Maze generation

Maze generation
You are encouraged to solve this task according to the task description, using any language you may know.

This page uses content from Wikipedia. The original article was at Maze generation algorithm. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

a maze

Task

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.

Related tasks

• 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;

   call_n(N, b_suffix, d, "+---");
   b_suffix(d, "+\n");

   call_n(N, b_suffix, d, "| * ");
   b_suffix(d, "|\n");

   call_n(N, b_extend, b, d);

   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 + (p = x_offsets[(r + i) & 3]);
       q = y_offsets[(r + i) & 3];
       q += y;

if (-1 < p && p < line_size && -1 < q && q < line_size * (N * 2 + 1)) { if (b[q + p] == '*') { walk_cell(b, N, line_size, p, q, x_offsets, y_offsets);

               b[(q + y) / 2 + (p + x) / 2] = ' ';
               if (p == x) {
                   b[(q + y) / 2 + p - 1] = ' ';
                   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;

   l_bill(x_offsets, 0, 4, 0, -4, 0);
   l_bill(y_offsets, 0, 0, line_size * 2, 0, 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_(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:

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

Alternative Version

http://rosettacode.org/wiki/Maze_solving#AutoHotkey

Generator and solver combined.

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:

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

Batch File

Works with: Windows NT

<lang dos>:amaze Rows Cols [wall char]

A stack-less, iterative, depth-first maze generator in native WinNT batch.

Rows and Cols must each be >1 and Rows*Cols cannot exceed 2096.

Default wall character is #, [wall char] is used if provided.

@ECHO OFF SETLOCAL EnableDelayedExpansion

check for valid input, else GOTO :help

IF /I "%~2" EQU "" GOTO :amaze_help FOR /F "tokens=* delims=0123456789" %%A IN ("%~1%~2") DO IF "%%~A" NEQ "" GOTO :amaze_help SET /A "rows=%~1, cols=%~2, mTmp=rows*cols" IF !rows! LSS 2 GOTO :amaze_help IF !cols! LSS 2 GOTO :amaze_help IF !mTmp! GTR 2096 GOTO :amaze_help

set map characters and use 1st character of %3 for wall, if defined

SET "wall=#" SET "hall= " SET "crumb=." IF "%~3" NEQ "" SET "wall=%~3" SET "wall=!wall:~0,1!"

assign width, height, cursor position, loop count, and offsets for NSEW

SET /A "cnt=0, wide=cols*2-1, high=rows*2-1, size=wide*high, N=wide*-2, S=wide*2, E=2, W=-2"

different random entrance points

...on top

SET /A "start=(!RANDOM! %% cols)*2"

...on bottom

SET /A "start=size-(!RANDOM! %% cols)*2-1"

...on top or bottom

SET /A ch=cols*2, ch=!RANDOM! %% ch

IF !ch! GEQ !cols! ( SET /A "start=size-(ch-cols)*2-1"

) ELSE SET /A start=ch*2

random entrance inside maze

SET /A "start=(!RANDOM! %% cols*2)+(!RANDOM! %% rows*2)*wide" SET /A "curPos=start, cTmp=curPos+1, loops=cols*rows*2+1"

fill the maze with 8186 wall characters, clip to size, and open 1st cell

SET "mz=!wall!" FOR /L %%A IN (1,1,6) DO SET mz=!mz!!mz!!mz!!mz! SET bdr=!mz:~-%wide%! SET mz=!mz:~3!!mz:~3! SET mz=!mz:~-%size%! SET mz=!mz:~0,%curPos%!!hall!!mz:~%cTmp%!

iterate #cells*2+1 steps of random depth-first search

FOR /L %%@ IN (1,1,%loops%) DO ( SET "rand=" & SET "crmPos=" REM set values for NSEW cell and wall positions SET /A "rCnt=rTmp=0, cTmp=curPos+1, np=curPos+N, sp=curPos+S, ep=curPos+E, wp=curPos+W, wChk=curPos/wide*wide, eChk=wChk+wide, nw=curPos-wide, sw=curPos+wide, ew=curPos+1, ww=curPos-1" REM examine adjacent cells, build direction list, and find last crumb position FOR /F "tokens=1-8" %%A IN ("!np! !sp! !ep! !wp! !nw! !sw! !ew! !ww!") DO ( IF !np! GEQ 0 IF "!mz:~%%A,1!" EQU "!wall!" ( SET /A rCnt+=1 & SET "rand=n !rand!" ) ELSE IF "!mz:~%%E,1!" EQU "!crumb!" SET /A crmPos=np, cw=nw IF !sp! LEQ !size! IF "!mz:~%%B,1!" EQU "!wall!" ( SET /A rCnt+=1 & SET "rand=s !rand!" ) ELSE IF "!mz:~%%F,1!" EQU "!crumb!" SET /A crmPos=sp, cw=sw IF !ep! LEQ !eChk! IF "!mz:~%%C,1!" EQU "!wall!" ( SET /A rCnt+=1 & SET "rand=e !rand!" ) ELSE IF "!mz:~%%G,1!" EQU "!crumb!" SET /A crmPos=ep, cw=ew IF !wp! GEQ !wChk! IF "!mz:~%%D,1!" EQU "!wall!" ( SET /A rCnt+=1 & SET "rand=w !rand!" ) ELSE IF "!mz:~%%H,1!" EQU "!crumb!" SET /A crmPos=wp, cw=ww ) IF DEFINED rand ( REM adjacent unvisited cell is available SET /A rCnt=!RANDOM! %% rCnt FOR %%A IN (!rand!) DO ( REM pick random cell + wall IF !rTmp! EQU !rCnt! SET /A "curPos=!%%Ap!, cTmp=curPos+1, mw=!%%Aw!, mTmp=mw+1" SET /A rTmp+=1 ) REM write the 2 new characters into the maze FOR /F "tokens=1-4" %%A IN ("!mw! !mTmp! !curPos! !cTmp!") DO ( SET "mz=!mz:~0,%%A!!crumb!!mz:~%%B!" SET "mz=!mz:~0,%%C!!hall!!mz:~%%D!" ) ) ELSE IF DEFINED crmPos ( REM follow the crumbs backward SET /A mTmp=cw+1 REM erase the crumb character and set new cursor position FOR /F "tokens=1-2" %%A IN ("!cw! !mTmp!") DO SET "mz=!mz:~0,%%A!!hall!!mz:~%%B!" SET "curPos=!crmPos!" ) ) SET /A open=cols/2*2, mTmp=open+1 ECHO !wall!!bdr:~0,%open%!!hall!!bdr:~%mTmp%!!wall! FOR /L %%A IN (0,!wide!,!size!) DO IF %%A LSS !size! ECHO !wall!!mz:~%%A,%wide%!!wall! ECHO !wall!!bdr:~0,%open%!!hall!!bdr:~%mTmp%!!wall! ENDLOCAL EXIT /B 0

