│┆└──┆│┆└─┼──┆│　└─────┤　└─┬─┘┆│
│　│╰┄┄┄╯│╰┄╮│╭┄╯│　　　　　　　│　　　│╭┄╯│
│　└─────┴─┐┆│┆┌─┴───┐　│　│　│　│┆──┤
│　　　　　　　　　│┆│┆│╭┄┄┄╮│　│　　　│　│╰┄╮│
│　──────┐　│┆│┆│┆──┐┆└─┤　┌─┘　└─┐┆│
│　　　　　　　│　│┆│╰┄╯　　│╰┄╮│　│　　　　　│┆│
│　┌─────┘　│┆├─────┴─┐┆│　│　──┬─┘┆│
│　│　　　　　　　│┆│╭┄┄┄┄┄╮│┆│　│　　　│╭┄╯│
├─┤　──┬─┬─┘┆│┆┌─┬──┆│┆└─┴─┐　│┆┌─┤
│　│　　　│　│╭┄╯│┆│　│╭┄╯│╰┄┄┄╮│　│┆│　│
│　└──　│　│┆──┘┆│　│┆──┴────┆│　│┆│　│
│　　　　　│　　╰┄┄┄╯│　　╰┄┄┄┄┄┄┄╯│　　╰┄┄│
└─────┴───────┴───────────┴─────┘

The very alternative version

Invoke as ./maze [width] [depth] [height], and output is in maze.pgm, which you can print out and cut to fold into a cuboid. Sample output with 15, 10 and 20 sizes.

<lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <string.h>

1. define CW 10 /* cell width. This decides how big the output is */

typedef struct cell_t cell_t, *cell;

enum { N, E, S, W, V }; struct cell_t { unsigned int flags; cell prev, next, nei[4]; /* neighbors */ };

int sx, sy, sz, w, h;

1. define C(y, x) c[(y) * w + x]
2. define P(y, x) pix[(y) * w2 + x]

void draw_maze(cell *c) {

1. define FOR(a, b) for(a = 0; a < b; a++)

FILE *fp; int w2 = w * CW + 8, h2 = h * CW + 7; char *pix = malloc(w2 * h2); memset(pix, 200, w2 * h2);

void draw_face(int x, int y, int ww, int hh, int px, int py) { int i, j, k, l; cell t;

px += 2, py += 2; for (i = py; i <= py + hh * CW; i++) memset(&P(i, px), 0, ww * CW+1);

px++, py++;

1. define mark(y, x) P(py + CW*i + y, px + CW*j + x) = 255

FOR (i, hh) FOR (j, ww) { FOR(k, CW - 1) FOR(l, CW - 1) mark(k, l);

t = C(y + i, x + j); if (t->flags & (1 << N)) FOR (l, CW - 1) mark(-1, l); if (t->flags & (1 << S)) FOR (l, CW - 1) mark(CW - 1, l); if (t->flags & (1 << E)) FOR (l, CW - 1) mark(l, CW - 1); if (t->flags & (1 << W)) FOR (l, CW - 1) mark(l, -1); } }

draw_face(0, 0, sx, sy, 0, 0); draw_face(0, sy, sx, sz, 0, CW*sy + 1); draw_face(sx, sy, sy, sz, CW*sx + 1, CW*sy + 1); draw_face(sx + sy, sy, sx, sz, CW*(sx + sy) + 2, CW*sy + 1); draw_face(sx + sy + sx, sy, sy, sz, CW*(sx + sy + sx) + 3, CW*sy + 1); draw_face(sx + sy, sy + sz, sx, sy, CW*(sx + sy) + 2, CW*(sy + sz) + 2);

fp = fopen("maze.pgm", "w+"); fprintf(fp, "P5\n%d %d\n255\n", w2, h2); fwrite(pix, 1, w2 * h2, fp); fclose(fp); }

cell rand_neighbor(cell x) { cell r = 0; int i, c = 1; for (i = N; i <= W; i++) { if (!x->nei[i] || (x->nei[i]->flags & (1 << V))) continue; if (rand() % c++ == 0) r = x->nei[i]; } return r; }

void link_cells(cell a, cell b) { int i; for (i = N; i <= W; i++) { if (a->nei[i] != b) continue; a->flags |= 1 << i; break; } for (i = N; i <= W; i++) { if (b->nei[i] != a) continue; b->flags |= 1 << i; break; } }

void walk(cell head) { cell tail = head, p, n;

while (head) { for (p = head; p; p = n) { p->flags |= 1 << V; n = rand_neighbor(p); if (!n) break; tail->next = n; n->prev = tail;

tail = n; link_cells(p, n); } while (head && !rand_neighbor(head)) head = head->next; } }

void make_maze(void) { int i, j; int n = (sx * sy + sx * sz + sy * sz) * 2; cell t, *c; cell_t * cells;

w = 2 * sx + 2 * sy, h = sy * 2 + sz; cells = calloc(sizeof(cell_t), n); c = calloc(sizeof(cell), w * h);

for (i = 0; i < sy; i++) for (j = 0; j < sx; j++) C(i, j) = cells + --n; for (; i < sy + sz; i++) for (j = 0; j < w; j++) C(i, j) = cells + --n; for (; i < h; i++) for (j = sx + sy; j < w - sy; j++) C(i, j) = cells + --n;

for (i = 0; i < h; i++) { for (j = 0; j < w; j++) { t = C(i, j); if (!t) continue; if (i) t->nei[N] = C(i - 1, j); if (i < h - 1) t->nei[S] = C(i + 1, j); if (j) t->nei[W] = C(i, j - 1); if (j < w - 1) t->nei[E] = C(i, j + 1); } }

for (j = 0; j < sx; j++) { C(0, j)->nei[N] = C(sy, w - sy - j - 1); C(sy, w - sy - j - 1)->nei[N] = C(0, j);

C(h - sy - 1, j)->nei[S] = C(h - 1, w - sy - j - 1); C(h - 1, w - sy - j - 1)->nei[S] = C(h - sy - 1, j); }

for (i = sy; i < sy + sz; i++) { C(i, 0)->nei[W] = C(i, w - 1); C(i, w - 1)->nei[E] = C(i, 0); }

for (i = 0; i < sy; i++) { C(i, 0)->nei[W] = C(sy, w - sy + i); C(sy, w - sy + i)->nei[N] = C(i, 0);

C(i, sx - 1)->nei[E] = C(sy, sx + sy - i - 1); C(sy, sx + sy - i - 1)->nei[N] = C(i, sx - 1);

C(h - sy - 1, sx + i)->nei[S] = C(h - 1 - i, sx + sy); C(h - 1 - i, sx + sy)->nei[W] = C(h - sy - 1, sx + i);

C(sy + sz + i, w - sy - 1)->nei[E] = C(sy + sz - 1, w - sy + i); C(sy + sz - 1, w - sy + i)->nei[S] = C(sy + sz + i, w - sy - 1); }

walk(C(0, 0)); draw_maze(c); }

int main(int c, char **v) { if (c < 2 || (sx = atoi(v[1])) <= 0) sx = 10; if (c < 3 || (sy = atoi(v[2])) <= 0) sy = sx; if (c < 4 || (sz = atoi(v[3])) <= 0) sz = sy;

make_maze();

return 0; }</lang>

C++

<lang cpp>

1. include <windows.h>
2. include <iostream>
3. include <string>

//-------------------------------------------------------------------------------------------------- using namespace std;

//-------------------------------------------------------------------------------------------------- const int BMP_SIZE = 512, CELL_SIZE = 8;

//-------------------------------------------------------------------------------------------------- enum directions { NONE, NOR = 1, EAS = 2, SOU = 4, WES = 8 };

//-------------------------------------------------------------------------------------------------- class myBitmap { public:

   myBitmap() : pen( NULL ) {}
   ~myBitmap()
   {

DeleteObject( pen ); DeleteDC( hdc ); DeleteObject( bmp );

   }

   bool create( int w, int h )
   {

BITMAPINFO bi; ZeroMemory( &bi, sizeof( bi ) ); bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h;

HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false;

hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc ); width = w; height = h;

return true;

   }

   void clear()
   {

ZeroMemory( pBits, width * height * sizeof( DWORD ) );

   }

   void setPenColor( DWORD clr )
   {

if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, 1, clr ); SelectObject( hdc, pen );

   }

   void saveBitmap( string path )
   {

BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD wb;

GetObject( bmp, sizeof( bitmap ), &bitmap );

DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );

delete [] dwpBits;

   }

   HDC getDC() const     { return hdc; }
   int getWidth() const  { return width; }
   int getHeight() const { return height; }

private:

   HBITMAP bmp;
   HDC	    hdc;
   HPEN    pen;
   void    *pBits;
   int	    width, height;

}; //-------------------------------------------------------------------------------------------------- class mazeGenerator { public:

   mazeGenerator()
   {

_world = 0; _bmp.create( BMP_SIZE, BMP_SIZE ); _bmp.setPenColor( RGB( 0, 255, 0 ) );

   }

   ~mazeGenerator() { killArray(); }

   void create( int side )
   {

_s = side; generate(); display();

   }

private:

   void generate()
   {

killArray(); _world = new BYTE[_s * _s]; ZeroMemory( _world, _s * _s ); _ptX = rand() % _s; _ptY = rand() % _s; carve();

   }

   void carve()
   {

while( true ) { int d = getDirection(); if( d < NOR ) return;

switch( d ) { case NOR: _world[_ptX + _s * _ptY] |= NOR; _ptY--; _world[_ptX + _s * _ptY] = SOU | SOU << 4; break; case EAS: _world[_ptX + _s * _ptY] |= EAS; _ptX++; _world[_ptX + _s * _ptY] = WES | WES << 4; break; case SOU: _world[_ptX + _s * _ptY] |= SOU; _ptY++; _world[_ptX + _s * _ptY] = NOR | NOR << 4; break; case WES: _world[_ptX + _s * _ptY] |= WES; _ptX--; _world[_ptX + _s * _ptY] = EAS | EAS << 4; } }

   }

   void display()
   {

_bmp.clear(); HDC dc = _bmp.getDC(); for( int y = 0; y < _s; y++ ) { int yy = y * _s; for( int x = 0; x < _s; x++ ) { BYTE b = _world[x + yy]; int nx = x * CELL_SIZE, ny = y * CELL_SIZE;

if( !( b & NOR ) ) { MoveToEx( dc, nx, ny, NULL ); LineTo( dc, nx + CELL_SIZE + 1, ny ); } if( !( b & EAS ) ) { MoveToEx( dc, nx + CELL_SIZE, ny, NULL ); LineTo( dc, nx + CELL_SIZE, ny + CELL_SIZE + 1 ); } if( !( b & SOU ) ) { MoveToEx( dc, nx, ny + CELL_SIZE, NULL ); LineTo( dc, nx + CELL_SIZE + 1, ny + CELL_SIZE ); } if( !( b & WES ) ) { MoveToEx( dc, nx, ny, NULL ); LineTo( dc, nx, ny + CELL_SIZE + 1 ); } } }

//_bmp.saveBitmap( "f:\\rc\\maze.bmp" ); BitBlt( GetDC( GetConsoleWindow() ), 10, 60, BMP_SIZE, BMP_SIZE, _bmp.getDC(), 0, 0, SRCCOPY );

   }

   int getDirection()
   {

int d = 1 << rand() % 4; while( true ) { for( int x = 0; x < 4; x++ ) { if( testDir( d ) ) return d; d <<= 1; if( d > 8 ) d = 1; } d = ( _world[_ptX + _s * _ptY] & 0xf0 ) >> 4; if( !d ) return -1; switch( d ) { case NOR: _ptY--; break; case EAS: _ptX++; break; case SOU: _ptY++; break; case WES: _ptX--; break; }

           d = 1 << rand() % 4;

}

   }

   bool testDir( int d )
   {

switch( d ) { case NOR: return ( _ptY - 1 > -1 && !_world[_ptX + _s * ( _ptY - 1 )] ); case EAS: return ( _ptX + 1 < _s && !_world[_ptX + 1 + _s * _ptY] ); case SOU: return ( _ptY + 1 < _s && !_world[_ptX + _s * ( _ptY + 1 )] ); case WES: return ( _ptX - 1 > -1 && !_world[_ptX - 1 + _s * _ptY] ); } return false;

   }

   void killArray() { if( _world ) delete [] _world; }

   BYTE*    _world;
   int      _s, _ptX, _ptY;
   myBitmap _bmp;

}; //-------------------------------------------------------------------------------------------------- int main( int argc, char* argv[] ) {

   ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );
   srand( GetTickCount() );

   mazeGenerator mg;
   int s;
   while( true )
   {

cout << "Enter the maze size, an odd number bigger than 2 ( 0 to QUIT ): "; cin >> s; if( !s ) return 0; if( !( s & 1 ) ) s++; if( s >= 3 ) mg.create( s ); cout << endl; system( "pause" ); system( "cls" );

   }
   return 0;

} //-------------------------------------------------------------------------------------------------- </lang>

C#

<lang csharp>using System; using System.Collections.Generic; using System.Diagnostics; using System.Linq; using System.Text; using System.Drawing;

namespace MazeGeneration {

   public static class Extensions
   {
       public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> source, Random rng)
       {
           var e = source.ToArray();
           for (var i = e.Length - 1; i >= 0; i--)
           {
               var swapIndex = rng.Next(i + 1);
               yield return e[swapIndex];
               e[swapIndex] = e[i];
           }
       }

       public static CellState OppositeWall(this CellState orig)
       {
           return (CellState)(((int) orig >> 2) | ((int) orig << 2)) & CellState.Initial;
       }
   }

   [Flags]
   public enum CellState
   {
       Top = 1,
       Right = 2,
       Bottom = 4,
       Left = 8,
       Visited = 128,
       Initial = Top | Right | Bottom | Left,
   }

   public struct RemoveWallAction
   {
       public Point Neighbour;
       public CellState Wall;
   }

   public class Maze
   {
       private readonly CellState[,] _cells;
       private readonly int _width;
       private readonly int _height;
       private readonly Random _rng;

       public Maze(int width, int height)
       {
           _width = width;
           _height = height;
           _cells = new CellState[width, height];
           for(var x=0; x<width; x++)
               for(var y=0; y<height; y++)
                   _cells[x, y] = CellState.Initial;
           _rng = new Random();
           VisitCell(_rng.Next(width), _rng.Next(height));
       }

       public CellState this[int x, int y]
       {
           get { return _cells[x,y]; }
           set { _cells[x,y] = value; }
       }

       public IEnumerable<RemoveWallAction> GetNeighbours(Point p)
       {
           if (p.X > 0) yield return new RemoveWallAction {Neighbour = new Point(p.X - 1, p.Y), Wall = CellState.Left};
           if (p.Y > 0) yield return new RemoveWallAction {Neighbour = new Point(p.X, p.Y - 1), Wall = CellState.Top};
           if (p.X < _width-1) yield return new RemoveWallAction {Neighbour = new Point(p.X + 1, p.Y), Wall = CellState.Right};
           if (p.Y < _height-1) yield return new RemoveWallAction {Neighbour = new Point(p.X, p.Y + 1), Wall = CellState.Bottom};
       }

       public void VisitCell(int x, int y)
       {
           this[x,y] |= CellState.Visited;
           foreach (var p in GetNeighbours(new Point(x, y)).Shuffle(_rng).Where(z => !(this[z.Neighbour.X, z.Neighbour.Y].HasFlag(CellState.Visited))))
           {
               this[x, y] -= p.Wall;
               this[p.Neighbour.X, p.Neighbour.Y] -= p.Wall.OppositeWall();
               VisitCell(p.Neighbour.X, p.Neighbour.Y);
           }
       }

       public void Display()
       {
           var firstLine = string.Empty;
           for (var y = 0; y < _height; y++)
           {
               var sbTop = new StringBuilder();
               var sbMid = new StringBuilder();
               for (var x = 0; x < _width; x++)
               {
                   sbTop.Append(this[x, y].HasFlag(CellState.Top) ? "+--" : "+  ");
                   sbMid.Append(this[x, y].HasFlag(CellState.Left) ? "|  " : "   ");
               }
               if (firstLine == string.Empty)
                   firstLine = sbTop.ToString();
               Debug.WriteLine(sbTop + "+");
               Debug.WriteLine(sbMid + "|");
               Debug.WriteLine(sbMid + "|");
           }
           Debug.WriteLine(firstLine);
       }
   }

   class Program
   {
       static void Main(string[] args)
       {
           var maze = new Maze(20, 20);
           maze.Display();
       }
   }

} </lang> Sample output:

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

Common Lisp

The remove-wall function has been written so as to be as close as possible to the specification. The walls are made from a single unicode character, specified by the block keyword, e. g. (maze 20 6 :block #\X). The BOX_DRAWINGS_LIGHT_DIAGONAL_CROSS character is used by default. <lang lisp>(defun shuffle (list)  ;; Z not uniform

 (sort list '> :key (lambda(x) (random 1.0))))

(defun neighbors (x y maze)

 (remove-if-not
  (lambda (x-y) (and (< -1 (first x-y) (array-dimension maze 0))
                (< -1 (second x-y) (array-dimension maze 1))))
  `((,x ,(+ y 2)) (,(- x 2) ,y) (,x ,(- y 2)) (,(+ x 2) ,y))))

(defun remove-wall (maze x y &optional visited)

 (labels ((walk (maze x y)
            (push (list x y) visited)
            (loop for (u v) in (shuffle (neighbors x y maze))
               unless (member (list u v) visited :test 'equal)
               do (setf (aref maze u v) #\space
                        (aref maze (/ (+ x u) 2) (/ (+ y v) 2)) #\space)
                  (walk maze u v))))
   (setf (aref maze x y) #\space)
   (walk maze x y)))

(defun draw-maze (width height &key (block #\BOX_DRAWINGS_LIGHT_DIAGONAL_CROSS))

 (let ((maze (make-array (list (1+ (* 2 height)) (1+ (* 2 width)))
                         :element-type 'character :initial-element block)))
   (remove-wall maze (1+ (* 2 (random height))) (1+ (* 2 (random width))))
   (loop for i below (array-dimension maze 0)
         do (fresh-line)
            (loop for j below (array-dimension maze 1)
                  do (princ (aref maze i j))))))

(draw-maze 20 6)</lang>

Output:

╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳
╳         ╳       ╳     ╳         ╳     ╳
╳ ╳╳╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳
╳ ╳     ╳   ╳ ╳ ╳     ╳       ╳ ╳ ╳     ╳
╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳╳╳╳╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳
╳   ╳ ╳ ╳     ╳ ╳   ╳     ╳     ╳ ╳   ╳ ╳
╳╳╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳
╳ ╳ ╳ ╳     ╳ ╳   ╳   ╳   ╳   ╳ ╳   ╳ ╳ ╳
╳ ╳ ╳ ╳╳╳╳╳╳╳ ╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳╳╳ ╳╳╳ ╳
╳   ╳   ╳ ╳   ╳ ╳   ╳ ╳     ╳     ╳   ╳ ╳
╳ ╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳ ╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳╳╳ ╳ ╳
╳       ╳         ╳         ╳ ╳         ╳
╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳

Another solution using unicode line drawing chars. Assumes they are single width on console. Code pretty horribly unreadable. <lang lisp>(setf *random-state* (make-random-state t))

(defun 2d-array (w h)

 (make-array (list h w) :initial-element 0))

(defmacro or-and (v a b c)

 `(if (or ,a (and ,b (= 1 ,c))) 0 ,v))

(defun make-maze (w h)

 (let ((vis (2d-array w h))

(ver (2d-array w h)) (hor (2d-array w h)))

   (labels
     ((walk (y x)