amaze_help

ECHO Usage:  %~0 Rows Cols [wall char] ECHO Rows^>1, Cols^>1, and Rows*Cols^<=2096 ECHO Example: %~0 11 39 @ ENDLOCAL EXIT /B 0 </lang>

Example output:

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@                   @     @   @         @     @     @       @   @         @   @
@ @@@@@@@@@@@ @@@@@@@ @ @ @ @ @ @@@@@ @ @ @ @ @@@ @ @@@ @@@ @ @@@ @ @@@@@ @@@ @
@ @       @   @       @ @ @ @   @     @ @ @ @ @   @     @     @   @ @         @
@ @ @@@@@@@ @@@ @@@@@@@ @ @ @@@@@ @@@@@ @@@ @ @ @@@@@@@@@@@@@@@ @@@ @@@@@@@@@@@
@ @ @     @ @   @   @   @ @ @   @   @       @   @   @         @ @ @     @     @
@ @ @ @@@ @ @ @@@@@ @ @ @@@ @ @ @@@ @@@@@@@ @@@@@ @ @ @@@@@@@ @ @ @@@@@ @ @@@ @
@   @   @ @ @     @ @ @ @   @ @   @   @   @ @     @ @ @ @     @   @   @     @ @
@@@ @@@ @ @ @@@@@ @ @ @ @ @@@ @ @ @@@ @ @ @@@ @@@@@ @ @ @ @@@ @@@ @ @@@@@@@@@ @
@     @ @ @     @   @ @ @   @ @ @   @   @       @   @   @ @   @   @       @   @
@ @@@@@ @ @@@ @ @@@ @ @@@@@ @ @ @@@@@@@@@@@@@@@@@ @@@@@ @ @@@@@ @@@ @@@@@ @ @@@
@   @   @ @   @   @ @ @     @ @ @   @       @   @   @   @ @     @ @ @   @ @   @
@@@@@ @@@ @ @ @@@@@ @ @ @@@@@ @ @ @ @ @@@@@ @ @ @@@ @ @@@ @ @@@@@ @ @ @ @ @@@@@
@     @     @ @     @ @     @ @   @     @   @ @     @ @ @   @       @ @ @   @ @
@ @@@@@@@@@@@ @ @@@@@ @@@@@ @ @@@@@@@ @@@ @ @ @@@@@ @ @ @@@@@@@@@ @@@ @@@ @ @ @
@ @         @ @     @     @ @   @   @ @   @ @     @ @ @         @ @   @   @ @ @
@ @ @@@@@@@ @@@@@@@ @@@ @@@ @@@ @ @ @@@ @@@ @@@@@ @@@ @@@@@@@ @ @ @ @ @ @@@ @ @
@ @     @ @       @ @   @   @   @ @ @   @   @ @   @   @     @ @ @   @ @ @ @ @ @
@ @@@@@ @ @@@ @@@@@ @ @ @ @@@@@@@ @ @ @@@ @@@ @ @@@ @@@ @@@ @ @ @@@@@@@ @ @ @ @
@       @   @       @ @ @   @   @ @   @ @ @   @ @   @   @   @ @ @       @ @   @
@ @@@@@@@ @ @@@@@@@@@ @@@@@ @ @ @ @@@@@ @ @ @ @ @ @@@ @@@ @@@ @ @ @@@@@@@ @@@ @
@         @         @         @   @         @ @       @       @   @           @
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

BASIC

This implementation was written using QB64. It should also be compatible with Qbasic, as it uses no QB64-exclusive features. <lang BASIC>OPTION BASE 0 RANDOMIZE TIMER

REM must be even width% = 40 height% = 20

REM make array and fill DIM maze$(width%, height%) FOR x% = 0 TO width%

   FOR y% = 0 TO height%
       maze$(x%, y%) = "#"
   NEXT y%

NEXT x%

REM initial start location currentx% = INT(RND * (width% - 1)) currenty% = INT(RND * (height% - 1)) REM value must be odd IF currentx% MOD 2 = 0 THEN currentx% = currentx% + 1 IF currenty% MOD 2 = 0 THEN currenty% = currenty% + 1 maze$(currentx%, currenty%) = " "

REM generate maze done% = 0 DO WHILE done% = 0

   FOR i% = 0 TO 99
       oldx% = currentx%
       oldy% = currenty%

       REM move in random direction
       SELECT CASE INT(RND * 4)
           CASE 0
               IF currentx% + 2 < width% THEN currentx% = currentx% + 2
           CASE 1
               IF currenty% + 2 < height% THEN currenty% = currenty% + 2
           CASE 2
               IF currentx% - 2 > 0 THEN currentx% = currentx% - 2
           CASE 3
               IF currenty% - 2 > 0 THEN currenty% = currenty% - 2
       END SELECT

       REM if cell is unvisited then connect it
       IF maze$(currentx%, currenty%) = "#" THEN
           maze$(currentx%, currenty%) = " "
           maze$(INT((currentx% + oldx%) / 2), ((currenty% + oldy%) / 2)) = " "
       END IF
   NEXT i%

   REM check if all cells are visited
   done% = 1
   FOR x% = 1 TO width% - 1 STEP 2
       FOR y% = 1 TO height% - 1 STEP 2
           IF maze$(x%, y%) = "#" THEN done% = 0
       NEXT y%
   NEXT x%

LOOP

REM draw maze FOR y% = 0 TO height%

   FOR x% = 0 TO width%
       PRINT maze$(x%, y%);
   NEXT x%
   PRINT

NEXT y%

REM wait DO: LOOP WHILE INKEY$ = ""</lang>

Output:

This used a slightly modified version that outputs to a text file. (You can't copy from a QB64 window.)

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

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:

Befunge

Dimensions are specified by the first two values pushed onto the stack - currently 20 (45*) by 16 (28*). Note, however, that the upper limit in a standard Befunge-93 implementation will be around 38 by 40 (1520 cells) due to the constrained page size.

Also note that this requires an interpreter with working read-write memory support, which is suprisingly rare in online implementations. Padding the code page with extra blank lines or spaces can sometimes help. Using smaller dimensions might also be preferable, especially on slower implementations.

<lang befunge>45*28*10p00p020p030p006p0>20g30g00g*+::"P"%\"P"/6+gv>$\1v@v1::\+g02+*g00+g03-\< 0_ 1!%4+1\-\0!::\-\2%2:p<pv0<< v0p+6/"P"\%"P":\+4%4<^<v-<$>+2%\1-*20g+\1+4%::v^

1. | +2%\1-*30g+\1\40g1-:v0+v2?1#<v>+:00g%!55+*>:#0>#,_^>:!|>\#%"P"v#:*+*g00g0<>1

02!:++`\0\`-1g01:\+`\< !46v3<^$$<^1,g2+1%2/2,g1+1<v%g00:\<*g01,<>:30p\:20p:v^3g 0#$g#<1#<-#<`#<\#<0#<^#_^/>#1+#4<>"P"%\"P"/6+g:2%^!>,1-:#v_$55+^|$$ "JH" $$>#<0

"P"%\"P"/6+g40p\40g+\:#^"P"%#\<^ ::$_,#!0#:<*"|"<^," _"<:g000 <> /6+g4/2%+#^_

</lang>

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:

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

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;
       }

       public static bool HasFlag(this CellState cs,CellState flag)
       {
           return ((int)cs & (int)flag) != 0;
       }
   }

   [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:

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

Clojure

<lang clojure>(ns maze.core

 (:require [clojure.set :refer [intersection
                                select]]
           [clojure.string :as str]))

Misc functions

(defn neighborhood

 ([] (neighborhood [0 0]))
 ([coord] (neighborhood coord 1))
 ([[y x] r]
  (let [y-- (- y r) y++ (+ y r)
        x-- (- x r) x++ (+ x r)]
    #{[y++ x] [y-- x] [y x--] [y x++]})))

(defn cell-empty? [maze coords]

 (= :empty (get-in maze coords)))

(defn wall? [maze coords]

 (= :wall (get-in maze coords)))

(defn filter-maze

 ([pred maze coords]
  (select (partial pred maze) (set coords)))
 ([pred maze]
  (filter-maze
    pred
    maze
    (for [y (range (count maze))
          x (range (count (nth maze y)))]
      [y x]))))

(defn create-empty-maze [width height]

 (let [width (inc (* 2 width))
       height (inc (* 2 height))]
   (vec (take height
              (interleave
                (repeat (vec (take width (repeat :wall))))
                (repeat (vec (take width (cycle [:wall :empty])))))))))

(defn next-step [possible-steps]

 (rand-nth (vec possible-steps)))

Algo

(defn create-random-maze [width height]

 (loop [maze (create-empty-maze width height)
        stack []
        nonvisited (filter-maze cell-empty? maze)
        visited #{}
        coords (next-step nonvisited)]
   (if (empty? nonvisited)
     maze
     (let [nonvisited-neighbors (intersection (neighborhood coords 2) nonvisited)]
       (cond
         (seq nonvisited-neighbors)
         (let [next-coords (next-step nonvisited-neighbors)
               wall-coords (map #(+ %1 (/ (- %2 %1) 2)) coords next-coords)]
           (recur (assoc-in maze wall-coords :empty)
                  (conj stack coords)
                  (disj nonvisited next-coords)
                  (conj visited next-coords)
                  next-coords))

         (seq stack)
         (recur maze (pop stack) nonvisited visited (last stack)))))))

Conversion to string

(def cell-code->str

 ["  " "  " "  " "  " "· " "╵ " "╴ " "┘ "
  "  " "  " "  " "  " "╶─" "└─" "──" "┴─"
  "  " "  " "  " "  " "╷ " "│ " "┐ " "┤ "
  "  " "  " "  " "  " "┌─" "├─" "┬─" "┼─"])

(defn cell-code [maze coord]