(setf (aref vis y x) 1) (loop (let (x2 y2) (loop for (dx dy) in '((-1 0) (1 0) (0 -1) (0 1)) with cnt = 0 do (let ((xx (+ x dx)) (yy (+ y dy))) (if (and (array-in-bounds-p vis yy xx) (zerop (aref vis yy xx)) (zerop (random (incf cnt)))) (setf x2 xx y2 yy)))) (if (not x2) (return-from walk)) (if (= x x2) (setf (aref hor (min y y2) x) 1) (setf (aref ver y (min x x2)) 1)) (walk y2 x2))))

     (show ()

(let ((g " │││─┘┐┤─└┌├─┴┬┼")) (loop for i from 0 to h do (loop for j from 0 to w do (format t "~c~a" (char g (+ (or-and 1 (= i 0) (> j 0) (aref ver (1- i) (1- j))) (or-and 2 (= i h) (> j 0) (aref ver i (1- j))) (or-and 4 (= j 0) (> i 0) (aref hor (1- i) (1- j))) (or-and 8 (= j w) (> i 0) (aref hor (1- i) j )))) (if (and (< j w) (or (= i 0) (= 0 (aref hor (1- i) j)))) "───" " "))) (terpri) (when (< i h) (loop for j from 0 below w do (format t (if (or (= j 0) (= 0 (aref ver i (1- j)))) "│ " " "))) (format t "│~%"))))))

     (walk (random h) (random w))
     (show))))

(make-maze 20 20)</lang>

Output:

┼───┴───┼───┴───┴───┼───┴───┴───┼
│       │           │           │
┼────   │   │   │   │   ┌───┐   ├
│       │   │   │   │   │   │   │
┤   ┌───┘   │   │   │   │   │   ├
│   │       │   │       │   │   │
┤   │   ┌───┘   ├───────┤   │   ├
│   │   │       │       │       │
┤   │   │   ────┤   │   │   ────┼
│       │       │   │   │       │
┤   ────┼───┐   │   │   └───┐   ├
│       │   │       │       │   │
┼───┐   │   └───────┼───┐   └───┼
│   │               │   │       │
┤   └────────────   │   └───┐   ├
│                           │   │
┼───┬───┬───┬───┬───┬───┬───┼───┼

D

<lang d>void main() @safe {

   import std.stdio, std.algorithm, std.range, std.random;

   enum uint w = 14, h = 10;
   auto vis = new bool[][](h, w),
        hor = iota(h + 1).map!(_ => ["+---"].replicate(w)).array,
        ver = h.iota.map!(_ => ["|   "].replicate(w) ~ "|").array;

   void walk(in uint x, in uint y) /*nothrow*/ @safe /*@nogc*/ {
       vis[y][x] = true;
       //foreach (immutable p; [[x-1,y], [x,y+1], [x+1,y], [x,y-1]].randomCover) {
       foreach (const p; [[x-1, y], [x, y+1], [x+1, y], [x, y-1]].randomCover) {
           if (p[0] >= w || p[1] >= h || vis[p[1]][p[0]]) continue;
           if (p[0] == x) hor[max(y, p[1])][x] = "+   ";
           if (p[1] == y) ver[y][max(x, p[0])] = "    ";
           walk(p[0], p[1]);
       }
   }
   walk(uniform(0, w), uniform(0, h));
   foreach (const a, const b; hor.zip(ver ~ []))
       join(a ~ "+\n" ~ b).writeln;

}</lang>

Output:

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

EGL

<lang EGL>program MazeGen

   // First and last columns/rows are "dead" cells. Makes generating
   // a maze with border walls much easier. Therefore, a visible
   // 20x20 maze has a maze size of 22. 	
   mazeSize int = 22;

   south boolean[][];
   west boolean[][];
   visited boolean[][];

   function main()
       initMaze();
       generateMaze();
       drawMaze();
   end

   private function initMaze()

       visited = createBooleanArray(mazeSize, mazeSize, false);

       // Initialize border cells as already visited
       for(col int from 1 to mazeSize)
           visited[col][1] = true;
           visited[col][mazeSize] = true;
       end
       for(row int from 1 to mazeSize)
           visited[1][row] = true;
           visited[mazeSize][row] = true;
       end

       // Initialize all walls as present
       south = createBooleanArray(mazeSize, mazeSize, true);
       west = createBooleanArray(mazeSize, mazeSize, true);

   end

   private function createBooleanArray(col int in, row int in, initialState boolean in) returns(boolean[][])

       newArray boolean[][] = new boolean[0][0];

       for(i int from 1 to col)
           innerArray boolean[] = new boolean[0];
           for(j int from 1 to row)
               innerArray.appendElement(initialState);
           end
           newArray.appendElement(innerArray);
       end

       return(newArray);

   end

   private function createIntegerArray(col int in, row int in, initialValue int in) returns(int[][])

       newArray int[][] = new int[0][0];

       for(i int from 1 to col)
           innerArray int[] = new int[0];
           for(j int from 1 to row)
               innerArray.appendElement(initialValue);
           end
           newArray.appendElement(innerArray);
       end

       return(newArray);

   end

   private function generate(col int in, row int in)

       // Mark cell as visited
       visited[col][row] = true;

       // Keep going as long as there is an unvisited neighbor
       while(!visited[col][row + 1] || !visited[col + 1][row] ||
               !visited[col][row - 1] || !visited[col - 1][row])

           while(true)
               r float = MathLib.random(); // Choose a random direction
               
               case
                   when(r < 0.25 && !visited[col][row + 1]) // Go south
                       south[col][row] = false; // South wall down
                       generate(col, row + 1);
                       exit while;
                   when(r >= 0.25 && r < 0.50 && !visited[col + 1][row]) // Go east 
                       west[col + 1][row] = false; // West wall of neighbor to the east down
                       generate(col + 1, row);
                       exit while;
                   when(r >= 0.5 && r < 0.75 && !visited[col][row - 1]) // Go north
                       south[col][row - 1] = false; // South wall of neighbor to the north down
                       generate(col, row - 1);
                       exit while;
                   when(r >= 0.75 && r < 1.00 && !visited[col - 1][row]) // Go west
                       west[col][row] = false; // West wall down
                       generate(col - 1, row);
                       exit while;
               end
           end
       end

   end

   private function generateMaze()

       // Pick random start position (within the visible maze space)
       randomStartCol int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
       randomStartRow int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);

       generate(randomStartCol, randomStartRow);

   end

   private function drawMaze()

       line string;

       // Iterate over wall arrays (skipping dead border cells as required). 
       // Construct a line at a time and output to console.
       for(row int from 1 to mazeSize - 1)

           if(row > 1)
               line = "";
               for(col int from 2 to mazeSize)
                   if(west[col][row])
                       line ::= "|   ";
                   else
                       line ::= "    ";
                   end
               end
               Syslib.writeStdout(line);
           end

           line = "";
           for(col int from 2 to mazeSize - 1)
               if(south[col][row])
                   line ::= "+---";
               else
                   line ::= "+   ";
               end
           end
           line ::= "+";
           SysLib.writeStdout(line);

       end

   end

end</lang>

Output example (for 10x10 maze):

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

Erlang

Erlang is single assignment. To get mutability I use processes. The code is over-enginered for this task, but the extra is used for Maze_solving. Also, Erlang starts counting at 1, not 0, so the co-ordinate of the lower left corner is 1,1. <lang Erlang> -module( maze ).

-export( [cell_accessible_neighbours/1, cell_content/1, cell_content_set/2, cell_pid/3, cell_position/1, display/1, generation/2, stop/1, task/0] ).

-record( maze, {dict, max_x, max_y, start} ). -record( state, {content=" ", controller, is_dug=false, max_x, max_y, neighbours=[], position, walls=[north, south, east, west], walk_done} ).

cell_accessible_neighbours( Pid ) -> read( Pid, accessible_neighbours ).

cell_content( Pid ) -> read( Pid, content ).

cell_content_set( Pid, Content ) -> Pid ! {content, Content, erlang:self()}.

cell_pid( X, Y, Maze ) -> dict:fetch( {X, Y}, Maze#maze.dict ).

cell_position( Pid ) -> read( Pid, position ).

display( #maze{dict=Dict, max_x=Max_x, max_y=Max_y} ) -> Position_pids = dict:to_list( Dict ), display( Max_x, Max_y, reads(Position_pids, content), reads(Position_pids, walls) ).

generation( Max_x, Max_y ) ->

      Controller = erlang:self(),
      Position_pids = cells_create( Controller, Max_x, Max_y ),
      Pids = [Y || {_X, Y} <- Position_pids],
      [X ! {position_pids, Position_pids} || X <- Pids],
      {Position, Pid} = lists:nth( random:uniform(Max_x * Max_y), Position_pids ),
      Pid ! {dig, Controller},
      receive
      {dig_done} -> ok
      end,
      #maze{dict=dict:from_list(Position_pids), max_x=Max_x, max_y=Max_y, start=Position}.

stop( #maze{dict=Dict} ) ->

     Controller = erlang:self(),
     Pids = [Y || {_X, Y} <- dict:to_list(Dict)],
     [X ! {stop, Controller} || X <- Pids],
     ok.

task() ->

      Maze = generation( 16, 8 ),
      io:fwrite( "Starting at ~p~n", [Maze#maze.start] ),
      display( Maze ),
      stop( Maze ).

cells_create( Controller, Max_x, Max_y ) -> [{{X, Y}, cell_create(Controller, Max_x, Max_y, {X, Y})} || X <- lists:seq(1, Max_x), Y<- lists:seq(1, Max_y)].

cell_create( Controller, Max_x, Max_y, {X, Y} ) -> erlang:spawn_link( fun() -> random:seed( X*1000, Y*1000, (X+Y)*1000 ), loop( #state{controller=Controller, max_x=Max_x, max_y=Max_y, position={X, Y}} ) end ).

display( Max_x, Max_y, Position_contents, Position_walls ) ->

       All_rows = [display_row( Max_x, Y, Position_contents, Position_walls ) || Y <- lists:seq(Max_y, 1, -1)],
       [io:fwrite("~s+~n~s|~n", [North, West]) || {North, West} <- All_rows],

io:fwrite("~s+~n", [lists:flatten(lists:duplicate(Max_x, display_row_north(true)))] ).

display_row( Max_x, Y, Position_contents, Position_walls ) -> North_wests = [display_row_walls(proplists:get_value({X,Y}, Position_contents), proplists:get_value({X,Y}, Position_walls)) || X <- lists:seq(1, Max_x)], North = lists:append( [North || {North, _West} <- North_wests] ), West = lists:append( [West || {_X, West} <- North_wests] ), {North, West}.

display_row_walls( Content, Walls ) -> {display_row_north( lists:member(north, Walls) ), display_row_west( lists:member(west, Walls), Content )}.

display_row_north( true ) -> "+---"; display_row_north( false ) -> "+ ".

display_row_west( true, Content ) -> "| " ++ Content ++ " "; display_row_west( false, Content ) -> " " ++ Content ++ " ".

loop( State ) ->

   receive
   {accessible_neighbours, Pid} ->
   	Pid ! {accessible_neighbours, loop_accessible_neighbours( State#state.neighbours, State#state.walls ), erlang:self()},
       loop( State );
   {content, Pid} ->
   	Pid ! {content, State#state.content, erlang:self()},
       loop( State );
   {content, Content, _Pid} ->
       loop( State#state{content=Content} );
   {dig, Pid} ->

Not_dug_neighbours = loop_not_dug( State#state.neighbours ), New_walls = loop_dig( Not_dug_neighbours, lists:delete( loop_wall_from_pid(Pid, State#state.neighbours), State#state.walls), Pid ), loop( State#state{is_dug=true, walls=New_walls, walk_done=Pid} );

   {dig_done} ->

Not_dug_neighbours = loop_not_dug( State#state.neighbours ), New_walls = loop_dig( Not_dug_neighbours, State#state.walls, State#state.walk_done ), loop( State#state{walls=New_walls} );

   {is_dug, Pid} ->
   	    Pid ! {is_dug, State#state.is_dug, erlang:self()},

loop( State );

   {position, Pid} ->
   	Pid ! {position, State#state.position, erlang:self()},
       loop( State );
   {position_pids, Position_pids} ->
       {_My_position, Neighbours} = lists:foldl( fun loop_neighbours/2, {State#state.position, []}, Position_pids ),
       erlang:garbage_collect(), % Shrink process after using large Pid_positions. For memory starved systems.
       loop( State#state{neighbours=Neighbours} );
   {stop, Controller} when Controller =:= State#state.controller ->
   	   ok;
   {walls, Pid} ->
   	    Pid ! {walls, State#state.walls, erlang:self()},

loop( State )

   end.

loop_accessible_neighbours( Neighbours, Walls ) -> [Pid || {Direction, Pid} <- Neighbours, not lists:member(Direction, Walls)].

loop_dig( [], Walls, Pid ) -> Pid ! {dig_done}, Walls; loop_dig( Not_dug_neighbours, Walls, _Pid ) ->

       {Dig_pid, Dig_direction} = lists:nth( random:uniform(erlang:length(Not_dug_neighbours)), Not_dug_neighbours ),
       Dig_pid ! {dig, erlang:self()},

lists:delete( Dig_direction, Walls ).

loop_neighbours( {{X, Y}, Pid}, {{X, My_y}, Acc} ) when Y =:= My_y + 1 -> {{X, My_y}, [{north, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{X, My_y}, Acc} ) when Y =:= My_y - 1 -> {{X, My_y}, [{south, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{My_x, Y}, Acc} ) when X =:= My_x + 1 -> {{My_x, Y}, [{east, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{My_x, Y}, Acc} ) when X =:= My_x - 1 -> {{My_x, Y}, [{west, Pid} | Acc]}; loop_neighbours( _Position_pid, Acc ) -> Acc.

loop_not_dug( Neighbours ) -> My_pid = erlang:self(), [Pid ! {is_dug, My_pid} || {_Direction, Pid} <- Neighbours], [{Pid, Direction} || {Direction, Pid} <- Neighbours, not read_receive(Pid, is_dug)].

loop_wall_from_pid( Pid, Neighbours ) -> loop_wall_from_pid_result( lists:keyfind(Pid, 2, Neighbours) ). loop_wall_from_pid_result( {Direction, _Pid} ) -> Direction; loop_wall_from_pid_result( false ) -> controller.

read( Pid, Key ) -> Pid ! {Key, erlang:self()}, read_receive( Pid, Key ).

read_receive( Pid, Key ) ->

       receive
       {Key, Value, Pid} -> Value
       end.

reads( Position_pids, Key ) ->

   My_pid = erlang:self(),
   [Pid ! {Key, My_pid} || {_Position, Pid} <- Position_pids],
   [{Position, read_receive(Pid, Key)} || {Position, Pid} <- Position_pids].

</lang>

Output:

5> maze:task().
Starting at {10,5}
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|                   |       |           |   |                   |
+---+   +---+---+   +   +   +   +---+   +   +   +   +---+---+   +
|       |       |       |   |       |   |       |           |   |
+   +---+   +   +---+   +---+---+   +   +---+---+---+---+   +   +
|   |       |       |   |           |           |           |   |
+   +---+   +---+---+   +   +---+---+---+---+   +   +---+---+   +
|       |   |           |   |           |       |   |   |       |
+   +   +   +   +---+---+   +   +---+---+   +---+   +   +   +---+
|   |   |       |           |           |   |       |       |   |
+---+   +---+---+   +---+---+---+---+   +   +   +---+   +---+   +
|       |       |           |       |   |   |   |       |       |
+   +   +   +   +---+---+   +   +---+   +   +   +---+   +   +   +
|   |   |   |           |   |       |       |       |       |   |
+   +---+   +   +---+---+   +---+   +---+---+---+   +---+---+   +
|           |                                       |           |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

F#

Using mutable state in the form of 2D arrays: <lang fsharp>let rnd : int -> int =

 let gen = new System.Random()
 fun max -> gen.Next(max)

// randomly choose an element of a list let choose (xs:_ list) = xs.[rnd xs.Length]

type Maze(width, height) =

 // (x,y) -> have we been here before?
 let visited = Array2D.create width height false
 // (x,y) -> is there a wall between (x,y) and (x+1,y)?
 let horizWalls = Array2D.create width height true
 // (x,y) -> is there a wall between (x,y) and (x,y+1)?
 let vertWalls = Array2D.create width height  true
 
 let isLegalPoint (x,y) =
   x >= 0 && x < width && y >= 0 && y < height
 
 let neighbours (x,y) = 
   [(x-1,y);(x+1,y);(x,y-1);(x,y+1)] |> List.filter isLegalPoint
   
 let removeWallBetween (x1,y1) (x2,y2) =
   if x1 <> x2 then
     horizWalls.[min x1 x2, y1] <- false
   else
     vertWalls.[x1, min y1 y2] <- false

 let rec visit (x,y as p) = 
   let rec loop ns =
     let (nx,ny) as n = choose ns
     if not visited.[nx,ny] then
       removeWallBetween p n
       visit n
     match List.filter ((<>) n) ns with
     | [] -> ()
     | others -> loop others

   visited.[x,y] <- true
   loop (neighbours p)

 do visit (rnd width, rnd height)

 member x.Print() =
   ("+" + (String.replicate width "-+")) ::
   [for y in 0..(height-1) do
      yield "\n|"
      for x in 0..(width-1) do 
        yield if horizWalls.[x,y] then " |" else "  "
      yield "\n+"
      for x in 0..(width-1) do 
        yield if vertWalls.[x,y] then "-+" else " +"
   ]
   |> String.concat ""
   |> printfn "%s"

let m = new Maze(10,10) m.Print()</lang>

Output example:

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

Go

<lang go>package main

import (

   "bytes"
   "fmt"
   "math/rand"
   "time"

)

type maze struct {

   c  []byte   // cell contents
   h  []byte   // horizontal walls above cells
   v  []byte   // vertical walls to the left of cells
   c2 [][]byte // cells by row
   h2 [][]byte // horizontal walls by row (ignore first row)
   v2 [][]byte // vertical walls by row (ignore first of each column)

}

func newMaze(rows, cols int) *maze {

   c := make([]byte, rows*cols)              // all cells
   h := bytes.Repeat([]byte{'-'}, rows*cols) // all horizontal walls
   v := bytes.Repeat([]byte{'|'}, rows*cols) // all vertical walls
   c2 := make([][]byte, rows)                // cells by row
   h2 := make([][]byte, rows)                // horizontal walls by row
   v2 := make([][]byte, rows)                // vertical walls by row
   for i := range h2 {
       c2[i] = c[i*cols : (i+1)*cols]
       h2[i] = h[i*cols : (i+1)*cols]
       v2[i] = v[i*cols : (i+1)*cols]
   }
   return &maze{c, h, v, c2, h2, v2}

}

func (m *maze) String() string {

   hWall := []byte("+---")
   hOpen := []byte("+   ")
   vWall := []byte("|   ")
   vOpen := []byte("    ")
   rightCorner := []byte("+\n") 
   rightWall := []byte("|\n")
   var b []byte
   // for all rows 
   for r, hw := range m.h2 {
       // draw h walls
       for _, h := range hw { 
           if h == '-' || r == 0 {
               b = append(b, hWall...)
           } else {
               b = append(b, hOpen...)
           }
       }
       b = append(b, rightCorner...)
       // draw v walls
       for c, vw := range m.v2[r] {
           if vw == '|' || c == 0 {
               b = append(b, vWall...)
           } else {
               b = append(b, vOpen...)
           }
           // draw cell contents
           if m.c2[r][c] != 0 {
               b[len(b)-2] = m.c2[r][c]
           }
       }
       b = append(b, rightWall...)
   }
   // draw bottom edge of maze
   for _ = range m.h2[0] {
       b = append(b, hWall...)
   }
   b = append(b, rightCorner...)
   return string(b)

}

func (m *maze) gen() {

   m.g2(rand.Intn(len(m.c2)), rand.Intn(len(m.c2[0])))

}

const (

   up = iota
   dn
   rt
   lf

)

func (m *maze) g2(r, c int) {

   m.c2[r][c] = ' '
   for _, dir := range rand.Perm(4) {
       switch dir {
       case up:
           if r > 0 && m.c2[r-1][c] == 0 {
               m.h2[r][c] = 0
               m.g2(r-1, c)
           }
       case lf:
           if c > 0 && m.c2[r][c-1] == 0 {
               m.v2[r][c] = 0
               m.g2(r, c-1)
           }
       case dn:
           if r < len(m.c2)-1 && m.c2[r+1][c] == 0 {
               m.h2[r+1][c] = 0
               m.g2(r+1, c)
           }
       case rt:
           if c < len(m.c2[0])-1 && m.c2[r][c+1] == 0 {
               m.v2[r][c+1] = 0
               m.g2(r, c+1)
           }
       }
   }

}

func main() {

   rand.Seed(time.Now().UnixNano())
   m := newMaze(4, 6)
   m.gen()
   fmt.Print(m)

}</lang>

Output:

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

Haskell

<lang haskell>import Control.Monad import Control.Monad.ST import Data.Array import Data.Array.ST import Data.STRef import System.Random

rand :: Random a => (a, a) -> STRef s StdGen -> ST s a rand range gen = do

   (a, g) <- liftM (randomR range) $ readSTRef gen
   gen `writeSTRef` g
   return a

data Maze = Maze {rightWalls, belowWalls :: Array (Int, Int) Bool}

maze :: Int -> Int -> StdGen -> ST s Maze maze width height gen = do

   visited <- mazeArray False
   rWalls <- mazeArray True
   bWalls <- mazeArray True
   gen <- newSTRef gen
   liftM2 (,) (rand (0, maxX) gen) (rand (0, maxY) gen) >>=
       visit gen visited rWalls bWalls
   liftM2 Maze (freeze rWalls) (freeze bWalls)
 where visit gen visited rWalls bWalls here = do
           writeArray visited here True
           let ns = neighbors here
           i <- rand (0, length ns - 1) gen
           forM_ (ns !! i : take i ns ++ drop (i + 1) ns) $ \there -> do
               seen <- readArray visited there
               unless seen $ do
                   removeWall here there
                   visit gen visited rWalls bWalls there
         where removeWall (x1, y1) (x2, y2) = writeArray 
                   (if x1 == x2 then bWalls else rWalls)
                   (min x1 x2, min y1 y2)
                   False

       neighbors (x, y) = 
           (if x == 0    then [] else [(x - 1, y    )]) ++
           (if x == maxX then [] else [(x + 1, y    )]) ++
           (if y == 0    then [] else [(x,     y - 1)]) ++
           (if y == maxY then [] else [(x,     y + 1)])

       maxX = width - 1
       maxY = height - 1

       mazeArray = newArray ((0, 0), (maxX, maxY))
           :: Bool -> ST s (STArray s (Int, Int) Bool)

printMaze :: Maze -> IO () printMaze (Maze rWalls bWalls) = do

   putStrLn $ '+' : (concat $ replicate (maxX + 1) "---+")
   forM_ [0 .. maxY] $ \y -> do
       putStr "|"
       forM_ [0 .. maxX] $ \x -> do
           putStr "   "
           putStr $ if rWalls ! (x, y) then "|" else " "
       putStrLn ""
       forM_ [0 .. maxX] $ \x -> do
           putStr "+"
           putStr $ if bWalls ! (x, y) then "---" else "   "
       putStrLn "+"
 where maxX = fst (snd $ bounds rWalls)
       maxY = snd (snd $ bounds rWalls)

main = getStdGen >>= stToIO . maze 11 8 >>= printMaze</lang>

Sample output:

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

Icon and Unicon

20x30 with two random openings

20x30 with opposite openings

<lang Icon>link printf

procedure main(A) # generate rows x col maze

  /mh := \A[1] | 12                            # or take defaults 12 x 16
  /mw := \A[2] | 16
  mz := DisplayMaze(GenerateMaze(mh,mw))
  WriteImage(mz.filename)                      # save file
  WAttrib(mz.window,"canvas=normal")           # show maze in hidden window
  until Event() == &lpress                     # wait for left mouse press
  close(mz.window)                            

end

$define FINISH 64 # exit $define START 32 # entrance $define PATH 128 $define SEEN 16 # bread crumbs for generator $define NORTH 8 # sides ... $define EAST 4 $define SOUTH 2 $define WEST 1 $define EMPTY 0 # like new

procedure GenerateMaze(r,c) #: Depth First Maze Generation static maze,h,w,rd

  if /maze then {                              # BEGING - No maze yet
     /h := integer(1 < r) | runerr(r,205)      # valid size 2x2 or better
     /w := integer(1 < c) | runerr(r,205)
     every !(maze := list(h)) := list(w,EMPTY) # shinny new empty maze
     start  := [?h,?w,?4-1,START]              # random [r,c] start & finish                 
     finish := [?h,?w,(start[3]+2)%4,FINISH]   # w/ opposite side exponent
     every x := start | finish do {
        case x[3] := 2 ^ x[3] of {             # get side from exponent and 
           NORTH : x[1] := 1                   # project r,c to selected edge
           EAST  : x[2] := w
           SOUTH : x[1] := h         
           WEST  : x[2] := 1
           }   
        maze[x[1],x[2]] +:= x[3] + x[4]        # transcribe s/f to maze
        }
     rd := [NORTH, EAST, SOUTH, WEST]          # initial list of directions     
     GenerateMaze(start[1],start[2])           # recurse through maze     
     return 1(.maze,maze := &null)             # return maze, reset for next
  }
  else {         # ----------------------- recursed to clear insize of maze
     if iand(maze[r,c],SEEN) = 0 then {        # in bounds and not SEEN yet?
        maze[r,c] +:= SEEN                     # Mark current cell as visited   
        every !rd :=: ?rd                      # randomize list of directions
        every d := !rd do
           case d of {                         # try all, succeed & clear wall
              NORTH :  maze[r,c] +:= ( GenerateMaze(r-1,c), NORTH)
              EAST  :  maze[r,c] +:= ( GenerateMaze(r,c+1),  EAST)
              SOUTH :  maze[r,c] +:= ( GenerateMaze(r+1,c), SOUTH)
              WEST  :  maze[r,c] +:= ( GenerateMaze(r,c-1),  WEST)   
              }
        return                                 # signal success to caller
        }
  }

end

$define CELL 20 # cell size in pixels $define BORDER 30 # border size in pixels

record mazeinfo(window,maze,filename) # keepers

procedure DisplayMaze(maze) #: show it off if CELL < 8 then runerr(205,CELL) # too small

wh := (ch := (mh := *maze ) * CELL) + 2 * BORDER # win, cell, maze height ww := (cw := (mw := *maze[1]) * CELL) + 2 * BORDER # win, cell, maze width

wparms := [ sprintf("Maze %dx%d",*maze,*maze[1]), # window parameters

           "g","bg=white","canvas=hidden",      
           sprintf("size=%d,%d",ww,wh),
           sprintf("dx=%d",BORDER),
           sprintf("dy=%d",BORDER)]

&window := open!wparms | stop("Unable to open Window")

Fg("black") # Draw full grid every DrawLine(x := 0 to cw by CELL,0,x,ch+1) # . verticals every DrawLine(0,y := 0 to ch by CELL,cw+1,y) # . horizontals

Fg("white") # Set to erase lines every y := CELL*((r := 1 to mh)-1) & x := CELL*((c := 1 to mw)-1) do {

  WAttrib("dx="||x+BORDER,"dy="||y+BORDER)         # position @ cell r,c
  if iand(maze[r,c],NORTH) > 0 then DrawLine(2,0,CELL-1,0)            
  if iand(maze[r,c],EAST)  > 0 then DrawLine(CELL,2,CELL,CELL-1)        
  if iand(maze[r,c],SOUTH) > 0 then DrawLine(2,CELL,CELL-1,CELL)                
  if iand(maze[r,c],WEST)  > 0 then DrawLine(0,2,0,CELL-1)            
  }   

return mazeinfo(&window,maze,sprintf("maze-%dx%d-%d.gif",r,c,&now)) end</lang> Note: The underlying maze structure (matrix) is uni-directional from the start

Library: Icon Programming Library

printf.icn provides formatting

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.

Translation of: PicoLisp

But 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>

Java

Works with: Java version 1.5+

<lang java5>package org.rosettacode;

import java.util.Collections; import java.util.Arrays;

/*

* recursive backtracking algorithm
* shamelessly borrowed from the ruby at
* http://weblog.jamisbuck.org/2010/12/27/maze-generation-recursive-backtracking
*/

public class MazeGenerator { private final int x; private final int y; private final int[][] maze;

public MazeGenerator(int x, int y) { this.x = x; this.y = y; maze = new int[this.x][this.y]; generateMaze(0, 0); }

public void display() { for (int i = 0; i < y; i++) { // draw the north edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 1) == 0 ? "+---" : "+ "); } System.out.println("+"); // draw the west edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 8) == 0 ? "| " : " "); } System.out.println("|"); } // draw the bottom line for (int j = 0; j < x; j++) { System.out.print("+---"); } System.out.println("+"); }

private void generateMaze(int cx, int cy) { DIR[] dirs = DIR.values(); Collections.shuffle(Arrays.asList(dirs)); for (DIR dir : dirs) { int nx = cx + dir.dx; int ny = cy + dir.dy; if (between(nx, x) && between(ny, y) && (maze[nx][ny] == 0)) { maze[cx][cy] |= dir.bit; maze[nx][ny] |= dir.opposite.bit; generateMaze(nx, ny); } } }

private static boolean between(int v, int upper) { return (v >= 0) && (v < upper); }

private enum DIR { N(1, 0, -1), S(2, 0, 1), E(4, 1, 0), W(8, -1, 0); private final int bit; private final int dx; private final int dy; private DIR opposite;

// use the static initializer to resolve forward references static { N.opposite = S; S.opposite = N; E.opposite = W; W.opposite = E; }

private DIR(int bit, int dx, int dy) { this.bit = bit; this.dx = dx; this.dy = dy; } };

public static void main(String[] args) { int x = args.length >= 1 ? (Integer.parseInt(args[0])) : 8; int y = args.length == 2 ? (Integer.parseInt(args[1])) : 8; MazeGenerator maze = new MazeGenerator(x, y); maze.display(); }

}</lang>

Output:

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

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]= [], verti =[]; for (var j= 0; j<x+1; j++) verti[j]= [], here = [Math.floor(Math.random()*x), Math.floor(Math.random()*y)], path = [here], 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 output:

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

For an animated presentation of the progress of this maze creation process, you can use display in each iteration of the main loop. You would also need to take steps to make sure you could see each intermediate result.

For example, change replace the line while (0<n) { with: <lang javascript> function step() { if (0<n) {</lang> And replace the closing brace for this while loop with: <lang javascript> document.getElementById('out').innerHTML= display({x: x, y: y, horiz: horiz, verti: verti, here: here}); setTimeout(step, 100); } } step();</lang> To better see the progress, you might want a marker in place, showing the position being considered. To do that, replace the line which reads if (0 == k%4) { with <lang javascript> if (m.here && m.here[0]*2+1 == j && m.here[1]*4+2 == k) line[k]= '#' else if (0 == k%4) {</lang> Note however that this leaves the final '#' in place on maze completion, and that the function maze no longer returns a result which represents a generated maze.

Note also that this display suggests an optimization. You can replace the line reading path.push(here= next); with: <lang javascript> here= next; if (1 < neighbors.length) path.push(here);</lang> And this does indeed save a negligible bit of processing, but the maze algorithm will still be forced to backtrack through a number of locations which have no unvisited neighbors.

HTML Table

Using HTML, CSS and table cells for maze. <lang html><html><head><title>Maze maker</title> <style type="text/css"> table { border-collapse: collapse } td { width: 1em; height: 1em; border: 1px solid } td.s { border-bottom: none } td.n { border-top: none } td.w { border-left: none } td.e { border-right: none } td.v { background: skyblue} </style> <script type="application/javascript"> Node.prototype.add = function(tag, cnt, txt) { for (var i = 0; i < cnt; i++) this.appendChild(ce(tag, txt)); } Node.prototype.ins = function(tag) { this.insertBefore(ce(tag), this.firstChild) } Node.prototype.kid = function(i) { return this.childNodes[i] } Node.prototype.cls = function(t) { this.className += ' ' + t }

NodeList.prototype.map = function(g) { for (var i = 0; i < this.length; i++) g(this[i]); }

function ce(tag, txt) { var x = document.createElement(tag); if (txt !== undefined) x.innerHTML = txt; return x }

function gid(e) { return document.getElementById(e) } function irand(x) { return Math.floor(Math.random() * x) }

function make_maze() { var w = parseInt(gid('rows').value || 8, 10); var h = parseInt(gid('cols').value || 8, 10); var tbl = gid('maze'); tbl.innerHTML = ; tbl.add('tr', h); tbl.childNodes.map(function(x) { x.add('th', 1); x.add('td', w, '*'); x.add('th', 1)}); tbl.ins('tr'); tbl.add('tr', 1); tbl.firstChild.add('th', w + 2); tbl.lastChild.add('th', w + 2); for (var i = 1; i <= h; i++) { for (var j = 1; j <= w; j++) { tbl.kid(i).kid(j).neighbors = [ tbl.kid(i + 1).kid(j), tbl.kid(i).kid(j + 1), tbl.kid(i).kid(j - 1), tbl.kid(i - 1).kid(j) ]; } } walk(tbl.kid(irand(h) + 1).kid(irand(w) + 1)); gid('solve').style.display='inline'; }

function shuffle(x) { for (var i = 3; i > 0; i--) { j = irand(i + 1); if (j == i) continue; var t = x[j]; x[j] = x[i]; x[i] = t; } return x; }

var dirs = ['s', 'e', 'w', 'n']; function walk(c) { c.innerHTML = ' '; var idx = shuffle([0, 1, 2, 3]); for (var j = 0; j < 4; j++) { var i = idx[j]; var x = c.neighbors[i]; if (x.textContent != '*') continue; c.cls(dirs[i]), x.cls(dirs[3 - i]); walk(x); } }

function solve(c, t) { if (c === undefined) { c = gid('maze').kid(1).kid(1); c.cls('v'); } if (t === undefined) t = gid('maze') .lastChild.previousSibling .lastChild.previousSibling;

if (c === t) return 1; c.vis = 1; for (var i = 0; i < 4; i++) { var x = c.neighbors[i]; if (x.tagName.toLowerCase() == 'th') continue; if (x.vis || !c.className.match(dirs[i]) || !solve(x, t)) continue;

x.cls('v'); return 1; } c.vis = null; return 0; }

</script></head> <body><form><fieldset> <label>rows </label><input id='rows' size="3"/> <label>colums </label><input id='cols' size="3"/> <a href="javascript:make_maze()">Generate</a> <a id='solve' style='display:none' href='javascript:solve(); void(0)'>Solve</a>

</fieldset></form>

</body></html></lang>

Julia

<lang julia>function walk(maze, cell, visited = {})

 push!(visited, cell)
 for neigh in shuffle(neighbors(cell, size(maze)))
   if !(neigh in visited)
      maze[int((cell+neigh)/2)...] = 0
      walk(maze, neigh, visited)
   end
 end
 maze

end

neighbors(c,b,d=2) = filter(check(b),map(m->c+d*m, {[0,1],[-1,0],[0,-1],[1,0]}))

check(bound) = cell -> all([1,1] .<= cell .<= [bound...])

maze(w, h) = walk([i%2|j%2 for i=1:2w+1,j=1:2h+1], 2*[rand(1:w),rand(1:h)])

pprint(maze) = print(mapslices(x-> [join(x)], maze, [2]))

function mprint(maze, wall = CharString("╹╸┛╺┗━┻╻┃┓┫┏┣┳╋"...))

 pprint([ maze[i,j] == 0 ? ' ' :
          wall[sum(c-> 2.0^.5(3c[1]+c[2]+3),
                   filter(x -> maze[x...] != 0,
                          neighbors([i,j],[size(maze)...],1)) .- {[i,j]})]
          for i = 1:2:size(maze,1), j = 1:size(maze,2)])

end</lang>

Output:

julia> mprint(maze(15,30))
┏━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━┳━━━━━━━┳━━━┳━━━━━━━━━┳━━━━━┓
┃ ╺━━━┳━━━┓ ╺━━━┛ ╻ ┏━╸ ┃ ╻ ┃ ╻ ┃ ╻ ╺━┳━┛ ╻ ╹ ╺━┓ ╺━┓ ┗━━━╸ ┃
┣━━━┓ ╹ ╻ ┣━━━━━━━┫ ┃ ┏━┛ ┃ ╹ ┃ ┃ ┣━┓ ╹ ┏━┻━━━┳━┻━┓ ┗━━━┳━━━┫
┃ ╺━┻━━━┫ ┃ ╺━┳━╸ ┃ ┗━┛ ┏━┻━┓ ┃ ┃ ┃ ┗━━━┛ ╻ ┏━┛ ╻ ┗━┓ ╻ ╹ ╻ ┃
┃ ╺━━━┓ ┃ ┃ ┏━┛ ┏━┻━━━━━┫ ╻ ┗━┛ ┃ ┃ ╻ ┏━┳━┛ ┃ ╺━╋━╸ ┃ ┗━┳━┛ ┃
┣━━━╸ ┃ ╹ ┃ ┃ ╻ ┃ ╺━┓ ╻ ┃ ┗━┳━┓ ┃ ┗━┛ ┃ ╹ ┏━╋━╸ ┃ ╺━╋━━━┛ ┏━┫
┃ ┏━━━┻━━━┻━┛ ┣━┻━╸ ┃ ┗━┻━┓ ┃ ╹ ┗━━━┳━┛ ┏━┛ ┃ ╺━┻━━━┫ ╺━┳━┛ ┃
┃ ┗━━━━━┓ ┏━╸ ┃ ╺━┳━┻━┓ ╺━┫ ┗━━━━━━━┛ ┏━┛ ┏━┻━━━━━┓ ┗━┓ ┃ ╺━┫
┣━━━━━╸ ┃ ┗━━━┻━┓ ┃ ╻ ┗━┓ ┗━━━━━━━┳━━━┫ ╺━┛ ┏━┓ ╺━╋━╸ ┃ ┗━┓ ┃
┃ ┏━━━┳━┻━┓ ╻ ╺━┛ ╹ ┣━┓ ┣━┓ ╺━━━┳━┛ ╻ ╹ ┏━━━┛ ┗━┓ ┃ ╺━┻━╸ ┃ ┃
┃ ╹ ╻ ╹ ╻ ┗━┻━━━┳━━━┫ ╹ ╹ ┗━┳━┓ ╹ ┏━┻━━━┫ ╺━┳━╸ ┃ ┗━━━┳━━━┛ ┃
┣━┳━┻━━━┻━━━━━┓ ╹ ╻ ┗━┳━━━╸ ╹ ┗━━━┛ ┏━╸ ┗━╸ ┃ ┏━┻━┓ ╻ ┗━━━╸ ┃
┃ ╹ ╻ ╺━━━┳━╸ ┣━━━┻━┓ ┃ ┏━━━┓ ┏━━━━━┻━┳━━━━━┫ ┃ ╻ ╹ ┣━┳━━━╸ ┃
┃ ╺━╋━━━┓ ┗━━━┫ ╻ ╺━┫ ┃ ┃ ╻ ┗━┛ ┏━━━┓ ╹ ┏━┓ ┗━┫ ┣━━━┫ ╹ ┏━━━┫
┣━╸ ┗━╸ ┗━━━┓ ╹ ┗━┓ ╹ ┗━┛ ┣━━━━━┛ ╻ ┗━━━┛ ┗━╸ ╹ ┃ ╺━┛ ╺━┛ ╻ ┃
┗━━━━━━━━━━━┻━━━━━┻━━━━━━━┻━━━━━━━┻━━━━━━━━━━━━━┻━━━━━━━━━┻━┛