 (transduce
   (comp
     (map (partial wall? maze))
     (keep-indexed (fn [idx el] (when el idx)))
     (map (partial bit-shift-left 1)))
   (completing bit-or)
   0
   (sort (cons coord (neighborhood coord)))))

(defn cell->str [maze coord]

 (get cell-code->str (cell-code maze coord)))

(defn maze->str [maze]

 (->> (for [y (range (count maze))]
        (for [x (range (count (nth maze y)))]
          (cell->str maze [y x])))
      (map str/join)
      (str/join \newline)))

Task

(println (maze->str (create-random-maze 10 10)))</lang>

Output:

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

Commodore BASIC

Written in Commodore BASIC V2 and tested on Commodore 64 and Commodore 128 hardware. (It will also run on the unexpanded Commodore VIC-20 if you reduce the maze size to 8x8.) Due to stack size limitations in the operating systems, this solution eschews recursive subroutine calls. Recursion is accomplished by conditional branching within the maze build routine and the use of an array-based stack for data elements.

<lang BASIC>100 MS=10:REM MAZE SIZE 110 DIM S(MS+1,MS+1):REM SOUTH WALLS 120 DIM W(MS+1,MS+1):REM WEST WALLS 130 DIM V(MS+1,MS+1):REM VISITED CELLS 140 PRINT "INITIALIZING..." 150 GOSUB 260:REM INITIALIZE MAZE 160 PRINT "BUILDING..." 170 DIM PC(MS*MS+1):DIM PR(MS*MS+1):REM STACK 180 REM PICK RANDOM STARTING CELL 190 X = RND(-TI) 200 C=(INT(RND(1)*MS)+1) 210 R=(INT(RND(1)*MS)+1) 220 GOSUB 400:REM BUILD MAZE 230 GOSUB 540:REM DRAW MAZE 240 END 250 REM -----INITIALIZE MAZE----- 260 REM SET WALLS ON AND VISITED CELLS OFF 270 T=MS+1 280 FOR C=0 TO T:FOR R=0 TO T: 290 S(C,R)=1:W(C,R)=1:V(C,R)=0 300 NEXT R:NEXT C 310 REM SET BORDER CELLS TO VISITED 320 FOR C=0 TO T 330 V(C,0)=1:V(C,T)=1 340 NEXT C 350 FOR R=0 TO T 360 V(0,R)=1:V(T,R)=1 370 NEXT R 380 RETURN 390 REM -----BUILD MAZE----- 400 U=U+1:PC(U)=C:PR(U)=R:REM PUSH 410 V(C,R)=1 420 IF V(C,R+1)=1 AND V(C+1,R)=1 AND V(C,R-1)=1 AND V(C-1,R)=1 THEN GOTO 500 430 Z=INT(RND(1)*4) 440 IF Z=0 AND V(C,R+1)=0 THEN S(C,R)=0:R=R+1:GOTO 400 450 IF Z=1 AND V(C+1,R)=0 THEN W(C+1,R)=0:C=C+1:GOTO 400 460 IF Z=2 AND V(C,R-1)=0 THEN S(C,R-1)=0:R=R-1:GOTO 400 470 IF Z=3 AND V(C-1,R)=0 THEN W(C,R)=0:C=C-1:GOTO 400 480 GOTO 430 500 C=PC(U):R=PR(U):U=U-1:REM POP 510 IF U > 0 THEN GOTO 420 520 RETURN 530 REM -----DRAW MAZE----- 540 REM OPEN 4,4:CMD 4:REM SEND OUTPUT TO PRINTER 550 PRINT "+--+--+--+--+--+--+--+--+--+--+" 560 FOR R = 1 TO MS 570 FOR C = 1 TO MS+1 580 IF W(C,R)=0 THEN PRINT " "; 590 IF W(C,R)=1 THEN PRINT ": "; 600 NEXT C 610 PRINT 620 FOR C = 1 TO MS 630 IF S(C,R)=0 THEN PRINT "+ "; 640 IF S(C,R)=1 THEN PRINT "+--"; 650 NEXT C 660 PRINT "+" 670 NEXT R 680 REM PRINT#4:CLOSE 4:REM CLOSE PRINTER DEVICE 690 RETURN</lang>

Output example (for 10x10 maze):

+--+--+--+--+--+--+--+--+--+--+
:     :        :              :  
+  +  +  +  +--+  +--+--+--+  +
:  :  :  :        :     :     :  
+  +  +  +--+  +--+  +  +  +--+
:  :     :  :  :     :  :     :  
+  +--+--+  +  +  +--+  +--+  +
:     :     :  :  :  :        :  
+--+  +  +--+--+  +  +--+--+  +
:  :  :  :        :  :        :  
+  +  +  +  +--+--+  +  +--+--+
:     :  :        :  :  :     :  
+  +--+  +--+--+  +  +  +  +  +
:     :  :        :     :  :  :  
+  +--+  +  +--+--+  +--+--+  +
:  :     :  :     :        :  :  
+  +  +--+  +  +--+--+--+  +  +
:  :     :  :  :        :  :  :  
+  +--+  +  +  +  +  +--+  +  +
:     :     :     :           :  
+--+--+--+--+--+--+--+--+--+--+

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):