Lua

Works with: Lua version 5.2

This is an implementation of the recursive backtracker maze generation algorithm found at Think Labyrinth! but without recursion :)

This solution consists of four files:

1. stack.lua - very simple implementation of the LIFO container, used for stacking the travel path
2. maze.lua - simple maze implementation
3. backtracker.lua - actual algorithm implementation
4. demo.lua - some code to show off the functionality

stack.lua: <lang Lua>Stack = {}

function Stack:Create()

 local stack = {}
 
 function stack:push(item)
   self[#self + 1] = item
 end
 
 function stack:pop()
   local item = self[#self]
   self[#self] = nil
   return item
 end
 
 return stack

end</lang>

maze.lua: <lang Lua>require "stack"

Maze = {

 directions =
 {
   north = { x = 0, y = -1 },
   east = { x = 1, y = 0 },
   south = { x = 0, y = 1 },
   west = { x = -1, y = 0 }
 }

}

function Maze:Create(width, height, closed)

 -- Actual maze setup
 local maze = {}
 for y = 1, height do
   maze[y] = {}
   for x = 1, width do
     maze[y][x] = { east = self:CreateDoor(closed), south = self:CreateDoor(closed)}
     
     -- Doors are shared beetween the cells to avoid out of sync conditions and data dublication
     if x ~= 1 then maze[y][x].west = maze[y][x - 1].east
     else maze[y][x].west = self:CreateDoor(closed) end
     
     if y ~= 1 then maze[y][x].north = maze[y - 1][x].south
     else maze[y][x].north = self:CreateDoor(closed) end
   end
 end
 
 function maze:resetDoors(close)
   for y = 1, #self do
     self[y][#self[1]].east:setOpened(not close)
     
     for i, cell in ipairs(self[y]) do
       cell.north:setOpened(not close)
       cell.west:setOpened(not close)
     end
   end
   
   for i, cell in ipairs(self[#self]) do
     cell.south:setOpened(not close)
   end
 end
 
 function maze:resetVisited()
   for y = 1, #self do
     for x = 1, #self[1] do
       self[y][x].visited = nil
     end
   end
 end
 
 function maze:tostring(wall, passage)
   wall = wall or "#"
   passage = passage or " "
   
   local result = ""
   
   local verticalBorder = ""
   for i = 1, #self[1] do
     verticalBorder = verticalBorder .. wall .. (self[1][i].north:isClosed() and wall or passage)
   end
   verticalBorder = verticalBorder .. wall
   result = result .. verticalBorder .. "\n"

   for y, row in ipairs(self) do
     local line = row[1].west:isClosed() and wall or passage
     local underline = wall
     for x, cell in ipairs(row) do
       line = line .. " " .. (cell.east:isClosed() and wall or passage)
       underline = underline .. (cell.south:isClosed() and wall or passage) .. wall
     end
     result = result .. line .. "\n" .. underline .. "\n"
   end
   
   return result
 end
 
 return maze

end

-- This function was designed to be easily replaced by the function generating Legend of Grimrock doors function Maze:CreateDoor(closed)

 local door = {}
 door._closed = closed and true or false
 
 function door:isClosed()
   return self._closed
 end
 
 function door:isOpened()
   return not self._closed
 end
 
 function door:close()
   self._closed = true
 end
 
 function door:open()
   self._closed = false
 end
 
 function door:setOpened(opened)
   if opened then
     self:open()
   else
     self:close()
   end
 end
 
 return door

end</lang>

backtracker.lua: <lang Lua>require "maze"

-- Backtracker algorithm (a variation of the recursive backtracker algorithm made without recursion) function Maze:Backtracker(maze)

 maze:resetDoors(true)
 
 local stack = Stack:Create()
 
 local cell = { x = 1, y = 1 }
 while true do
   maze[cell.y][cell.x].visited = true
   
   -- Gathering all possible travel direction in a list
   local directions = {}
   for key, value in pairs(self.directions) do
     local newPos = { x = cell.x + value.x, y = cell.y + value.y }
     -- Checking if the targeted cell is in bounds and was not visited previously
     if maze[newPos.y] and maze[newPos.y][newPos.x] and not maze[newPos.y][newPos.x].visited then
       directions[#directions + 1] = { name = key, pos = newPos }
     end
   end
       
   -- If there are no possible travel directions - backtracking
   if #directions == 0 then
     if #stack > 0 then
       cell = stack:pop()
       goto countinue
     else break end -- Stack is empty and there are no possible directions - maze is generated
   end
   
   -- Choosing a random direction from a list of possible direction and carving
   stack:push(cell)
   local dir = directions[math.random(#directions)]
   maze[cell.y][cell.x][dir.name]:open() 
   cell = dir.pos
   
   ::countinue::
 end
 
 maze:resetVisited()

end</lang>

demo.lua: <lang Lua>require "maze" require "backtracker"

maze = Maze:Create(30, 10, true) --[[ Maze generation depends on the random seed, so you will get exactly

     identical maze every time you pass exactly identical seed ]]

math.randomseed(os.time()) Maze:Backtracker(maze) print(maze:tostring())</lang>

Output:

#############################################################
# #     #       #       #       # #   #         #     #   # #
# # # ### ### ### ### # ### ### # # # # # ### ### # # # # # #
# # #     # #     #   #     #   #   #   #   # #   # #   #   #
# ### ##### ####### ######### ##### ####### # # ### ####### #
#   #     #     # #     #   #     #       # # # # #       # #
### ##### ### # # ##### # ####### ####### # ### # ####### # #
# # #     #   #   #     #       #     #   # #   #   # #   # #
# # # ##### ### ### ##### ### ####### # ### # ### # # # ### #
#   #       #   #   # #   # #         # #   # #   #   #   # #
# ########### ### ### # ### ############# # # ### ### ### ###
#     # #     #   #     #             #   # #     #     #   #
##### # # ##### ### ####### ######### # ##### ######### ### #
#     #   #   # # # #     # #       # #       #     # #   # #
# ######### # # # # ### # # # # ##### ####### # ### # # ### #
# #         #   # #     #   # #       #     # # # # # # #   #
# ### ########### ########### ######### ### # # # # # # # # #
#   #   #   #               # #   #   # #   # # #   #   # # #
### ### # # # ##### ######### # # # # # # ##### # ####### # #
#       # #       #             #   #   #       #         # #
#############################################################

Mathematica

<lang mathematica>MazeGraphics[m_, n_] :=

Block[{$RecursionLimit = Infinity, 
  unvisited = Tuples[Range /@ {m, n}], maze}, 
 maze = Graphics[{Line[{{#, # - {0, 1}}, {#, # - {1, 0}}}] & /@ 
     unvisited, 
    Line[{{0, n}, {0, 0}, {m, 0}}]}]; {unvisited = 
     DeleteCases[unvisited, #]; 
    Do[If[MemberQ[unvisited, neighbor], 
      maze = DeleteCases[
        maze, {#, 
          neighbor - {1, 1}} | {neighbor, # - {1, 1}}, {5}]; #0@
       neighbor], {neighbor, 
      RandomSample@{# + {0, 1}, # - {0, 1}, # + {1, 0}, # - {1, 
          0}}}]} &@RandomChoice@unvisited; maze];

maze = MazeGraphics[21, 13]</lang>

Output:

Graph

Works with: Mathematica version 9.0

Here I generate a maze as a graph. Vertices of the graph are cells and edges of the graph are removed walls. This version is mush faster and is convenient to solve. <lang mathematica>MazeGraph[m_, n_] :=

Block[{$RecursionLimit = Infinity, grid = GridGraph[{m, n}], 
  unvisitedQ}, unvisitedQ[_] := True; 
 Graph[Range[m n], Reap[{unvisitedQ[#] = False;
       Do[
        If[unvisitedQ[neighbor], 
         Sow[# <-> neighbor]; #0@neighbor], {neighbor, 
         RandomSample@AdjacencyList[grid, #]}]} &@
     RandomChoice@VertexList@grid]2, 1, 
  GraphLayout -> {"GridEmbedding", "Dimension" -> {m, n}}]];

maze = MazeGraph[13, 21]</lang>

Output:

MATLAB / Octave

<lang Matlab>function M = makeMaze(n)

   showProgress = false;

   colormap([1,1,1;1,1,1;0,0,0]);
   set(gcf,'color','w');

   NoWALL      = 0;
   WALL        = 2;
   NotVISITED  = -1;
   VISITED     = -2;

   m = 2*n+3;
   M = NotVISITED(ones(m));
   offsets = [-1, m, 1, -m];

   M([1 2:2:end end],:) = WALL;
   M(:,[1 2:2:end end]) = WALL;

   currentCell = sub2ind(size(M),3,3);
   M(currentCell) = VISITED;
   
   S = currentCell;
   
   while (~isempty(S))
       moves = currentCell + 2*offsets;
       unvistedNeigbors = find(M(moves)==NotVISITED);

       if (~isempty(unvistedNeigbors))
           next = unvistedNeigbors(randi(length(unvistedNeigbors),1));
           M(currentCell + offsets(next)) = NoWALL;

           newCell = currentCell + 2*offsets(next);
           if (any(M(newCell+2*offsets)==NotVISITED))
               S = [S newCell];
           end
           
           currentCell = newCell;
           M(currentCell) = VISITED;
       else
           currentCell = S(1);
           S = S(2:end);
       end

       if (showProgress)
           image(M-VISITED);
           axis equal off;
           drawnow;
           pause(.01);
       end
   end

   image(M-VISITED);
   axis equal off;</lang>

Nim

Translation of: D

<lang nim>import math, sequtils, strutils randomize()

template newSeqWith(len: int, init: expr): expr =

 var result {.gensym.} = newSeq[type(init)](len)
 for i in 0 .. <len:
   result[i] = init
 result

iterator randomCover[T](xs: openarray[T]): T =

 var js = toSeq 0..xs.high
 for i in countdown(js.high, 0):
   let j = random(i + 1)
   swap(js[i], js[j])
 for j in js:
   yield xs[j]

const

 w = 14
 h = 10

var

 vis = newSeqWith(h, newSeq[bool](w))
 hor = newSeqWith(h+1, newSeqWith(w, "+---"))
 ver = newSeqWith(h, newSeqWith(w, "|   ") & "|")

proc walk(x, y) =

 vis[y][x] = true
 for p in [[x-1,y], [x,y+1], [x+1,y], [x,y-1]].randomCover:
   if p[0] notin 0 .. <w or p[1] notin 0 .. <h or vis[p[1]][p[0]]: continue
   if p[0] == x: hor[max(y, p[1])][x] = "+   "
   if p[1] == y: ver[y][max(x, p[0])] = "    "
   walk p[0], p[1]

walk random(0..w), random(0..h) for a,b in zip(hor, ver & @[""]).items:

 echo join(a & "+\n" & b)</lang>

Example output:

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

OCaml

<lang ocaml>let seen = Hashtbl.create 7 let mark t = Hashtbl.add seen t true let marked t = Hashtbl.mem seen t

let walls = Hashtbl.create 7 let ord a b = if a <= b then (a,b) else (b,a) let join a b = Hashtbl.add walls (ord a b) true let joined a b = Hashtbl.mem walls (ord a b)

let () =

 let nx = int_of_string Sys.argv.(1) in
 let ny = int_of_string Sys.argv.(2) in

 let rec random_order = function
   | [] -> []
   | [a] -> [a]
   | x -> let i = Random.int (List.length x) in
     let rec del i = function
       | [] -> failwith "del"
       | h::t -> if i = 0 then t else h :: del (i-1) t in
     (List.nth x i) :: random_order (del i x) in

 let get_neighbours (x,y) =
   let lim n k = (0 <= k) && (k < n) in
   let bounds (x,y) = lim nx x && lim ny y in
   List.filter bounds [(x-1,y);(x+1,y);(x,y-1);(x,y+1)] in

 let rec visit cell =
   mark cell;
   let check k =
     if not (marked k) then (join cell k; visit k) in
   List.iter check (random_order (get_neighbours cell)) in

 let print_maze () =
   begin
   for i = 1 to nx do print_string "+---";done; print_endline "+";
   let line n j k l s t u =
     for i = 0 to n do print_string (if joined (i,j) (i+k,j+l) then s else t) done;
     print_endline u in
   for j = 0 to ny-2 do
     print_string "|   ";
     line (nx-2) j 1 0 "    " "|   " "|";
     line (nx-1) j 0 1 "+   " "+---" "+";
   done;
   print_string "|   ";
   line (nx-2) (ny-1) 1 0 "    " "|   " "|";
   for i = 1 to nx do print_string "+---";done; print_endline "+";
  end in

 Random.self_init();
 visit (Random.int nx, Random.int ny);
 print_maze ();</lang>

Output from 'ocaml gen_maze.ml 10 10':

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

Perl

<lang perl>use List::Util 'max';

my ($w, $h) = @ARGV; $w ||= 26; $h ||= 127; my $avail = $w * $h;

1. cell is padded by sentinel col and row, so I don't check array bounds

my @cell = (map([(('1') x $w), 0], 1 .. $h), [() x ($w + 1)]); my @ver = map([("| ") x $w], 1 .. $h); my @hor = map([("+--") x $w], 0 .. $h);

sub walk { my ($x, $y) = @_; $cell[$y][$x] = ; $avail-- or return; # no more bottles, er, cells

my @d = ([-1, 0], [0, 1], [1, 0], [0, -1]); while (@d) { my $i = splice @d, int(rand @d), 1; my ($x1, $y1) = ($x + $i->[0], $y + $i->[1]);

$cell[$y1][$x1] or next;

if ($x == $x1) { $hor[ max($y1, $y) ][$x] = '+ ' } if ($y == $y1) { $ver[$y][ max($x1, $x) ] = ' ' } walk($x1, $y1); } }

walk(int rand $w, int rand $h); # generate

for (0 .. $h) { # display print @{$hor[$_]}, "+\n"; print @{$ver[$_]}, "|\n" if $_ < $h; }</lang> Run as maze.pl [width] [height] or use default dimensions.

Sample 4 x 1 output:

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

Perl 6

Supply a width and height and optionally the x,y grid coords for the starting cell. If no starting cell is supplied, a random one will be selected automatically. 0,0 is the top left corner. <lang perl6>constant mapping = :OPEN(' '), :N< ╵ >, :E< ╶ >, :NE< └ >, :S< ╷ >, :NS< │ >, :ES< ┌ >, :NES< ├ >, :W< ╴ >, :NW< ┘ >, :EW< ─ >, :NEW< ┴ >, :SW< ┐ >, :NSW< ┤ >, :ESW< ┬ >, :NESW< ┼ >, :TODO< x >, :TRIED< · >;

enum Code (mapping.map: *.key); my @code = mapping.map: *.value;

enum Direction <DeadEnd Up Right Down Left>;

sub gen_maze ( $X,

              $Y,
              $start_x = (^$X).pick * 2 + 1,
              $start_y = (^$Y).pick * 2 + 1 )

{

   my @maze;
   push @maze, [ ES, -N, (ESW, EW) xx $X - 1, SW ];
   push @maze, [ (NS, TODO) xx $X, NS ];
   for 1 ..^ $Y {

push @maze, [ NES, EW, (NESW, EW) xx $X - 1, NSW ]; push @maze, [ (NS, TODO) xx $X, NS ];

   }
   push @maze, [ NE, (EW, NEW) xx $X - 1, -NS, NW ];
   @maze[$start_y][$start_x] = OPEN;

   my @stack;
   my $current = [$start_x, $start_y];
   loop {
       if my $dir = pick_direction( $current ) {
           @stack.push: $current;
           $current = move( $dir, $current );
       }
       else {
           last unless @stack;
           $current = @stack.pop;
       }
   }
   return @maze;

   sub pick_direction([$x,$y]) {

my @neighbors = (Up if @maze[$y - 2][$x]), (Down if @maze[$y + 2][$x]), (Left if @maze[$y][$x - 2]), (Right if @maze[$y][$x + 2]); @neighbors.pick or DeadEnd;

   }

   sub move ($dir, @cur) {

my ($x,$y) = @cur; given $dir { when Up { @maze[--$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y--][$x+1] -= W; } when Down { @maze[++$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y++][$x+1] -= W; } when Left { @maze[$y][--$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x--] -= N; } when Right { @maze[$y][++$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x++] -= N; } } @maze[$y][$x] = 0; [$x,$y];

   }

}

sub display (@maze) {

   for @maze -> @y {

for @y -> $w, $c { print @code[abs $w]; if $c >= 0 { print @code[$c] x 3 } else { print ' ', @code[abs $c], ' ' } } say @code[@y[*-1]];

   }

}

display gen_maze( 29, 19 );</lang>

Output:

┌ ╵ ────────────────────────────┬───────────────────────────────────────────┬───────────┬───────────────────────────┐
│                               │                                           │           │                           │
│   ╶───────────┬───────────┐   │   ┌───────────────────────╴   ┌───────┐   ├───╴   ╷   │   ┌───────────┬───┬───╴   │
│               │           │   │   │                           │       │   │       │   │   │           │   │       │
│   ┌───────┐   ╵   ┌───┐   ├───┘   │   ┌───────────┬───────────┤   ╶───┤   │   ╶───┴───┤   │   ┌───┐   │   │   ╶───┤
│   │       │       │   │   │       │   │           │           │       │   │           │   │   │   │   │   │       │
│   └───╴   └───────┤   │   ╵   ┌───┘   │   ╷   ╶───┤   ┌───┐   │   ╷   │   ├───────╴   │   ╵   │   │   │   └───┐   │
│                   │   │       │       │   │       │   │   │   │   │   │   │           │       │   │   │       │   │
├───────┬───────┐   │   ├───────┤   ╶───┤   └───┐   ╵   │   │   ╵   │   ╵   │   ┌───┐   └───┬───┘   │   │   ╷   │   │
│       │       │   │   │       │       │       │       │   │       │       │   │   │       │       │   │   │   │   │
│   ╶───┤   ╷   ╵   │   ╵   ╷   └───┐   ├───┐   ├───────┤   └───────┴───────┘   │   └───┐   └───╴   │   ╵   ├───┘   │
│       │   │       │       │       │   │   │   │       │                       │       │           │       │       │
├───╴   │   ├───────┴───┐   ├───╴   │   │   │   ╵   ╷   └───┐   ╶───┬───────┬───┘   ┌───┴───────╴   │   ┌───┘   ╷   │
│       │   │           │   │       │   │   │       │       │       │       │       │               │   │       │   │
│   ╷   │   │   ╶───┐   └───┤   ╷   │   │   └───────┴───┐   └───╴   │   ╷   ╵   ╷   ╵   ╶───────┬───┤   │   ┌───┴───┤
│   │   │   │       │       │   │   │   │               │           │   │       │               │   │   │   │       │
│   │   │   │   ╷   ├───╴   ╵   │   │   │   ┌───────┐   └───────────┤   └───┬───┴───────────┐   ╵   │   │   ╵   ╷   │
│   │   │   │   │   │           │   │   │   │       │               │       │               │       │   │       │   │
│   │   │   ├───┘   │   ┌───────┴───┘   │   ╵   ┌───┴───────╴   ╷   ├───┐   │   ╶───────┐   └───┐   │   └───┬───┘   │
│   │   │   │       │   │               │       │               │   │   │   │           │       │   │       │       │
│   └───┘   │   ┌───┘   │   ┌───┬───────┼───╴   │   ╶───┬───────┤   ╵   │   └───┬───╴   ├───┐   │   └───┐   │   ╷   │
│           │   │       │   │   │       │       │       │       │       │       │       │   │   │       │   │   │   │
│   ┌───────┘   ├───────┤   │   ╵   ╷   │   ┌───┴───┐   │   ╶───┘   ┌───┴───╴   │   ┌───┘   │   │   ┌───┘   │   │   │
│   │           │       │   │       │   │   │       │   │           │           │   │       │   │   │       │   │   │
│   └───╴   ╷   │   ╷   │   └───┐   │   ╵   │   ╷   ╵   ├───────┐   │   ╶───────┤   └───┐   │   └───┤   ┌───┘   │   │
│           │   │   │   │       │   │       │   │       │       │   │           │       │   │       │   │       │   │
├───────────┤   │   │   └───╴   │   └───────┤   └───────┘   ╷   └───┴───┬───╴   ├───╴   │   └───┐   │   │   ╶───┴───┤
│           │   │   │           │           │               │           │       │       │       │   │   │           │
│   ┌───╴   │   │   ├───╴   ┌───┴───────┬───┴───┐   ┌───────┴───────┐   ╵   ┌───┤   ╶───┤   ╷   │   ╵   └───┬───╴   │
│   │       │   │   │       │           │       │   │               │       │   │       │   │   │           │       │
│   │   ╶───┘   │   │   ╶───┤   ╶───┐   ╵   ╷   │   └───╴   ┌───╴   └───────┘   ├───╴   │   ├───┴───────┬───┘   ╷   │
│   │           │   │       │       │       │   │           │                   │       │   │           │       │   │
│   ├───────┬───┘   ├───────┴───┐   ├───────┤   └───────────┤   ┌───────────┐   │   ┌───┘   │   ╶───┐   ╵   ┌───┘   │
│   │       │       │           │   │       │               │   │           │   │   │       │       │       │       │
│   └───╴   │   ╷   │   ╶───┐   ╵   │   ╷   └───────────┐   │   │   ┌───┐   └───┘   │   ╶───┴───┐   └───────┴───────┤
│           │   │   │       │       │   │               │   │   │   │   │           │           │                   │
├───────╴   │   └───┴───╴   └───────┴───┴───────────╴   │   └───┘   ╵   └───────────┴───╴   ╷   └───────────────┐   │
│           │                                           │                                   │                   │   │
└───────────┴───────────────────────────────────────────┴───────────────────────────────────┴───────────────────┴ │ ┘