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

Elixir

Translation of: D

<lang elixir>defmodule Maze do

 def generate(w, h) do
   maze = (for i <- 1..w, j <- 1..h, into: Map.new, do: {{:vis, i, j}, true})
          |> walk(:rand.uniform(w), :rand.uniform(h))
   print(maze, w, h)
   maze
 end
 
 defp walk(map, x, y) do
   Enum.shuffle( [[x-1,y], [x,y+1], [x+1,y], [x,y-1]] )
   |> Enum.reduce(Map.put(map, {:vis, x, y}, false), fn [i,j],acc ->
     if acc[{:vis, i, j}] do
       {k, v} = if i == x, do: {{:hor, x, max(y, j)}, "+   "},
                         else: {{:ver, max(x, i), y}, "    "}
       walk(Map.put(acc, k, v), i, j)
     else
       acc
     end
   end)
 end
 
 defp print(map, w, h) do
   Enum.each(1..h, fn j ->
     IO.puts Enum.map_join(1..w, fn i -> Map.get(map, {:hor, i, j}, "+---") end) <> "+"
     IO.puts Enum.map_join(1..w, fn i -> Map.get(map, {:ver, i, j}, "|   ") end) <> "|"
   end)
   IO.puts String.duplicate("+---", w) <> "+"
 end

end

Maze.generate(20, 10)</lang>

Output:

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

Elm

<lang elm>import Maybe as M import Result as R import Matrix import Mouse import Random exposing (Seed) import Matrix.Random import Time exposing (Time, every, second) import Set exposing (Set, fromList) import List exposing (..) import String exposing (join) import Html exposing (Html, br, input, h1, h2, text, div, button) import Html.Events as HE import Html.Attributes as HA import Html.App exposing (program) import Json.Decode as JD import Svg import Svg.Attributes exposing (version, viewBox, cx, cy, r, x, y, x1, y1, x2, y2, fill,points, style, width, height, preserveAspectRatio)

minSide = 10 maxSide = 40 w = 700 h = 700 dt = 0.001

type alias Direction = Int down = 0 right = 1

type alias Door = (Matrix.Location, Direction)

type State = Initial | Generating | Generated | Solved

type alias Model =

 { rows : Int
 , cols : Int
 , animate : Bool
 , boxes : Matrix.Matrix Bool
 , doors : Set Door
 , current : List Matrix.Location
 , state : State
 , seedStarter : Int
 , seed : Seed
 }

initdoors : Int -> Int -> Set Door initdoors rows cols =

 let 
   pairs la lb = List.concatMap (\at -> List.map ((,) at) lb) la
   downs = pairs (pairs [0..rows-2] [0..cols-1]) [down] 
   rights = pairs (pairs [0..rows-1] [0..cols-2]) [right] 
 in downs ++ rights |> fromList

initModel : Int -> Int -> Bool -> State -> Int -> Model initModel rows cols animate state starter =

 let rowGenerator = Random.int 0 (rows-1)
     colGenerator = Random.int 0 (cols-1)
     locationGenerator = Random.pair rowGenerator colGenerator
     (c, s)= Random.step locationGenerator (Random.initialSeed starter)
 in { rows = rows
    , cols = cols 
    , animate = animate
    , boxes = Matrix.matrix rows cols (\location -> state == Generating && location == c)
    , doors = initdoors rows cols
    , current = if state == Generating then [c] else []
    , state = state
    , seedStarter = starter -- updated every Tick until maze generated.
    , seed = s
    }

view model =

 let
   borderLineStyle = style "stroke:green;stroke-width:0.3"
   wallLineStyle = style "stroke:green;stroke-width:0.1" 

   x1Min = x1 <| toString 0
   y1Min = y1 <| toString 0
   x1Max = x1 <| toString model.cols
   y1Max = y1 <| toString model.rows
   x2Min = x2 <| toString 0
   y2Min = y2 <| toString 0
   x2Max = x2 <| toString model.cols
   y2Max = y2 <| toString model.rows

   borders = [ Svg.line [ x1Min, y1Min, x2Max, y2Min, borderLineStyle ] []
             , Svg.line [ x1Max, y1Min, x2Max, y2Max, borderLineStyle ] []
             , Svg.line [ x1Max, y1Max, x2Min, y2Max, borderLineStyle ] []
             , Svg.line [ x1Min, y1Max, x2Min, y2Min, borderLineStyle ] []
             ]

   doorToLine door = 
     let (deltaX1, deltaY1) = if (snd door == right) then (1,0) else (0,1)
         (row, column) = fst door
     in Svg.line [ x1 <| toString (column + deltaX1)
                 , y1 <| toString (row    + deltaY1)
                 , x2 <| toString (column + 1)
                 , y2 <| toString (row    + 1)
                 , wallLineStyle ] []

   doors = (List.map doorToLine <| Set.toList model.doors )

   circleInBox (row,col) color = 
     Svg.circle [ r "0.25"
     , fill (color)
     , cx (toString (toFloat col + 0.5))
     , cy (toString (toFloat row + 0.5))
     ] [] 

   showUnvisited location box =
      if box then [] else [ circleInBox location "yellow" ]

   unvisited = model.boxes 
                 |> Matrix.mapWithLocation showUnvisited 
                 |> Matrix.flatten 
                 |> concat

   current = 
     case head model.current of
         Nothing -> []
         Just c -> [circleInBox c "black"]

   maze = 
     if model.animate || model.state /= Generating
     then [ Svg.g [] <| doors ++ borders ++ unvisited ++ current ] 
     else [ Svg.g [] <| borders ]
 in
   div 
     []
     [ h2 [centerTitle] [text "Maze Generator"]
     , div 
         [floatLeft] 
         (  slider "rows" minSide maxSide model.rows SetRows
         ++ [ br [] [] ] 

         ++ slider "cols" minSide maxSide model.cols SetCols
         ++ [ br [] [] ]

         ++ checkbox "Animate" model.animate SetAnimate 
         ++ [ br [] [] ]

         ++ [ button 
                [ HE.onClick Generate ]
                [ text "Generate"] 
            ] )
     , div 
         [floatLeft] 
         [ Svg.svg 
             [ version "1.1"
             , width (toString w)
             , height (toString h)
             , viewBox (join " " 
                          [ 0          |> toString
                          , 0          |> toString
                          , model.cols |> toString
                          , model.rows |> toString ])
             ] 
             maze
         ]
     ] 

checkbox label checked msg =

 [ input
     [ HA.type' "checkbox"
     , HA.checked checked
     , HE.on "change" (JD.map msg HE.targetChecked)
     ]
     []
   , text label
 ]

slider name min max current msg =

 [ input
   [ HA.value (if current >= min then current |> toString else "")
   , HE.on "input" (JD.map msg HE.targetValue )
   , HA.type' "range"
   , HA.min <| toString min
   , HA.max <| toString max
   ]
   []
 , text <| name ++ "=" ++ (current |> toString)
 ]

floatLeft = HA.style [ ("float", "left") ] centerTitle = HA.style [ ( "text-align", "center") ]

unvisitedNeighbors : Model -> Matrix.Location -> List Matrix.Location unvisitedNeighbors model (row,col) =

 [(row, col-1), (row-1, col), (row, col+1), (row+1, col)]
   |> List.filter (\l -> fst l >= 0 && snd l >= 0 && fst l < model.rows && snd l < model.cols)
   |> List.filter (\l -> (Matrix.get l model.boxes) |> M.withDefault False |> not)

updateModel' : Model -> Int -> Model updateModel' model t =

 case head model.current of
   Nothing -> {model | state = Generated, seedStarter = t }
   Just prev ->
     let neighbors = unvisitedNeighbors model prev
     in if (length neighbors) > 0 then
          let (neighborIndex, seed) = Random.step (Random.int 0 (length neighbors-1)) model.seed
              next = head (drop neighborIndex neighbors) |> M.withDefault (0,0) 
              boxes = Matrix.set next True model.boxes 
              dir = if fst prev == fst next then right else down
              doorCell = if (  (dir == down)   && (fst prev < fst next))  
                            || (dir == right ) && (snd prev < snd next) then prev else next
              doors = Set.remove (doorCell, dir) model.doors 
          in {model | boxes=boxes, doors=doors, current=next :: model.current, seed=seed, seedStarter = t}
        else
          let tailCurrent = tail model.current |> M.withDefault [] 
          in updateModel' {model | current = tailCurrent} t

updateModel : Msg -> Model -> Model updateModel msg model =

 let stringToCellCount s =
   let v' = String.toInt s |> R.withDefault minSide
   in if v' < minSide then minSide else v'
 in case msg of 
      Tick tf -> 
        let t = truncate tf
        in 
          if (model.state == Generating) then updateModel' model t
          else { model | seedStarter = t } 

      Generate -> 
        initModel model.rows model.cols model.animate Generating model.seedStarter

      SetRows countString -> 
        initModel (stringToCellCount countString) model.cols model.animate Initial model.seedStarter

      SetCols countString -> 
        initModel model.rows (stringToCellCount countString) model.animate Initial model.seedStarter

      SetAnimate b -> 
        { model | animate = b } 

      NoOp -> model 

type Msg = NoOp | Tick Time | Generate | SetRows String | SetCols String | SetAnimate Bool

subscriptions model = every (dt * second) Tick

main =

 let 
   update msg model = (updateModel msg model, Cmd.none)
   init = (initModel 21 36 False Initial 0, Cmd.none)
 in program 
      { init = init
      , view = view
      , update = update
      , subscriptions = subscriptions
      }</lang>

Link to live demo: http://dc25.github.io/mazeGenerationElm/

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.

Using multiple processes

<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}
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|                   |       |           |   |                   |
+---+   +---+---+   +   +   +   +---+   +   +   +   +---+---+   +
|       |       |       |   |       |   |       |           |   |
+   +---+   +   +---+   +---+---+   +   +---+---+---+---+   +   +
|   |       |       |   |           |           |           |   |
+   +---+   +---+---+   +   +---+---+---+---+   +   +---+---+   +
|       |   |           |   |           |       |   |   |       |
+   +   +   +   +---+---+   +   +---+---+   +---+   +   +   +---+
|   |   |       |           |           |   |       |       |   |
+---+   +---+---+   +---+---+---+---+   +   +   +---+   +---+   +
|       |       |           |       |   |   |   |       |       |
+   +   +   +   +---+---+   +   +---+   +   +   +---+   +   +   +
|   |   |   |           |   |       |       |       |       |   |
+   +---+   +   +---+---+   +---+   +---+---+---+   +---+---+   +
|           |                                       |           |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Using 2 digraphs

Uses 2 digraph "objects": a) the 'matrix', a fully connected digraph of MxN vertices and b) the 'maze', an unconnected digraph, also MxN, that is populated while walking.

Employs a faux Visitor pattern to populate the maze while traversing the matrix in depth-first order.