PHP

This solution use Php Gd for graphical randering. Source code : https://github.com/gallien69/phpMaze Demo online : http://gallien69.tk/ <lang PHP> <?php

// Convert Hex Color to RGB

function hexrgb(&$h) { return(array(hexdec($h[0].$h[1]),hexdec($h[2].$h[3]),hexdec($h[4].$h[5]))); }

// Allocate a color for an image from RGB

function rgbc(&$i, &$c) { return(imagecolorallocate($i, $c[0], $c[1], $c[2])); }

class Maze {

/* H : horizontal walls V : vertical walls x : number of rows y : numbers of cols r : resolve the maze b : walls thickness c : cell size f : background color m : walls color e : entrance color s : exit color i : gd image identifier

• /

private $H, $V, $x, $y, $r, $b, $c, $f, $m, $e, $s, $i;

// Initialize Maze class

function __construct($x, $y, $r, $b, $c, $f, $m, $e, $s) { $this->x = $x; $this->y = $y; $this->r = $r; $this->b = $b; $this->c = $c; $this->f = hexrgb($f); $this->m = hexrgb($m); $this->e = hexrgb($e); $this->s = hexrgb($s); }

// Checks if cell is a closed room

function isroom($x, $y) { return((empty($this->H[$x][$y]) && empty($this->V[$x][$y]) && empty($this->H[$x][$y+1]) && empty($this->V[$x+1][$y])) ? true : false); }

// Save the stack as solution path

function save(&$x, &$y, &$m) { if ($this->r == 1 && $x == $this->x - 1 && $y == $this->y - 1) { $this->r = $m; array_push($this->r, array($x, $y)); } }

// Dig the maze

function dig() { $x = 0; $y = 0; $cc = $this->x * $this->y; $v = 1; $m = array(); while ($v < $cc) { $c = ; if ($y > 0 && $this->isroom($x, $y - 1)) $c .= 'N'; if ($y < $this->y - 1 && $this->isroom($x, $y + 1)) $c .= 'S'; if ($x < $this->x - 1 && $this->isroom($x + 1, $y)) $c .= 'E'; if ($x > 0 && $this->isroom($x - 1, $y)) $c .= 'W'; if ($c) { $v++; array_push($m, array($x, $y)); $d = $c[rand(0, strlen($c) - 1)]; if ($d == 'N') $this->H[$x][$y--] = true; if ($d == 'S') $this->H[$x][$y++ + 1] = true; if ($d == 'E') $this->V[$x++ + 1][$y] = true; if ($d == 'W') $this->V[$x--][$y] = true; } else list($x, $y) = array_pop($m); $this->save($x, $y, $m); } $this->save($x, $y, $m); $this->V[0][0] = 1; $this->V[$this->x][$this->y - 1] = 1; }

// Draw the maze full grid

function grid(&$m) { for ($y = 0; $y <= $this->y; ++$y) { imagefilledrectangle($this->i, 0, $y * ($this->c + $this->b), $this->b + $this->x * ($this->c + $this->b) - 1, $this->b + $y * ($this->c + $this->b) - 1, $m); } for ($x = 0; $x <= $this->x; ++$x) { imagefilledrectangle($this->i, $x * ($this->c + $this->b), 0, $this->b + $x * ($this->c + $this->b) - 1, $this->b + $this->y * ($this->c + $this->b) - 1, $m); } }

// Breaks the horizontal walls

function line($x, $y, &$f) { imagefilledrectangle($this->i, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b), $x * ($this->c + $this->b) + $this->b + $this->c - 1, $y * ($this->c + $this->b) + $this->b, $f); }

// Breaks the vertical walls

function col($x, $y, &$f) { imagefilledrectangle($this->i, $x * ($this->c + $this->b), $y * ($this->c + $this->b) + $this->b, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b) + $this->b + $this->c - 1, $f); }

// Breaks the walls

function dot(&$f) { for ($x = 0; $x <= $this->x; ++$x) { for ($y = 0; $y <= $this->y; ++$y) { if (isset($this->H[$x][$y])) $this->line($x, $y, $f); if (isset($this->V[$x][$y])) $this->col($x, $y, $f); } } }

// Fill color cell

function cellfill(&$x, &$y, &$c) { imagefilledrectangle($this->i, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b) + $this->b, $x * ($this->c + $this->b) + $this->b + $this->c - 1, $y * ($this->c + $this->b) + $this->b + $this->c - 1, $c); }

// Draw solution

function path() { $l = count($this->r); for ($i = 0; $i < $l; ++$i) { list($x, $y) = $this->r[$i]; $r = ($this->e[0] * ($l - $i) + $this->s[0] * $i) / $l; $g = ($this->e[1] * ($l - $i) + $this->s[1] * $i) / $l; $b = ($this->e[2] * ($l - $i) + $this->s[2] * $i) / $l; if (!isset($c[$r][$g][$b])) $c[$r][$g][$b] = imagecolorallocate($this->i, $r, $g, $b); $this->cellfill($x, $y, $c[$r][$g][$b]); if (isset($ox, $oy)) { if ($ox - $x == -1) $this->col($x, $y, $c[$r][$g][$b]); if ($oy - $y == -1) $this->line($x, $y, $c[$r][$g][$b]); if ($ox - $x == 1) $this->col($ox, $oy, $c[$r][$g][$b]); if ($oy - $y == 1) $this->line($ox, $oy, $c[$r][$g][$b]); } if ($i == 0) $this->col(0, 0, $c[$r][$g][$b]); if ($i == $l - 1) $this->col($x + 1, $y, $c[$r][$g][$b]); $ox = $x; $oy = $y; } }

// Call digger and make rendering

function __destruct() { $this->dig(); $this->i = imagecreatetruecolor( $this->b + $this->x * ($this->c + $this->b), $this->b + $this->y * ($this->c + $this->b)); $f = rgbc($this->i, $this->f); $m = rgbc($this->i, $this->m); unset($this->f, $this->m); imagefill($this->i, 0, 0, $f); $this->grid($m); $this->dot($f); unset($f, $m, $this->H, $this->V); if ($this->r) $this->path(); unset($this->r, $this->e, $this->s); header('content-disposition:inline;filename="maze.png"'); header('cache-control:no-store,no-cache,must-revalidate'); header('content-type:image/png'); imagepng($this->i, NULL, 9, PNG_ALL_FILTERS); imagedestroy($this->i); } } </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

PL/I

<lang pli>*process source attributes xref or(!);

mgg: Proc Options(main);
/* REXX ***************************************************************
* 04.09.2013 Walter Pachl translated from REXX version 2
**********************************************************************/
Dcl (MIN,MOD,RANDOM,REPEAT,SUBSTR) Builtin;
Dcl SYSIN    STREAM INPUT;
Dcl print Print;
Dcl imax Bin Fixed(31) init(10);
Dcl jmax Bin Fixed(31) init(15);
Dcl seed Bin Fixed(31) init(4711);
Get File(sysin) Data(imax,jmax,seed);
Dcl ii   Bin Fixed(31);
Dcl jj   Bin Fixed(31);
Dcl id   Bin Fixed(31);
Dcl jd   Bin Fixed(31);
id=2*imax+1;                        /* vertical dimension of a.i.j   */
jd=2*jmax+1;                        /* horizontal dimension of a.i.j */
Dcl c Char(2000) Var;
c=repeat('123456789'!!'abcdefghijklmnopqrstuvwxyz'!!
                      'ABCDEFGHIJKLMNOPQRSTUVWXYZ',20);
Dcl x Bin Float(53);
x=random(seed);
Dcl ps Bin Fixed(31) Init(1);         /* first position             */
Dcl na Bin Fixed(31) Init(1);         /* number of points used      */
Dcl si Bin Fixed(31);                 /* loop to compute paths      */
Begin;
Dcl a(id,jd) Bin Fixed(15);
Dcl p(imax,jmax) Char(1);
Dcl 1 pl(imax*jmax),
     2 ic Bin Fixed(15),
     2 jc Bin Fixed(15);
Dcl 1 np(imax*jmax),
     2 ic Bin Fixed(15),
     2 jc Bin Fixed(15);
Dcl 1 pos(imax*jmax),
     2 ic Bin Fixed(15),
     2 jc Bin Fixed(15);
Dcl npl Bin Fixed(31) Init(0);
a=1;                                   /* mark all borders present   */
p='.';                                 /* Initialize all grid points */
ii=rnd(imax);                          /* find a start position      */
jj=rnd(jmax);
Do si=1 To 1000;                       /* Do Forever - see Leave     */
  Call path(ii,jj);              /* compute a path starting at ii/jj */
  If na=imax*jmax Then                 /* all points used            */
    Leave;                             /* we are done                */
  Call select_next(ii,jj);             /* get a new start from a path*/
  End;
Call show;
Return;

path: Procedure(ii,jj);
/**********************************************************************
* compute a path starting from point (ii,jj)
**********************************************************************/
Dcl ii   Bin Fixed(31);
Dcl jj   Bin Fixed(31);
Dcl nb   Bin Fixed(31);
Dcl ch   Bin Fixed(31);
Dcl pp   Bin Fixed(31);
  p(ii,jj)='1';
  pos.ic(ps)=ii;
  pos.jc(ps)=jj;
  Do pp=1 to 50;               /* compute a path of maximum length 50*/
    nb=neighbors(ii,jj);               /* number of free neighbors   */
    Select;
      When(nb=1)                       /* just one                   */
        Call advance((1),ii,jj);       /* go for it                  */
      When(nb>0) Do;                   /* more Than 1                */
        ch=rnd(nb);                    /* choose one possibility     */
        Call advance(ch,ii,jj);        /* and go for that            */
        End;
      Otherwise                        /* none available             */
        Leave;
      End;
    End;
  End;

neighbors: Procedure(i,j) Returns(Bin Fixed(31));
/**********************************************************************
* count the number of free neighbors of point (i,j)
**********************************************************************/
Dcl i    Bin Fixed(31);
Dcl j    Bin Fixed(31);
Dcl in   Bin Fixed(31);
Dcl jn   Bin Fixed(31);
Dcl nb   Bin Fixed(31) Init(0);
  in=i-1; If in>0     Then Call check(in,j,nb);
  in=i+1; If in<=imax Then Call check(in,j,nb);
  jn=j-1; If jn>0     Then Call check(i,jn,nb);
  jn=j+1; If jn<=jmax Then Call check(i,jn,nb);
  Return(nb);
End;

check: Procedure(i,j,n);
/**********************************************************************
* check if point (i,j) is free and note it as possible successor
**********************************************************************/
Dcl i    Bin Fixed(31);
Dcl j    Bin Fixed(31);
Dcl n    Bin Fixed(31);
  If p(i,j)='.' Then Do;               /* point is free              */
    n+=1;                              /* number of free neighbors   */
    np.ic(n)=i;                        /* note it as possible choice */
    np.jc(n)=j;
    End;
End;

advance: Procedure(ch,ii,jj);
/**********************************************************************
* move to the next point of the current path
**********************************************************************/
Dcl ch   Bin Fixed(31);
Dcl ii   Bin Fixed(31);
Dcl jj   Bin Fixed(31);
Dcl ai   Bin Fixed(31);
Dcl aj   Bin Fixed(31);
Dcl pii  Bin Fixed(31) Init((ii));
Dcl pjj  Bin Fixed(31) Init((jj));
Dcl z    Bin Fixed(31);
  ii=np.ic(ch);
  jj=np.jc(ch);
  ps+=1;                               /* position number            */
  pos.ic(ps)=ii;                       /* note its coordinates       */
  pos.jc(ps)=jj;
  p(ii,jj)=substr(c,ps,1);             /* mark the point as used     */
  ai=pii+ii;                           /* vertical border position   */
  aj=pjj+jj;                           /* horizontal border position */
  a(ai,aj)=0;                          /* tear the border down       */
  na+=1;                               /* number of used positions   */
  z=npl+1;                             /* add the point to the list  */
  pl.ic(z)=ii;                         /* of follow-up start pos.    */
  pl.jc(z)=jj;
  npl=z;
  End;

show: Procedure;
/*********************************************************************
* Show the resulting maze
*********************************************************************/
Dcl i Bin Fixed(31);
Dcl j Bin Fixed(31);
Dcl ol Char(300) Var;
  Put File(print) Edit('mgg',imax,jmax,seed)(Skip,a,3(f(4)));
  Put File(print) Skip Data(na);
  Do i=1 To id;
    ol=;
    Do j=1 To jd;
      If mod(i,2)=1 Then Do;            /* odd lines                 */
        If a(i,j)=1 Then Do;            /* border to be drawn        */
          If mod(j,2)=0 Then
            ol=ol!!'---';               /* draw the border           */
          Else
            ol=ol!!'+';
          End;
        Else Do;                        /* border was torn down      */
          If mod(j,2)=0 Then
            ol=ol!!'   ';               /* blanks instead of border  */
          Else
            ol=ol!!'+';
          End;
        End;
      Else Do;                          /* even line                 */
        If a(i,j)=1 Then Do;
          If mod(j,2)=0 Then            /* even column               */
            ol=ol!!'   ';               /* moving space              */
          Else                          /* odd column                */
            ol=ol!!'!';                 /* draw the border           */
          End;
        Else                            /* border was torn down      */
          ol=ol!!' ';                   /* blank instead of border   */
        End;
      End;
    Select;
      When(i=6) substr(ol,11,1)='A';
      When(i=8) substr(ol, 3,1)='B';
      Otherwise;
      End;
    Put File(print) Edit(ol,i)(Skip,a,f(3));
    End;
  End;

select_next: Procedure(is,js);
/**********************************************************************
* look for a point to start the nnext path
**********************************************************************/
Dcl is Bin Fixed(31);
Dcl js Bin Fixed(31);
Dcl n  Bin Fixed(31);
Dcl nb Bin Fixed(31);
Dcl s  Bin Fixed(31);
  Do Until(nb>0);                       /* loop until one is found   */
    n=npl;                              /* number of points recorded */
    s=rnd(n);                           /* pick a random index       */
    is=pl.ic(s);                        /* its coordinates           */
    js=pl.jc(s);
    nb=neighbors(is,js);                /* count free neighbors      */
    If nb=0 Then Do;                    /* if there is none          */
      pl.ic(s)=pl.ic(n);                /* remove this point         */
      pl.jc(s)=pl.jc(n);
      npl-=1;
      End;
    End;
End;

rnd: Proc(n) Returns(Bin Fixed(31));
/*********************************************************************
* return a pseudo-random integer between 1 and n
*********************************************************************/
dcl (r,n) Bin Fixed(31);
r=min(random()*n+1,n);
Return(r);
End;

End;
End;</lang>

Output:

�mgg   5  15  43
NA=            75;
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+  1
!       !                                       !       !   !  2
+   +   +   +---+---+---+   +---+---+   +---+   +   +   +   +  3
!   !       !           !           !       !       !       !  4
+   +---+---+   +---+---+---+---+   +---+   +---+---+---+---+  5
!         A !           !           !   !       !           !  6
+---+---+   +---+---+   +   +---+---+   +---+   +   +---+---+  7
! B     !       !       !                   !       !       !  8
+   +   +---+   +   +   +---+---+---+---+---+---+   +   +   +  9
!   !               !                           !       !   ! 10
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 11            

Prolog

Works with SWI-Prolog and XPCE. <lang Prolog>:- dynamic cell/2.

maze(Lig,Col) :- retractall(cell(_,_)),

new(D, window('Maze')),

% creation of the grid forall(between(0,Lig, I), (XL is 50, YL is I * 30 + 50, XR is Col * 30 + 50, new(L, line(XL, YL, XR, YL)), send(D, display, L))),

forall(between(0,Col, I), (XT is 50 + I * 30, YT is 50, YB is Lig * 30 + 50, new(L, line(XT, YT, XT, YB)), send(D, display, L))),

SX is Col * 30 + 100, SY is Lig * 30 + 100, send(D, size, new(_, size(SX, SY))),

% choosing a first cell L0 is random(Lig), C0 is random(Col), assert(cell(L0, C0)), \+search(D, Lig, Col, L0, C0), send(D, open).

search(D, Lig, Col, L, C) :- Dir is random(4), nextcell(Dir, Lig, Col, L, C, L1, C1), assert(cell(L1,C1)), assert(cur(L1,C1)), erase_line(D, L, C, L1, C1), search(D, Lig, Col, L1, C1).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% erase_line(D, L, C, L, C1) :- ( C < C1 -> C2 = C1; C2 = C), XT is C2 * 30 + 50, YT is L * 30 + 51, YR is (L+1) * 30 + 50, new(Line, line(XT, YT, XT, YR)), send(Line, colour, white), send(D, display, Line).

erase_line(D, L, C, L1, C) :- XT is 51 + C * 30, XR is 50 + (C + 1) * 30, ( L < L1 -> L2 is L1; L2 is L), YT is L2 * 30 + 50, new(Line, line(XT, YT, XR, YT)), send(Line, colour, white), send(D, display, Line).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nextcell(Dir, Lig, Col, L, C, L1, C1) :- next(Dir, Lig, Col, L, C, L1, C1); ( Dir1 is (Dir+3) mod 4, next(Dir1, Lig, Col, L, C, L1, C1)); ( Dir2 is (Dir+1) mod 4, next(Dir2, Lig, Col, L, C, L1, C1)); ( Dir3 is (Dir+2) mod 4, next(Dir3, Lig, Col, L, C, L1, C1)).

% 0 => northward next(0, _Lig, _Col, L, C, L1, C) :- L > 0, L1 is L - 1, \+cell(L1, C).

% 1 => rightward next(1, _Lig, Col, L, C, L, C1) :- C < Col - 1, C1 is C + 1, \+cell(L, C1).

% 2 => southward next(2, Lig, _Col, L, C, L1, C) :- L < Lig - 1, L1 is L + 1, \+cell(L1, C).

% 3 => leftward next(2, _Lig, _Col, L, C, L, C1) :- C > 0, C1 is C - 1, \+cell(L, C1).

</lang>

Output:

PureBasic

<lang PureBasic>Enumeration

 ;indexes for types of offsets from maze coordinates (x,y)
 #visited ;used to index visited(x,y) in a given direction from current maze cell
 #maze    ;used to index maze() in a given direction from current maze cell
 #wall    ;used to index walls in maze() in a given direction from current maze cell
 #numOffsets = #wall 
 ;direction indexes
 #dir_ID = 0 ;identity value, produces no changes
 #firstDir
 #dir_N = #firstDir
 #dir_E
 #dir_S
 #dir_W
 #numDirs = #dir_W 

EndEnumeration

DataSection

 ;maze(x,y) offsets for visited, maze, & walls for each direction
 Data.i 1, 1,  0,  0, 0, 0 ;ID
 Data.i 1, 0,  0, -1, 0, 0 ;N
 Data.i 2, 1,  1,  0, 1, 0 ;E
 Data.i 1, 2,  0,  1, 0, 1 ;S
 Data.i 0, 1, -1,  0, 0, 0 ;W
 Data.i %00, %01, %10, %01, %10 ;wall values for ID, N, E, S, W

EndDataSection

1. cellDWidth = 4

Structure mazeOutput

 vWall.s
 hWall.s

EndStructure

setup reference values indexed by type and direction from current map cell

Global Dim offset.POINT(#numOffsets, #numDirs) Define i, j For i = 0 To #numDirs

 For j = 0 To #numOffsets
   Read.i offset(j, i)\x: Read.i offset(j, i)\y
 Next

Next

Global Dim wallvalue(#numDirs) For i = 0 To #numDirs: Read.i wallvalue(i): Next

Procedure makeDisplayMazeRow(Array mazeRow.mazeOutput(1), Array maze(2), y)

 ;modify mazeRow() to produce output of 2 strings showing the vertical walls above and horizontal walls across a given maze row
 Protected x, vWall.s, hWall.s
 Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2)
 
 vWall = "": hWall = ""
 For x = 0 To mazeWidth
   If maze(x, y) & wallvalue(#dir_N): vWall + "+   ": Else: vWall + "+---": EndIf 
   If maze(x, y) & wallvalue(#dir_W): hWall + "    ": Else: hWall + "|   ": EndIf 
 Next
 mazeRow(0)\vWall = Left(vWall, mazeWidth * #cellDWidth + 1)
 If y <> mazeHeight: mazeRow(0)\hWall = Left(hWall, mazeWidth * #cellDWidth + 1): Else: mazeRow(0)\hWall = "": EndIf

EndProcedure

Procedure displayMaze(Array maze(2))

 Protected x, y, vWall.s, hWall.s, mazeHeight = ArraySize(maze(), 2)
 Protected Dim mazeRow.mazeOutput(0)
 
 For y = 0 To mazeHeight
   makeDisplayMazeRow(mazeRow(), maze(), y)
   PrintN(mazeRow(0)\vWall): PrintN(mazeRow(0)\hWall)
 Next

EndProcedure

Procedure generateMaze(Array maze(2), mazeWidth, mazeHeight)

 Dim maze(mazeWidth, mazeHeight) ;Each cell specifies walls present above and to the left of it,
                                 ;array includes an extra row and column for the right and bottom walls
 Dim visited(mazeWidth + 1, mazeHeight + 1) ;Each cell represents a cell of the maze, an extra line of cells are included
                                            ;as padding around the representative cells for easy border detection
 
 Protected i
 ;mark outside border as already visited (off limits)
 For i = 0 To mazeWidth
   visited(i + offset(#visited, #dir_N)\x, 0 + offset(#visited, #dir_N)\y) = #True
   visited(i + offset(#visited, #dir_S)\x, mazeHeight - 1 + offset(#visited, #dir_S)\y) = #True
 Next
 For i = 0 To mazeHeight
   visited(0 + offset(#visited, #dir_W)\x, i + offset(#visited, #dir_W)\y) = #True
   visited(mazeWidth - 1 + offset(#visited, #dir_E)\x, i + offset(#visited, #dir_E)\y) = #True
 Next
 
 ;generate maze
 Protected x = Random(mazeWidth - 1), y = Random (mazeHeight - 1), cellCount, nextCell
 visited(x + offset(#visited, #dir_ID)\x, y + offset(#visited, #dir_ID)\y) = #True
 PrintN("Maze of size " + Str(mazeWidth) + " x " + Str(mazeHeight) + ", generation started at " + Str(x) + " x " + Str(y))
 
 NewList stack.POINT()
 Dim unvisited(#numDirs - #firstDir)
 Repeat
   cellCount = 0
   For i = #firstDir To #numDirs
     If Not visited(x + offset(#visited, i)\x, y + offset(#visited, i)\y)
       unvisited(cellCount) = i: cellCount + 1
     EndIf 
   Next 
   
   If cellCount
     nextCell = unvisited(Random(cellCount - 1))
     visited(x + offset(#visited, nextCell)\x, y + offset(#visited, nextCell)\y) = #True
     maze(x + offset(#wall, nextCell)\x, y + offset(#wall, nextCell)\y) | wallvalue(nextCell)
     
     If cellCount > 1
       AddElement(stack())
       stack()\x = x: stack()\y = y
     EndIf 
     x + offset(#maze, nextCell)\x: y + offset(#maze, nextCell)\y
   ElseIf ListSize(stack()) > 0
     x = stack()\x: y = stack()\y
     DeleteElement(stack())
   Else 
     Break  ;end maze generation
   EndIf 
 ForEver
 
 ; ;mark random entry and exit point
 ; x = Random(mazeWidth - 1): y = Random(mazeHeight - 1)
 ; maze(x, 0) | wallvalue(#dir_N): maze(mazeWidth, y) | wallvalue(#dir_E)
 ProcedureReturn

EndProcedure

If OpenConsole()

 Dim maze(0, 0)
 Define mazeWidth = Random(5) + 7: mazeHeight = Random(5) + 3
 generateMaze(maze(), mazeWidth, mazeHeight)
 displayMaze(maze())
 
 Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
 CloseConsole()

EndIf</lang> The maze is represented by an array of cells where each cell indicates the walls present above (#dir_N) and to its left (#dir_W). Maze generation is done with a additional array marking the visited cells. Neither an entry nor an exit are created, these were not part of the task. A simple means of doing so is included but has been commented out.

Sample output:

Maze of size 11 x 8, generation started at 9 x 3
+---+---+---+---+---+---+---+---+---+---+---+
|   |           |           |               |
+   +   +---+   +   +---+   +   +---+   +   +
|   |       |       |       |   |       |   |
+   +---+   +---+---+   +---+   +   +---+---+
|   |       |       |           |           |
+   +   +---+---+   +---+---+---+---+---+   +
|       |           |       |       |       |
+   +---+   +---+   +   +---+   +   +---+---+
|           |   |   |           |           |
+---+---+---+   +   +   +---+---+   +---+   +
|           |       |           |       |   |
+   +---+---+   +---+   +---+---+   +   +---+
|       |       |       |       |   |       |
+   +   +   +---+---+---+   +   +---+---+   +
|   |                       |               |
+---+---+---+---+---+---+---+---+---+---+---+

Python

<lang python>from random import shuffle, randrange

def make_maze(w = 16, h = 8): vis = [[0] * w + [1] for _ in range(h)] + [[1] * (w + 1)] ver = [["| "] * w + ['|'] for _ in range(h)] + [[]] hor = [["+--"] * w + ['+'] for _ in range(h + 1)]

def walk(x, y): vis[y][x] = 1

d = [(x - 1, y), (x, y + 1), (x + 1, y), (x, y - 1)] shuffle(d) for (xx, yy) in d: if vis[yy][xx]: continue if xx == x: hor[max(y, yy)][x] = "+ " if yy == y: ver[y][max(x, xx)] = " " walk(xx, yy)

walk(randrange(w), randrange(h)) for (a, b) in zip(hor, ver): print(.join(a + ['\n'] + b))

make_maze()</lang>

Output:

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

Racket

Maze generator <lang racket>

1. lang racket

the structure representing a maze of size NxM

(struct maze (N M tbl))

managing cell properties

(define (connections tbl c) (dict-ref tbl c '()))

(define (connect! tbl c n)

 (dict-set! tbl c (cons n (connections tbl c)))
 (dict-set! tbl n (cons c (connections tbl n))))

(define (connected? tbl a b) (member a (connections tbl b)))

Returns a maze of a given size

build-maze

: Index Index -> Maze

(define (build-maze N M)

 (define tbl (make-hash))
 (define (visited? tbl c) (dict-has-key? tbl c))
 (define (neigbours c)
   (filter 
    (match-lambda [(list i j) (and (<= 0 i (- N 1)) (<= 0 j (- M 1)))])
    (for/list ([d '((0 1) (0 -1) (-1 0) (1 0))]) (map + c d))))
 ; generate the maze
 (let move-to-cell ([c (list (random N) (random M))])
   (for ([n (shuffle (neigbours c))] #:unless (visited? tbl n))
     (connect! tbl c n)
     (move-to-cell n)))
 ; return the result
 (maze N M tbl))

</lang>

Printing out the maze

<lang racket>

Shows a maze

(define (show-maze m)

 (match-define (maze N M tbl) m)
 (for ([i N]) (display "+---"))
 (displayln "+")
 (for ([j M])
   (display "|")
   (for ([i (- N 1)])
     (if (connected? tbl (list i j) (list (+ 1 i) j))
         (display "    ")
         (display "   |")))
   (display "   |")
   (newline)
   (for ([i N])
     (if (connected? tbl (list i j) (list i (+ j 1)))
         (display "+   ")
         (display "+---")))
   (displayln "+"))
 (newline))

</lang>

Example:

-> (define m (build-maze 10 7))
-> (show-maze m)
+---+---+---+---+---+---+---+---+---+---+
|       |       |       |               |
+   +---+---+   +   +   +---+   +---+   +
|           |   |   |       |       |   |
+   +   +---+   +   +---+   +---+---+   +
|   |       |       |   |           |   |
+   +---+   +---+---+   +---+---+   +   +
|   |   |               |       |       |
+   +   +---+---+---+   +   +   +---+   +
|       |       |       |   |   |       |
+---+   +   +---+   +---+   +   +   +---+
|   |       |       |       |       |   |
+   +---+   +   +---+   +---+---+---+   +
|           |                           |
+---+---+---+---+---+---+---+---+---+---+

Rascal

Translation of: Python

<lang rascal>import IO; import util::Math; import List;

public void make_maze(int w, int h){ vis = _ <- [1..w | _ <- [1..h]]; ver = "| _ <- [1..w + ["|"] | _ <- [1..h]] + [[]]; hor = _ <- [1..w + ["+"] | _ <- [1..h + 1]];

void walk(int x, int y){ vis[y][x] = 1;

d = [<x - 1, y>, <x, y + 1>, <x + 1, y>, <x, y - 1>]; while (d != []){ <<xx, yy>, d> = takeOneFrom(d); if (xx < 0 || yy < 0 || xx >= w || yy >= w) continue; if (vis[yy][xx] == 1) continue; if (xx == x) hor[max([y, yy])][x] = "+ "; if (yy == y) ver[y][max([x, xx])] = " "; walk(xx, yy); }

	}
	

walk(arbInt(w), arbInt(h)); for (<a, b> <- zip(hor, ver)){ println(("" | it + "<z>" | z <- a)); println(("" | it + "<z>" | z <- b)); } }</lang>

rascal>make_maze(10,10)
+--+--+--+--+--+--+--+--+--+--+
|     |        |              |
+  +--+  +--+  +--+--+--+  +  +
|  |     |  |           |  |  |
+  +  +--+  +--+--+--+  +  +  +
|  |     |     |        |  |  |
+  +--+--+  +  +  +--+--+--+  +
|           |  |  |           |
+  +--+--+--+  +  +  +--+--+--+
|        |     |  |  |        |
+  +--+  +--+--+  +  +  +--+  +
|  |     |        |        |  |
+  +  +--+  +--+--+  +--+--+  +
|  |  |     |     |  |  |     |
+--+  +  +--+  +--+  +  +  +  +
|     |     |           |  |  |
+  +  +--+  +--+--+--+--+  +  +
|  |  |     |     |     |  |  |
+  +--+  +--+  +  +  +  +  +  +
|              |     |     |  |
+--+--+--+--+--+--+--+--+--+--+

ok

REXX

prettified maze version

In order to preserve the aspect ratio (for most display terminals), several   changestr   instructions and
some other instructions were added to increase the horizontal dimension (columns). <lang rexx>/*REXX program generates and displays a (rectangular) solvable maze. */ height=0; @.=0 /*default for all cells visited.*/ parse arg rows cols seed . /*allow user to specify maze size*/ if rows= | rows==',' then rows=19 /*No rows given? Use the default*/ if cols= | cols==',' then cols=19 /*No cols given? Use the default*/ if seed\== then call random ,,seed /*use a seed for repeatability. */ call buildRow '┌'copies('~┬',cols-1)'~┐' /*build the top edge of maze.*/

                                      /*(below)  build the maze's grid.*/
 do    r=1  for rows;  _=;     __=;          hp= '|';    hj='├'
    do c=1  for cols;  _= _||hp'1';     __=__||hj'~';    hj='┼';   hp='│'
    end   /*c*/
                   call buildRow  _'│'    /*build  right edge of cells.*/
 if r\==rows  then call buildRow __'┤'    /*  "      "     "   "  maze.*/
 end      /*r*/

call buildRow '└'copies('~┴',cols-1)'~┘' /*build the bottom maze edge.*/ r!=random(1,rows)*2; c!=random(1,cols)*2; @.r!.c!=0 /*choose 1st cell*/

                                      /* [↓]  traipse through the maze.*/
 do forever;    n=hood(r!,c!);     if n==0  then  if \fcell()  then leave
 call ?;        @._r._c=0             /*get the (next) direction to go.*/
 ro=r!; co=c!;  r!=_r;   c!=_c        /*save original cell coordinates.*/
 ?.zr=?.zr%2;   ?.zc=?.zc%2           /*get the row and cell directions*/
 rw=ro+?.zr;    cw=co+?.zc            /*calculate the next row and col.*/
 @.rw.cw='·'                          /*mark the cell as being visited.*/
 end   /*forever*/

   do     r=1  for height;         _=              /*display the maze. */
       do c=1  for cols*2 + 1;     _=_ || @.r.c;   end  /*c*/
   if \(r//2)  then _=translate(_, '\', "·")       /*trans to backslash*/
   @.r=_                                           /*save the row in @.*/
   end   /*r*/

     do #=1  for height;   _=@.#      /*display maze to the terminal.  */
     call makeNice                    /*make some cell corners prettier*/
     _=changestr(1,_,111)             /*these four ────────────────────*/
     _=changestr(0,_,000)             /*─── statements are ────────────*/
     _=changestr('·',_,"   ")         /*──────── used for preserving ──*/
     _=changestr('~',_,"───")         /*──────────── the aspect ratio. */
     say translate(_, '─│', "═|\10")  /*make it presentable for screen.*/
     end   /*#*/

exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────@ subroutine────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a cell.*/ /*──────────────────────────────────? subroutine────────────────────────*/ ?: do forever;  ?.=0;  ?=random(1,4); if ?==1 then ?.zc=-2 /*north*/

                                      if ?==2  then ?.zr=+2     /* east*/
                                      if ?==3  then ?.zc=+2     /*south*/
                                      if ?==4  then ?.zr=-2     /* west*/
  _r=r!+?.zr;   _c=c!+?.zc;     if @._r._c==1  then return
  end   /*forever*/

/*──────────────────────────────────BUILDROW subroutine─────────────────*/ buildRow: parse arg z; height=height+1; width=length(z)

          do c=1  for width;   @.height.c=substr(z,c,1);   end;    return

/*──────────────────────────────────FCELL subroutine────────────────────*/ fcell: do r=1 for rows; r2=r+r

        do c=1  for cols;  c2=c+c
        if hood(r2,c2)==1  then do; r!=r2; c!=c2; @.r!.c!=0; return 1;end
        end   /*c*/
      end     /*r*/

return 0 /*──────────────────────────────────HOOD subroutine─────────────────────*/ hood: parse arg rh,ch; return @(rh+2,ch)+@(rh-2,ch)+@(rh,ch-2)+@(rh,ch+2) /*──────────────────────────────────MAKENICE subroutine─────────────────*/ makeNice: width=length(_); old=#-1; new=#+1; old_=@.old; new_=@.new if left(_,2) =='├·' then _=translate(_, '|', "├") if right(_,2)=='·┤' then _=translate(_, '|', "┤")

                                        /* [↓] handle the top grid row.*/
  do  k=1  for  width  while #==1;      z=substr(_,k,1) /*maze top row.*/
  if z\=='┬'     then iterate
  if substr(new_,k,1)=='\'  then _=overlay('═',_,k)
  end   /*k*/

  do  k=1  for  width  while #==height; z=substr(_,k,1) /*maze bot row.*/
  if z\=='┴'     then iterate
  if substr(old_,k,1)=='\'  then _=overlay('═',_,k)
  end   /*k*/
                                        /* [↓] handle the mid grid rows*/
  do  k=3  to  width-2 by 2 while #//2; z=substr(_,k,1) /*maze mid rows*/
  if z\=='┼'     then iterate
  le=substr(_,k-1,1)
  ri=substr(_,k+1,1)
  up=substr(old_,k,1)
  dw=substr(new_,k,1)
      select
      when le=='·' & ri=='·' & up=='│' & dw=='│'  then _=overlay('|',_,k)
      when le=='~' & ri=='~' & up=='\' & dw=='\'  then _=overlay('═',_,k)
      when le=='~' & ri=='~' & up=='\' & dw=='│'  then _=overlay('┬',_,k)
      when le=='~' & ri=='~' & up=='│' & dw=='\'  then _=overlay('┴',_,k)
      when le=='~' & ri=='·' & up=='\' & dw=='\'  then _=overlay('═',_,k)
      when le=='·' & ri=='~' & up=='\' & dw=='\'  then _=overlay('═',_,k)
      when le=='·' & ri=='·' & up=='│' & dw=='\'  then _=overlay('|',_,k)
      when le=='·' & ri=='·' & up=='\' & dw=='│'  then _=overlay('|',_,k)
      when le=='·' & ri=='~' & up=='\' & dw=='│'  then _=overlay('┌',_,k)
      when le=='·' & ri=='~' & up=='│' & dw=='\'  then _=overlay('└',_,k)
      when le=='~' & ri=='·' & up=='\' & dw=='│'  then _=overlay('┐',_,k)
      when le=='~' & ri=='·' & up=='│' & dw=='\'  then _=overlay('┘',_,k)
      when le=='~' & ri=='·' & up=='│' & dw=='│'  then _=overlay('┤',_,k)
      when le=='·' & ri=='~' & up=='│' & dw=='│'  then _=overlay('├',_,k)
      otherwise  nop
      end   /*select*/
  end     /*k*/

return</lang> Some older REXXes don't have a changestr bif, so one is included here ──► CHANGESTR.REX.

output when using the input of 23 19 55
(using Regina)