Vertices: 0 .. MxN - 1

Rows: 0 .. M - 1

Cols: 0 .. N - 1

Usage: start with generate_default/0. Use generate_MxN() to test other maze sizes. <lang Erlang> -module(maze). -record(maze, {g, m, n}). -export([generate_default/0, generate_MxN/2]).

make_maze(M, N) ->

   Maze = #maze{g = digraph:new(), m = M, n = N},
   lists:foreach(fun(X) -> digraph:add_vertex(Maze#maze.g, X) end, lists:seq(0, M * N - 1)),
   Maze.

row_at(V, Maze) -> trunc(V / Maze#maze.n). col_at(V, Maze) -> V - row_at(V, Maze) * Maze#maze.n. vertex_at(Row, Col, Maze) -> Cell_Exists = cell_exists(Row, Col, Maze), if Cell_Exists -> Row * Maze#maze.n + Col; true -> -1 end. cell_exists(Row, Col, Maze) -> (Row >= 0) and (Row < Maze#maze.m) and (Col >= 0) and (Col < Maze#maze.n).

adjacent_cells(V, Maze) -> % ordered: left, up, right, down

   adjacent_cell(cell_left, V, Maze)++adjacent_cell(cell_up, V, Maze)++adjacent_cell(cell_right, V, Maze)++adjacent_cell(cell_down, V, Maze).

adjacent_cell(cell_left, V, Maze) -> case (col_at(V, Maze) == 0) of true -> []; _Else -> [V - 1] end; adjacent_cell(cell_up, V, Maze) -> case (row_at(V, Maze) == 0) of true -> []; _Else -> [V - Maze#maze.n] end; adjacent_cell(cell_right, V, Maze) -> case (col_at(V, Maze) == Maze#maze.n - 1) of true -> []; _Else -> [V + 1] end; adjacent_cell(cell_down, V, Maze) -> case (row_at(V, Maze) == Maze#maze.m - 1) of true -> []; _Else -> [V + Maze#maze.n] end.

connect_all(V, Maze) ->

   lists:foreach(fun(X) -> digraph:add_edge(Maze#maze.g, V, X) end, adjacent_cells(V, Maze)).

make_maze(M, N, all_connected) ->

   Maze = make_maze(M, N),
   lists:foreach(fun(X) -> connect_all(X, Maze) end, lists:seq(0, M * N - 1)),
   Maze.

maze_parts(Maze) ->

   SPR = Maze#maze.n + 1,      % slots per row is #columns + 1
   NPR = (Maze#maze.m * 2) + 1,    % # part rows is #(rows * 2) + 1
   [make_part(Maze, trunc(Index/SPR), Index - trunc(Index/SPR) * SPR) || Index <- lists:seq(0, (SPR * NPR) - 1)].

draw_part(Part) ->

   case Part of
       {pwall, pclosed} -> io:format("+---");
       {pwall, popen} -> io:format("+   ");
       {pwall, pend} -> io:format("+~n");
       {phall, pclosed} -> io:format("|   ");
       {phall, popen} -> io:format("    ");
       {phall, pend} -> io:format("|~n")
   end.

has_neighbour(Maze, Row, Col, Direction) ->

   V = vertex_at(Row, Col, Maze),
   if
       V >= 0 ->
           Adjacent = adjacent_cell(Direction, V, Maze),
           if 
               length(Adjacent) > 0 ->
                   Neighbours = digraph:out_neighbours(Maze#maze.g, lists:nth(1, Adjacent)),
                   lists:member(V, Neighbours);
               true -> false
           end;
       true -> false
   end.

make_part(Maze, DoubledRow, Col) ->

   if
       trunc(DoubledRow/2) * 2 == DoubledRow -> % --- (even row) making a wall above the cell
           make_part(Maze, trunc(DoubledRow/2), Col, cell_up, pwall);
       true -> % ---otherwise (odd row) making a hall through the cell
           make_part(Maze, trunc(DoubledRow/2), Col, cell_left, phall)
   end.

make_part(Maze, _, Col, _, Part_Type) when Col == Maze#maze.n -> {Part_Type, pend}; make_part(Maze, Row, Col, Direction, Part_Type) ->

   Has_Neighbour = has_neighbour(Maze, Row, Col, Direction),
   if
       Has_Neighbour -> {Part_Type, popen};
       true -> {Part_Type, pclosed}
   end.

shuffle([], Acc) -> Acc; shuffle(List, Acc) ->

   Elem = lists:nth(random:uniform(length(List)), List),
   shuffle(lists:delete(Elem, List), Acc++[Elem]).

processDepthFirst(Maze) ->

   if
       Maze#maze.m * Maze#maze.n == 0 -> [{pwall, pend}];
       true ->
           Visited = array:new([{size, Maze#maze.m * Maze#maze.n},{fixed,true},{default,false}]),
           {_, Path} = processDepthFirst(Maze, -1, random:uniform(Maze#maze.m * Maze#maze.n) - 1, {Visited, []}),
           Path
   end.

processDepthFirst(Maze, Vfrom, V, VandP) ->

   {Visited, Path} = VandP,
   Was_Visited = array:get(V, Visited),
   if
       not Was_Visited ->
           Walker = fun(X, Acc) -> processDepthFirst(Maze, V, X, Acc) end,
           Random_Neighbours = shuffle(digraph:out_neighbours(Maze#maze.g, V), []),
           lists:foldl(Walker, {array:set(V, true, Visited), Path++[{Vfrom, V}]}, Random_Neighbours);
       true -> VandP
   end.

open_wall(_, {-1, _}) -> ok; open_wall(Maze, {V, V2}) ->

   case (V2 > V) of true -> digraph:add_edge(Maze#maze.g, V, V2); _Else -> digraph:add_edge(Maze#maze.g, V2, V) end.

generate_MxN(M, N) ->

   Maze = make_maze(M, N),
   Matrix = make_maze(M, N, all_connected),
   Trail = processDepthFirst(Matrix),
   lists:foreach(fun(X) -> open_wall(Maze, X) end, Trail),
   Parts = maze_parts(Maze),
   lists:foreach(fun(X) -> draw_part(X) end, Parts).

generate_default() ->

   generate_MxN(9, 9).