┌───┬───────────────────┬───────────┬───────────────────────────────────────┐
│   │                   │           │                                       │
│   │   │   │   ┌───────┘   ┌────   │   │   │   ────┐   │   ┌────   ┌────   │
│   │   │   │   │           │       │   │   │       │   │   │       │       │
│   │   │   │   │   ────────┤   ────┘   │   └───┐   ├───┘   └───────┤   ────┤
│   │   │   │   │           │           │       │   │               │       │
│   │   │   └───┴────────   ├───────┐   └───┐   │   │   ┌───┬────   └───┐   │
│   │   │                   │       │       │   │   │   │   │           │   │
│   │   └───┐   ┌───────┬───┘   │   └───────┤   │   │   │   │   ────┐   └───┤
│   │       │   │       │       │           │   │   │       │       │       │
├───┴───┐   │   │   ┌───┘   ┌───┴───────┐   │   │   └───────┼────   ├────   │
│       │   │       │       │           │       │           │       │       │
│   ────┘   ├───────┘   ┌───┴────────   │   ────┼───────┬───┘   │   │   │   │
│           │           │               │       │       │       │   │   │   │
├───────────┘   ┌───────┘   │   ┌───────┼───────┘   │   │   ────┴───┤   └───┤
│               │           │   │       │           │   │           │       │
│   ────┬───────┤   ────────┤   └────   │   │   │   │   └────────   │   │   │
│       │       │           │           │   │   │   │               │   │   │
│   │   │   │   ├────────   ├───────────┘   │   └───┴───┐   ────┬───┴───┘   │
│   │       │   │           │               │           │       │           │
│   ├───────┤   │   │   │   │   ────┬───────┴───────┐   ├────   │   │   ────┤
│   │       │       │   │   │       │               │   │       │   │       │
│   │   │   ├───────┤   │   └───┐   └───┬───────┐   │   └───────┼───┴───┐   │
│       │   │       │   │       │       │       │   │           │       │   │
├───┬───┘   │   │   │   └───────┴───┐   │   │   │   │   ┌────   │   ────┘   │
│   │       │   │   │               │   │   │   │   │   │       │           │
│   │   ┌───┘   │   └───────┬────   │   │   │   │   │   │   ────┴───┐   │   │
│       │       │           │       │       │   │   │   │           │   │   │
│   ────┤   ┌───┴───────────┘   │   ├───────┘   │   └───┤   ┌────   │   │   │
│       │   │                   │   │           │       │   │       │   │   │
├────   │   │   ┌───────────────┴───┘   │   ┌───┴───┐   └───┤   │   │   │   │
│       │       │                       │   │       │       │   │   │   │   │
│   ┌───┴───────┤   ┌───────┬───────┬───┘   │   │   ├────   │   │   │   │   │
│   │           │   │       │       │       │   │   │       │   │   │   │   │
│   ├───────┐   │   │   │   │   │   │   ────┤   │   │   ────┘   │   │   │   │
│   │       │   │   │   │   │   │   │       │   │   │           │   │   │   │
│   │   │   │   │   ├───┘   │   └───┼────   │   └───┴───────┐   ├───┘   │   │
│       │       │   │       │       │       │               │   │       │   │
│   │   └───────┤   │   ┌───┴───┐   │   │   └───────┐   │   └───┘   ┌───┘   │
│   │           │       │       │       │           │   │           │       │
│   ├────────   │   ┌───┴───┐   │   ┌───┴───┬────   │   └───┬───┬───┘   ┌───┤
│   │           │   │       │   │   │       │       │       │   │       │   │
│   │   ────┬───┴───┤   │   │   └───┤   │   │   │   └───┐   │   │   ┌───┘   │
│   │       │       │   │   │       │   │   │   │       │       │   │       │
│   └───────┘   │   │   │   └────   │   │   │   ├────   │   ────┤   │   │   │
│               │       │           │   │       │       │       │       │   │
└───────────────┴───────┴───────────┴───┴───────┴───────┴───────┴───────┴───┘

simpler version of above

The above REXX version had a quite of bit of code to "dress up" the maze presentation,
so another slimmed down version was coded. <lang rexx>/*REXX program generates and displays a (rectangular) solvable maze. */ height=0; @.=0 /*default for all cells visited.*/ parse arg rows cols seed . /*allow user to specify maze size*/ if rows= | rows==',' then rows=19 /*No rows given? Use the default*/ if cols= | cols==',' then cols=19 /*No cols given? Use the default*/ if seed\== then call random ,,seed /*use a seed for repeatability. */ call buildRow '┌'copies('─┬',cols-1)'─┐' /*build the top edge of maze.*/

                                      /*(below)  build the maze's grid.*/
 do    r=1  for rows;  _=;     __=;          hp= '|';    hj='├'
    do c=1  for cols;  _= _||hp'1';     __=__||hj'─';    hj='┼';   hp='│'
    end   /*c*/
                   call buildRow  _'│'    /*build  right edge of cells.*/
 if r\==rows  then call buildRow __'┤'    /*  "      "     "   "  maze.*/
 end      /*r*/

call buildRow '└'copies('─┴',cols-1)'─┘' /*build the bottom maze edge.*/ r!=random(1,rows)*2; c!=random(1,cols)*2; @.r!.c!=0 /*choose 1st cell*/

                                      /* [↓]  traipse through the maze.*/
 do forever;    n=hood(r!,c!);     if n==0  then  if \fcell()  then leave
 call ?;        @._r._c=0             /*get the (next) direction to go.*/
 ro=r!; co=c!;  r!=_r;   c!=_c        /*save original cell coordinates.*/
 ?.zr=?.zr%2;   ?.zc=?.zc%2           /*get the row and cell directions*/
 rw=ro+?.zr;    cw=co+?.zc            /*calculate the next row and col.*/
 @.rw.cw='·'                          /*mark the cell as being visited.*/
 end   /*forever*/

        do     r=1  for height;       _=           /*display the maze. */
            do c=1  for cols*2 + 1;   _=_ || @.r.c;   end  /*c*/
        if \(r//2)  then _=translate(_, '\', "·")  /*trans to backslash*/
        _=changestr(1,_,111)          /*these four ────────────────────*/
        _=changestr(0,_,000)          /*─── statements are ────────────*/
        _=changestr('·',_,"   ")      /*──────── used for preserving ──*/
        _=changestr('─',_,"───")      /*──────────── the aspect ratio. */
        say translate(_,'│',"|\10")   /*make it presentable for screen.*/
        end   /*r*/

exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────@ subroutine────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a cell.*/ /*──────────────────────────────────? subroutine────────────────────────*/ ?: do forever;  ?.=0;  ?=random(1,4); if ?==1 then ?.zc=-2 /*north*/

                                      if ?==2  then ?.zr=+2     /* east*/
                                      if ?==3  then ?.zc=+2     /*south*/
                                      if ?==4  then ?.zr=-2     /* west*/
    _r=r!+?.zr;   _c=c!+?.zc;   if @._r._c==1  then return
    end   /*forever*/

/*──────────────────────────────────BUILDROW subroutine─────────────────*/ buildRow: parse arg z; height=height+1; width=length(z)

          do c=1  for width;   @.height.c=substr(z,c,1);   end;    return

/*──────────────────────────────────FCELL subroutine────────────────────*/ fcell: do r=1 for rows; r2=r+r

        do c=1  for cols;  c2=c+c
        if hood(r2,c2)==1  then do; r!=r2; c!=c2; @.r!.c!=0; return 1;end
        end   /*c*/
      end     /*r*/

return 0 /*──────────────────────────────────HOOD subroutine─────────────────────*/ hood: parse arg rh,ch; return @(rh+2,ch)+@(rh-2,ch)+@(rh,ch-2)+@(rh,ch+2)</lang> output when using the input: 10 10

┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│   │           │                   │   │
├   ┼   ┼───┼───┼   ┼   ┼───┼───┼   ┼   ┤
│   │   │           │       │   │       │
├   ┼   ┼   ┼   ┼───┼───┼   ┼   ┼───┼   ┤
│   │   │   │   │       │   │       │   │
├   ┼   ┼   ┼   ┼───┼   ┼   ┼   ┼   ┼   ┤
│   │   │   │           │   │   │   │   │
├   ┼   ┼   ┼───┼───┼───┼   ┼   ┼   ┼   ┤
│       │               │   │   │   │   │
├   ┼───┼───┼───┼───┼   ┼   ┼   ┼   ┼   ┤
│   │           │       │   │   │   │   │
├───┼   ┼───┼   ┼   ┼───┼   ┼───┼   ┼   ┤
│       │       │       │           │   │
├   ┼───┼   ┼───┼───┼   ┼───┼───┼───┼   ┤
│       │               │           │   │
├   ┼   ┼───┼───┼───┼───┼   ┼───┼───┼   ┤
│   │       │           │   │           │
├   ┼───┼   ┼───┼───┼   ┼   ┼   ┼   ┼───┤
│       │               │       │       │
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

version 3

<lang rexx>/* REXX ***************************************************************

• 04.09.2013 Walter Pachl
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

Parse Arg imax jmax seed If imax= Then imax=10 If jmax= Then jmax=15 If seed= Then seed=4711 c='123456789'||,

 'abcdefghijklmnopqrstuvwxyz'||,
 translate('abcdefghijklmnopqrstuvwxyz')

c=copies(c,10) call random 1,10,seed id=2*imax+1 /* vertical dimension of a.i.j */ jd=2*jmax+1 /* horizontal dimension of a.i.j */ a.=1 /* mark all borders present */ p.='.' /* Initialize all grid points */ pl.=0 /* path list */ ii=random(1,imax) /* find a start position */ jj=random(1,jmax) p=1 /* first position */ na=1 /* number of points used */ Do si=1 To 1000 /* Do Forever - see Leave */

 /* Say 'loop' si na                     show progress              */
 Call path ii,jj                /* compute a path starting at ii/jj */
 If na=imax*jmax Then                 /* all points used            */
   Leave                              /* we are done                */
 Parse Value select_next() With ii jj /* get a new start from a path*/
 End

/*************** Do i=1 To imax

 ol=
 Do j=1 To jmax
   ol=ol||p.i.j
   End
   Say ol
 End

Say ' '

• • • • • • • • • • • • • • • /

Call show /*********************** Do pi=1 To imax*jmax

 Say right(pi,3) pos.pi
 End

• • • • • • • • • • • • • • • • • • • • • • • /

Exit

path: Procedure Expose p. np. p pl. c a. na imax jmax id jd pos. /**********************************************************************

• compute a path starting from point (ii,jj)
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 Parse Arg ii,jj
 p.ii.jj='1'
 pos.p=ii jj
 Do pp=1 to 50                /* compute a path of maximum length 50*/
   neighbors=neighbors(ii,jj)         /* number of free neighbors   */
   Select
     When neighbors=1 Then            /* just one                   */
       Call advance 1,ii,jj           /* go for it                  */
     When neighbors>0 Then Do         /* more Than 1                */
       ch=random(1,neighbors)         /* choose one possibility     */
       Call advance ch,ii,jj          /* and go for that            */
       End
     Otherwise                        /* none available             */
       Leave
     End
   End
 Return

neighbors: Procedure Expose p. np. imax jmax neighbors pl. /**********************************************************************

• count the number of free neighbors of point (i,j)
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 Parse Arg i,j
 neighbors=0
 in=i-1; If in>0     Then Call check in,j
 in=i+1; If in<=imax Then Call check in,j
 jn=j-1; If jn>0     Then Call check i,jn
 jn=j+1; If jn<=jmax Then Call check i,jn
 Return neighbors

check: Procedure Expose p. imax jmax np. neighbors pl. /**********************************************************************

• check if point (i,j) is free and note it as possible successor
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 Parse Arg i,j
 If p.i.j='.' Then Do                 /* point is free              */
   neighbors=neighbors+1              /* number of free neighbors   */
   np.neighbors=i j                   /* note it as possible choice */
   End
 Return

advance: Procedure Expose p pos. np. p. c ii jj a. na pl. pos. /**********************************************************************

• move to the next point of the current path
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 Parse Arg ch,pii,pjj
 Parse Var np.ch ii jj
 p=p+1                                /* position number            */
 pos.p=ii jj                          /* note its coordinates       */
 p.ii.jj=substr(c,p,1)                /* mark the point as used     */
 ai=pii+ii                            /* vertical border position   */
 aj=pjj+jj                            /* horizontal border position */
 a.ai.aj=0                            /* tear the border down       */
 na=na+1                              /* number of used positions   */
 z=pl.0+1                             /* add the point to the list  */
 pl.z=ii jj                           /* of follow-up start pos.    */
 pl.0=z
 Return

show: Procedure Expose id jd a. na /*********************************************************************

• Show the resulting maze
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 say 'mgg 6 18 4711'
 say 'show na='na
 Do i=1 To id
   ol=
   Do j=1 To jd
     If i//2=1 Then Do                /* odd lines                 */
       If a.i.j=1 Then Do             /* border to be drawn        */
         If j//2=0 Then
           ol=ol||'---'               /* draw the border           */
         Else
           ol=ol'+'
         End
       Else Do                        /* border was torn down      */
         If j//2=0 Then
           ol=ol||'   '               /* blanks instead of border  */
         Else
           ol=ol||'+'
         End
       End
     Else Do                          /* even line                 */
       If a.i.j=1 Then Do
         If j//2=0 Then               /* even column               */
           ol=ol||'   '               /* moving space              */
         Else                         /* odd column                */
           ol=ol||'|'                 /* draw the border           */
         End
       Else                           /* border was torn down      */
         ol=ol||' '                   /* blank instead of border   */
       End
     End
   Select
     When i=6 Then ol=overlay('A',ol,11)
     When i=8 Then ol=overlay('B',ol, 3)
     Otherwise Nop
     End
   Say ol format(i,2)
   End
 Return

select_next: Procedure Expose p. pl. imax jmax /*********************************************************************

• look for a point to start the nnext path
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 Do Until neighbors>0                 /* loop until one is found   */
   n=pl.0                             /* number of points recorded */
   s=random(1,n)                      /* pick a random index       */
   Parse Var pl.s is js               /* its coordinates           */
   neighbors=neighbors(is,js)         /* count free neighbors      */
   If neighbors=0 Then Do             /* if there is none          */
     pl.s=pl.n                        /* remove this point         */
     pl.0=pl.0-1
     End
   End
 Return is js                         /* return the new start point*/</lang>

Output:

rexx mgg 6 18 4711
show na=108
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+  1
|           |   |       |           |               |           |       |  2
+   +---+   +   +   +   +   +---+   +   +---+---+   +   +---+   +   +---+  3
|       |   |       |           |   |   |       |       |   |   |       |  4
+---+---+   +   +---+---+---+   +   +   +   +   +---+---+   +   +---+   +  5
|       | A                 |   |   |       |   |           |           |  6
+   +   +---+---+---+---+   +---+   +---+---+   +   +---+   +   +---+---+  7
| B |   |       |       |       |       |       |   |       |   |       |  8
+   +   +---+   +   +   +---+   +   +   +   +---+   +---+   +   +   +   +  9
|   |   |       |   |       |   |   |   |       |       |   |       |   | 10
+   +   +   +---+---+---+   +   +   +   +---+---+---+   +   +   +---+   + 11
|   |                           |   |                   |       |       | 12
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 13   

Ruby

<lang ruby>class Maze

 DIRECTIONS = [ [1, 0], [-1, 0], [0, 1], [0, -1] ]
 
 def initialize(width, height)
   @width   = width
   @height  = height
   @start_x = rand(width)
   @start_y = 0
   @end_x   = rand(width)
   @end_y   = height - 1
   
   # Which walls do exist? Default to "true". Both arrays are
   # one element bigger than they need to be. For example, the
   # @vertical_walls[x][y] is true if there is a wall between
   # (x,y) and (x+1,y). The additional entry makes printing easier.
   @vertical_walls   = Array.new(width) { Array.new(height, true) }
   @horizontal_walls = Array.new(width) { Array.new(height, true) }
   # Path for the solved maze.
   @path             = Array.new(width) { Array.new(height) }
   
   # "Hack" to print the exit.
   @horizontal_walls[@end_x][@end_y] = false
   
   # Generate the maze.
   generate
 end
 
 # Print a nice ASCII maze.
 def print
   # Special handling: print the top line.
   puts @width.times.inject("+") {|str, x| str << (x == @start_x ? "   +" : "---+")}
   
   # For each cell, print the right and bottom wall, if it exists.
   @height.times do |y|
     line = @width.times.inject("|") do |str, x|
       str << (@path[x][y] ? " * " : "   ") << (@vertical_walls[x][y] ? "|" : " ")
     end
     puts line
     
     puts @width.times.inject("+") {|str, x| str << (@horizontal_walls[x][y] ? "---+" : "   +")}
   end
 end
 
 private
 
 # Reset the VISITED state of all cells.
 def reset_visiting_state
   @visited = Array.new(@width) { Array.new(@height) }
 end
 
 # Is the given coordinate valid and the cell not yet visited?
 def move_valid?(x, y)
   (0...@width).cover?(x) && (0...@height).cover?(y) && !@visited[x][y]
 end
 
 # Generate the maze.
 def generate
   reset_visiting_state
   generate_visit_cell(@start_x, @start_y)
 end
 
 # Depth-first maze generation.
 def generate_visit_cell(x, y)
   # Mark cell as visited.
   @visited[x][y] = true
   
   # Randomly get coordinates of surrounding cells (may be outside
   # of the maze range, will be sorted out later).
   coordinates = DIRECTIONS.shuffle.map { |dx, dy| [x + dx, y + dy] }
   
   for new_x, new_y in coordinates
     next unless move_valid?(new_x, new_y)
     
     # Recurse if it was possible to connect the current and
     # the cell (this recursion is the "depth-first" part).
     connect_cells(x, y, new_x, new_y)
     generate_visit_cell(new_x, new_y)
   end
 end
 
 # Try to connect two cells. Returns whether it was valid to do so.
 def connect_cells(x1, y1, x2, y2)
   if x1 == x2
     # Cells must be above each other, remove a horizontal wall.
     @horizontal_walls[x1][ [y1, y2].min ] = false
   else
     # Cells must be next to each other, remove a vertical wall.
     @vertical_walls[ [x1, x2].min ][y1] = false
   end
 end

end

1. Demonstration:

maze = Maze.new 20, 10 maze.print</lang>

Output:

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

Scala

<lang scala>import scala.util.Random

object MazeTypes {

 case class Direction(val dx: Int, val dy: Int)

 case class Loc(val x: Int, val y: Int) {
   def +(that: Direction): Loc = Loc(x + that.dx, y + that.dy)
 }
 
 case class Door(val from: Loc, to: Loc)

 val North = Direction(0,-1)
 val South = Direction(0,1)
 val West = Direction(-1,0)
 val East = Direction(1,0)
 val directions = Set(North, South, West, East)

}

object MazeBuilder {

 import MazeTypes._

 def shuffle[T](set: Set[T]): List[T] = Random.shuffle(set.toList)
 
 def buildImpl(current: Loc, grid: Grid): Grid = {
   var newgrid = grid.markVisited(current)
   val nbors = shuffle(grid.neighbors(current))
   nbors.foreach { n =>
     if (!newgrid.isVisited(n)) {
       newgrid = buildImpl(n, newgrid.markVisited(current).addDoor(Door(current, n)))
     }
   }
   newgrid
 }
   
 def build(width: Int, height: Int): Grid = {
   val exit = Loc(width-1, height-1)
   buildImpl(exit, new Grid(width, height, Set(), Set()))
 }  

}

class Grid(val width: Int, val height: Int, val doors: Set[Door], val visited: Set[Loc]) {

 def addDoor(door: Door): Grid = 
   new Grid(width, height, doors + door, visited)
 
 def markVisited(loc: Loc): Grid = 
   new Grid(width, height, doors, visited + loc)
 
 def isVisited(loc: Loc): Boolean = 
   visited.contains(loc)
   
 def neighbors(current: Loc): Set[Loc] = 
   directions.map(current + _).filter(inBounds(_)) -- visited
   
 def printGrid(): List[String] = {
   (0 to height).toList.flatMap(y => printRow(y))
 }
 
 private def inBounds(loc: Loc): Boolean = 
   loc.x >= 0 && loc.x < width && loc.y >= 0 && loc.y < height

 private def printRow(y: Int): List[String] = {
   val row = (0 until width).toList.map(x => printCell(Loc(x, y)))
   val rightSide = if (y == height-1) " " else "|"
   val newRow = row :+ List("+", rightSide)
   List.transpose(newRow).map(_.mkString)
 }
 
 private val entrance = Loc(0,0)

 private def printCell(loc: Loc): List[String] = {
   if (loc.y == height) 
     List("+--")
   else List(
     if (openNorth(loc)) "+  " else "+--", 
     if (openWest(loc) || loc == entrance) "   " else "|  "
   )
 }
 
 def openNorth(loc: Loc): Boolean = openInDirection(loc, North)
 
 def openWest(loc: Loc): Boolean = openInDirection(loc, West)
   
 private def openInDirection(loc: Loc, dir: Direction): Boolean = 
   doors.contains(Door(loc, loc + dir)) || doors.contains(Door(loc + dir, loc))

}</lang>

Output:

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

Sidef

<lang ruby>var(w:5, h:5) = ARGV.map{.to_i}...;

var avail = (w * h); var d = [[-1, 0], [0, 1], [1, 0], [0, -1]];

1. cell is padded by sentinel col and row, so I don't check array bounds

var cell = (1..h -> map {([true] * w) + [false]} + [[false] * w+1]); var ver = (1..h -> map {["| "] * w }); var hor = (0..h -> map {["+--"] * w });

func walk(x, y) {

   cell[y][x] = false;
   avail-- > 0 || return;  # no more bottles, er, cells

   {
       var i = d.pick;
       var (x1, y1) = (x + i[0], y + i[1]);

       cell[y1][x1] || next;

       if (x == x1) { hor[[y1, y].max][x] = '+  ' };
       if (y == y1) { ver[y][[x1, x].max] = '   ' };
       walk(x1, y1);
   } * d.len;

}

walk(w.rand.int, h.rand.int); # generate

0...h each { |i|

   say (hor[i].join() + '+');
   if (i < h) {
       say (ver[i].join() + '|');
   }

}</lang>

Output:

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

Swift

Translation of: Java

<lang Swift>import Foundation

class Direction {

   var vect:(Int, Int, Int)
   var bit:Int {
       let (bit, dx, dy) = vect
       return bit
   }
   
   var dx:Int {
       let (bit, dx, dy) = vect
       return dx
   }
   
   var dy:Int {
       let (bit, dx, dy) = vect
       return dy
   }
   
   var opposite:Direction {
       switch (vect) {
       case (1, 0, -1):
           return Direction(bit: 2, dx: 0, dy: 1)
       case (2, 0, 1):
           return Direction(bit: 1, dx: 0, dy: -1)
       case (4, 1, 0):
           return Direction(bit: 8, dx: -1, dy: 0)
       case (8, -1, 0):
           return Direction(bit: 4, dx: 1, dy: 0)
       default:
           return Direction(bit: 0, dx: 0, dy: 0)
       }
   }
   
   init(bit:Int, dx:Int, dy:Int) {
       self.vect = (bit, dx, dy)
   }

}

let N = Direction(bit: 1, dx: 0, dy: -1) let S = Direction(bit: 2, dx: 0, dy: 1) let E = Direction(bit: 4, dx: 1, dy: 0) let W = Direction(bit: 8, dx: -1, dy: 0)

class MazeGenerator {

   let x:Int!
   let y:Int!
   var maze:Int!
   
   init(_ x:Int, _ y:Int) {
       self.x  = x
       self.y = y
       var col = [Int](count: y, repeatedValue: 0)
       self.maze = Int(count: x, repeatedValue: col)
       generateMaze(0, 0)
   }
   
   func display() {
       for i in 0..<y {
           // Draw top edge
           for j in 0..<x {
               print((maze[j][i] & 1) == 0 ? "+---" : "+   ")
           }
           println("+")
           
           // Draw left edge
           for j in 0..<x {
               print((maze[j][i] & 8) == 0 ? "|   " : "    ")
           }
           println("|")
       }
       
       // Draw bottom edge
       for j in 0..<x {
           print("+---")
       }
       println("+")
   }
   
   func generateMaze(cx:Int, _ cy:Int) {
       var dirs = [N, S, E, W] as NSMutableArray
       for i in 0..<dirs.count {
           let x1 = Int(arc4random()) % dirs.count
           let x2 = Int(arc4random()) % dirs.count
           dirs.exchangeObjectAtIndex(x1, withObjectAtIndex: x2)
       }
       
       for dir in dirs {
           var dir = dir as Direction
           let nx = cx + dir.dx
           let ny = cy + dir.dy
           if (between(nx, self.x) && between(ny, self.y) && (maze[nx][ny] == 0)) {
                   maze[cx][cy] |= dir.bit
                   maze[nx][ny] |= dir.opposite.bit
                   generateMaze(nx, ny)
           }
           
       }
   }
   
   func between(v:Int, _ upper:Int) -> Bool {
       return (v >= 0) && (v < upper)
   }

}

let x = 10 let y = 10 let maze = MazeGenerator(x, y) maze.display()</lang>

Output:

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

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 content
   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 $x [lrepeat $y 0]]] # This matrix holds the output for the Maze Solving task; not used for generation set content [lrepeat $x [lrepeat $y " "]] set unvisited [lrepeat [expr {$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] } }

rename unvisited= {}

   }

   # 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 && $k%4==2} { # At the centre of the cell, put the "content" of the cell append line [expr {idx($content, $j/2, $k/4)}] } elseif {$j%2 && ($k%4 || $k && idx($horiz, $j/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:

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

TXR

Simple, Depth-First

Legend: cu = current location; vi = boolean hash of visited locations; pa = hash giving a list neighboring cells to which there is a path from a given cell.

<lang txr>@(bind (width height) (15 15)) @(do

  (defvar *r* (make-random-state nil))
  (defvar vi)
  (defvar pa)

  (defun scramble (list)
    (let ((out ()))
      (each ((item list))
        (let ((r (random *r* (+ 1 (length out)))))
          (set [out r..r] (list item))))
      out))

  (defun neigh (loc)
    (tree-bind (x . y) loc
      (list (- x 1)..y (+ x 1)..y
            x..(- y 1) x..(+ y 1))))

  (defun make-maze-rec (cu)
    (set [vi cu] t)
    (each ((ne (scramble (neigh cu))))
      (cond ((not [vi ne])
             (push ne [pa cu])
             (push cu [pa ne])
             (make-maze-rec ne)))))

  (defun make-maze (w h)
    (let ((vi (hash :equal-based))
          (pa (hash :equal-based)))
      (each ((x (range -1 w)))
        (set [vi x..-1] t)
        (set [vi x..h] t))
      (each ((y (range* 0 h)))
        (set [vi -1..y] t)
        (set [vi w..y] t))
      (make-maze-rec 0..0)
      pa))

  (defun print-tops (pa w j)
    (each ((i (range* 0 w)))
      (if (memqual i..(- j 1) [pa i..j])
        (put-string "+    ")
        (put-string "+----")))
    (put-line "+"))

  (defun print-sides (pa w j)
    (let ((str ""))
      (each ((i (range* 0 w)))
        (if (memqual (- i 1)..j [pa i..j])
          (set str `@str     `)
          (set str `@str|    `)))
      (put-line `@str|\n@str|`)))

  (defun print-maze (pa w h)
    (each ((j (range* 0 h)))
      (print-tops pa w j)
      (print-sides pa w j))
    (print-tops pa w h)))

@;; @(bind m @(make-maze width height)) @(do (print-maze m width height))</lang>

Output:

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

Quality Breadth-First

The following is a complete, self-contained command line utility.

The algorithm is quite different from the previous. This version is not recursive. This algorithm divides the maze cells into visited cells, frontier cells and unvisited cells. As in the DFS version, border cells outside of the maze area are pre-initialized as visited, for convenience. The frontier set initially contains the upper left hand corner.

The algorithm's main loop iterates while there are frontier cells. As the generation progresses, unvisited cells adjacent to frontier cells added to the frontier set. Frontier cells that are only surrounded by other frontier cells or visited cells are removed from the frontier set and become visited cells. Eventually, all unvisited cells become frontier cells and then visited cells, at which point the frontier set becomes empty and the algorithm terminates.

At every step, the algorithm picks the first cell in the frontier list. In the code, the frontier cells are kept in a hash called fr and also in a queue q. The algorithm tries to extend the frontier around the frontier cell which is at the head of the queue q by randomly choosing an adjacent unvisited cell. (If there is no such cell, the node is not a frontier node any more and is popped from the queue and fr set). If an unvisited node is picked, then a two-way path is broken from the given frontier cell to that cell, and that cell is added to the frontier set. Important: the new frontier cell is added to the head of the queue, rather than the tail.

The algorithm is modified by a "straightness" parameter, which is used to initialize a counter. Every time a new frontier node is added to the front of the queue, the counter decrements. When it reaches zero, the frontier queue is scrambled, and the counter is reset. As long as the count is nonzero, the maze growth proceeds from the previously traversed node, because the new node is placed at the head of the queue. This behavior mimics the DFS algorithm, resulting in long corridors without a lot of branching.

At the user interface level, the straightness parameter is represented as a percentage. This percentage is converted to a number of cells based on the width and height of the maze. For instance if the straightness parameter is 15, and the maze size is 20x20, it means that 15% out of 400 cells, or 60 cells will be traversed before the queue is scrambled. Then another 60 will be traversed and the queue will be scrambled, and so forth.

<lang txr>@(do

  (defvar vi)  ;; visited hash
  (defvar pa)  ;; path connectivity hash
  (defvar sc)  ;; count, derived from straightness fator

  (defun scramble (list)
    (let ((out ()))
      (each ((item list))
        (let ((r (rand (+ 1 (length out)))))
          (set [out r..r] (list item))))
      out))

  (defun rnd-pick (list)
    (if list [list (rand (length list))]))

  (defmacro while (expr . body)
    ^(for () (,expr) () ,*body))

  (defun neigh (loc)
    (tree-bind (x . y) loc
      (list (- x 1)..y (+ x 1)..y
            x..(- y 1) x..(+ y 1))))

  (defun make-maze-impl (cu)
    (let ((fr (hash :equal-based))
          (q (list cu))
          (c sc))
      (set [fr cu] t)
      (while q
        (let* ((cu (first q))
               (ne (rnd-pick (remove-if (orf vi fr) (neigh cu)))))
          (cond (ne (set [fr ne] t)
                    (push ne [pa cu])
                    (push cu [pa ne])
                    (push ne q)
                    (cond ((<= (dec c) 0)
                           (set q (scramble q))
                           (set c sc))))
                (t (set [vi cu] t)
                   (del [fr cu])
                   (pop q)))))))

  (defun make-maze (w h sf)
    (let ((vi (hash :equal-based))
          (pa (hash :equal-based))
          (sc (max 1 (trunc (* sf w h) 100))))
      (each ((x (range -1 w)))
        (set [vi x..-1] t)
        (set [vi x..h] t))
      (each ((y (range* 0 h)))
        (set [vi -1..y] t)
        (set [vi w..y] t))
      (make-maze-impl 0..0)
      pa))

  (defun print-tops (pa w j)
    (each ((i (range* 0 w)))
      (if (memqual i..(- j 1) [pa i..j])
        (put-string "+    ")
        (put-string "+----")))
    (put-line "+"))

  (defun print-sides (pa w j)
    (let ((str ""))
      (each ((i (range* 0 w)))
        (if (memqual (- i 1)..j [pa i..j])
          (set str `@str     `)
          (set str `@str|    `)))
      (put-line `@str|\n@str|`)))

  (defun print-maze (pa w h)
    (each ((j (range* 0 h)))
      (print-tops pa w j)
      (print-sides pa w j))
    (print-tops pa w h))

  (defun usage ()
    (let ((invocation (ldiff *full-args* *args*)))
      (put-line "usage: ")
      (put-line `@invocation <width> <height> [<straightness>]`)
      (put-line "straightness-factor is a percentage, defaulting to 15")
      (exit 1)))

  (let ((args [mapcar int-str *args*])
        (*random-state* (make-random-state nil)))
    (if (memq nil args)
      (usage))
    (tree-case args
      ((w h s ju . nk) (usage))
      ((w h : (s 15)) (set w (max 1 w))
                      (set h (max 1 h))
                      (print-maze (make-maze w h s) w h))
      (else (usage)))))</lang>

Output:

Three mazes are generated, at the lowest, intermediate and highest "straightness factors".

It is immediately obvious that the style of each maze is quite different.

# 10x10 maze with zero percent "straightness factor"
$ txr maze-generation3.txr 10 10 0
+----+----+----+----+----+----+----+----+----+----+
|                   |    |                        |
|                   |    |                        |
+    +    +----+----+    +    +    +----+----+----+
|    |         |              |         |         |
|    |         |              |         |         |
+    +    +----+    +----+----+----+----+    +    +
|    |    |                   |              |    |
|    |    |                   |              |    |
+    +----+    +----+    +----+    +----+----+----+
|                   |                             |
|                   |                             |
+----+    +    +    +    +    +    +----+----+----+
|         |    |    |    |    |                   |
|         |    |    |    |    |                   |
+----+    +    +----+----+    +----+----+----+    +
|         |              |                   |    |
|         |              |                   |    |
+    +----+    +----+----+    +    +    +----+    +
|    |                   |    |    |         |    |
|    |                   |    |    |         |    |
+    +----+    +    +    +    +    +    +    +    +
|    |         |    |    |    |    |    |    |    |
|    |         |    |    |    |    |    |    |    |
+----+    +    +----+    +    +    +----+----+    +
|         |         |    |    |         |         |
|         |         |    |    |         |         |
+    +    +    +    +----+----+----+----+----+    +
|    |    |    |                        |         |
|    |    |    |                        |         |
+----+----+----+----+----+----+----+----+----+----+


# with 10% straightnes factor
$ txr maze-generation3.txr 10 10 10
+----+----+----+----+----+----+----+----+----+----+
|    |              |         |         |         |
|    |              |         |         |         |
+    +    +----+    +    +    +    +    +----+    +
|              |         |         |              |
|              |         |         |              |
+    +----+----+    +----+----+----+----+----+----+
|    |         |         |                        |
|    |         |         |                        |
+----+    +    +----+    +    +----+----+    +    +
|         |              |         |    |    |    |
|         |              |         |    |    |    |
+    +----+----+    +----+    +    +    +    +----+
|    |                   |    |         |    |    |
|    |                   |    |         |    |    |
+    +    +----+----+----+----+----+----+    +    +
|    |                   |                        |
|    |                   |                        |
+    +    +----+    +    +    +    +----+----+----+
|    |    |         |    |    |    |         |    |
|    |    |         |    |    |    |         |    |
+    +----+    +----+    +----+    +    +    +    +
|    |         |                   |    |         |
|    |         |                   |    |         |
+    +    +----+----+    +----+    +    +----+----+
|    |         |         |         |         |    |
|    |         |         |         |         |    |
+----+----+    +----+    +    +----+----+    +    +
|                   |    |                        |
|                   |    |                        |
+----+----+----+----+----+----+----+----+----+----+

# with 100 percent straight factor
$ txr maze-generation3.txr 10 10 100
+----+----+----+----+----+----+----+----+----+----+
|         |                             |         |
|         |                             |         |
+----+    +----+    +----+----+    +    +    +    +
|    |         |              |    |    |    |    |
|    |         |              |    |    |    |    |
+    +----+    +----+----+----+    +    +    +    +
|         |    |         |         |    |    |    |
|         |    |         |         |    |    |    |
+    +----+    +    +    +    +----+    +----+    +
|    |         |    |    |         |              |
|    |         |    |    |         |              |
+    +    +----+    +    +    +    +----+----+    +
|    |    |         |    |    |         |         |
|    |    |         |    |    |         |         |
+    +    +----+    +    +----+    +    +----+----+
|    |              |         |    |              |
|    |              |         |    |              |
+    +----+----+----+----+    +----+----+----+    +
|              |         |              |         |
|              |         |              |         |
+    +----+----+    +    +----+----+    +    +    +
|         |         |         |    |         |    |
|         |         |         |    |         |    |
+    +    +    +----+    +    +    +----+----+    +
|    |         |         |                   |    |
|    |         |         |                   |    |
+    +----+----+    +----+----+----+----+----+    +
|              |                                  |
|              |                                  |
+----+----+----+----+----+----+----+----+----+----+

XPL0

<lang XPL0>code Ran=1, CrLf=9, Text=12; \intrinsic routines def Cols=20, Rows=6; \dimensions of maze (cells) int Cell(Cols+1, Rows+1, 3); \cells (plus right and bottom borders) def LeftWall, Ceiling, Connected; \attributes of each cell (= 0, 1 and 2)

proc ConnectFrom(X, Y); \Connect cells starting from cell X,Y int X, Y; int Dir, Dir0; [Cell(X, Y, Connected):= true; \mark current cell as connected Dir:= Ran(4); \randomly choose a direction Dir0:= Dir; \save this initial direction repeat case Dir of \try to connect to cell at Dir

         0: if X+1<Cols & not Cell(X+1, Y, Connected) then     \go right
               [Cell(X+1, Y, LeftWall):= false; ConnectFrom(X+1, Y)];
         1: if Y+1<Rows & not Cell(X, Y+1, Connected) then     \go down
               [Cell(X, Y+1, Ceiling):= false;  ConnectFrom(X, Y+1)];
         2: if X-1>=0 & not Cell(X-1, Y, Connected) then       \go left
               [Cell(X, Y, LeftWall):= false;   ConnectFrom(X-1, Y)];
         3: if Y-1>=0 & not Cell(X, Y-1, Connected) then       \go up
               [Cell(X, Y, Ceiling):= false;    ConnectFrom(X, Y-1)]
       other   [];             \(never occurs)
       Dir:= Dir+1 & $03;      \next direction

until Dir = Dir0; ];

int X, Y; [for Y:= 0 to Rows do

   for X:= 0 to Cols do
       [Cell(X, Y, LeftWall):= true;           \start with all walls and
        Cell(X, Y, Ceiling):= true;            \ ceilings in place
        Cell(X, Y, Connected):= false;         \ and all cells disconnected
       ];

Cell(0, 0, LeftWall):= false; \make left and right doorways Cell(Cols, Rows-1, LeftWall):= false; ConnectFrom(Ran(Cols), Ran(Rows)); \randomly pick a starting cell for Y:= 0 to Rows do \display the maze

       [CrLf(0);
       for X:= 0 to Cols do
               Text(0, if X#Cols & Cell(X, Y, Ceiling)  then "+--" else "+  ");
       CrLf(0);
       for X:= 0 to Cols do
               Text(0, if Y#Rows & Cell(X, Y, LeftWall) then "|  " else "   ");
       ];

]</lang>

Output:

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

zkl

Generate a maze without marked entry or exit points.

Translation of: Python

<lang zkl> fcn make_maze(w = 16, h = 8){

  // make arrays with lists of lists (all mutable)
  vis:=(w.pump(List().write,0)+1)*h + w.pump(List().write,1);
  ver:=(w.pump(List().write,T(Void,"|   ")) + "|")*h + T;
  hor:=(w.pump(List().write,T(Void,"+---")) + "+")*(h + 1);

  fcn(x,y,vis,ver,hor){
     vis[y][x] = 1;

     d:=L(T(x - 1, y), T(x, y + 1), T(x + 1, y), T(x, y - 1)).shuffle();
     foreach xx,yy in (d){

if(vis[yy][xx]) continue; if(xx==x) hor[y.max(yy)][x]="+ "; if(yy==y) ver[y][x.max(xx)]=" "; self.fcn(xx,yy,vis,ver,hor);

     }
  }((0).random(w),(0).random(h),vis,ver,hor);
  foreach a,b in (hor.zip(ver)) { println(a.concat(),"\n",b.concat()) }
  return(ver,hor);

} make_maze();</lang>

Output:

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