</lang>

Output:

8> maze:generate_default().
+---+---+---+---+---+---+---+---+---+
|       |                           |
+   +   +---+   +---+---+---+---+   +
|   |       |           |       |   |
+   +---+   +---+---+   +   +   +   +
|   |       |   |       |   |       |
+   +   +   +   +   +---+---+---+   +
|   |   |   |   |       |       |   |
+   +   +---+   +   +   +   +   +---+
|   |           |   |       |       |
+   +---+---+---+---+---+---+---+   +
|   |                           |   |
+   +   +---+---+   +---+---+   +   +
|   |           |   |           |   |
+   +---+---+---+   +---+   +---+   +
|   |           |       |       |   |
+   +   +---+   +---+   +---+   +   +
|       |               |           |
+---+---+---+---+---+---+---+---+---+
ok
9> 

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:

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

FreeBASIC

<lang freebasic>' version 04-12-2016 ' compile with: fbc -s console ' when generating a big maze it's possible to run out of stack space ' increase stack with the -t xxxx (xxxx is the amount you want in Kbytes)

ReDim Shared As String d() ' directions ReDim Shared As ULong c() ' cell's

Sub cell(x As ULong, y As ULong, s As ULong)

   Dim As ULong x1, y1, di_n
   c(x,y) = 1 ' mark as visited

   Do
       Dim As String di = d(x, y)
       Dim As Long l = Len(di) -1
       If l < 0 Then Exit Sub ' no directions left then exit
       di_n = di[l] ' get direction
       If l = 0 Then
           d(x,y) = ""
       Else
           d(x,y) = Left(di,l)
       End If

       Select Case di_n ' 0,0 is upper left corner
           Case Asc("N")
               x1 = x    : y1 = y -1
           Case Asc("E")
               x1 = x +1 : y1 = y
           Case Asc("S")
               x1 = x    : y1 = y +1
           Case Asc("W")
               x1 = x -1 : y1 = y
       End Select

       If c(x1,y1) <> 0 Then Continue Do

       Select Case di_n ' 0,0 is upper left corner
           Case Asc("N")
               Line (x * s +1 , y * s) - ((x +1) * s -1, y * s),0
           Case Asc("E")
               Line (x1 * s, y * s +1) - (x1 * s, (y +1) * s -1),0
           Case Asc("S")
               Line (x * s +1, y1 * s) - ((x +1) * s -1, y1 * s),0
           Case Asc("W")
               Line (x * s , y * s +1) - (x * s, (y +1) * s -1),0
       End Select

       cell(x1, y1, s)
   Loop

End Sub

Sub gen_maze(w As ULong, h As ULong, s As ULong)

   ReDim d(w, h)
   ReDim c(w, h)
   Dim As ULong x, y, r, i
   Dim As String di

   d(0, 0) = "SE"       ' cornes
   d(0, h -1) ="NE"
   d(w -1, 0) ="SW"
   d(w -1, h -1) ="NW"

   For x = 1 To w -2  ' sides
       d(x,0) = "EWS"
       d(x,h -1) = "NEW"
   Next

   For y = 1 To h -2
       d(0, y) = "NSE"
       d(w -1, y) ="NSW"
   Next

   For x = 0 To w -1     ' shuffle directions
       For y = 0 To h -1
           di = d(x,y)
           If di = "" Then di = "NEWS"
           i = Len(di)
           Do
               r = Fix(Rnd * i)
               i = i - 1
               Swap di[r], di[i]
           Loop Until i = 0
           d(x,y) = di
       Next
   Next

   ScreenRes w * s +1, h * s +1, 8
   ' draw the grid
   For x = 0 To w
       Line (x * s, 0) - (x * s, h * s), 2 ' green color
   Next

   For y = 0 To h
       Line(0, y * s) - (w* s, y * s),2
   Next
   ' choice the start cell
   x = Fix(Rnd * w)
   y = Fix(Rnd * h)

   cell(x, y, s)

End Sub

' ------=< MAIN >=------

Randomize Timer

Dim As ULong t

Do

   ' gen_maxe(width, height, cell size)
   gen_maze(30, 30, 20)
   WindowTitle " S to save, N for next maze, other key to stop"
   Do
   Var key = Inkey
   key = UCase(key)
   If key = "S" Then
       t = t +1
       BSave("maze" + Str(t) + ".bmp"), 0
       key = ""
   End If
   If key = "N" Then Continue Do, Do
   If key <> "" Then Exit Do, Do 
   Loop

Loop

End</lang>

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>{-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE TypeFamilies #-}

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 library: <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. (The sequences of coordinates in display are the relative coordinates for the doors. For example, 2 1;2 2;2 3 are where we put spaces for each vertical door. The variable text is an ascii representation of the maze grid before the doors are placed.)

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>

Node.js

Translation of: Javascript

This difers of the basic Javascript in that in NodeJS we take advantage of the asynchronous behaviour. This code was modified from the plain Javascript section to make it Asynchronous and able to run under strict mode.

<lang javascript> 'use strict'; /*

* Imported from http://rosettacode.org/wiki/Maze_generation#JavaScript
* Added asynchronous behaviour to the maze generation.
* 
* Port by sigmasoldier
*/

/**

* Generates the maze asynchronously.
* @param {Number} x Width of the maze.
* @param {Number} y Height of the maze.
* @returns {Promise} finished when resolved.
*/

function maze(x,y) { return new Promise((resolve, reject) => { let n=x*y-1; if (n<0) { reject(new Error(`illegal maze dimensions (${x} x ${y} < 1)`)); } else { let horiz =[]; for (let j= 0; j<x+1; j++) horiz[j]= []; let verti =[]; for (let j= 0; j<x+1; j++) verti[j]= []; let here = [Math.floor(Math.random()*x), Math.floor(Math.random()*y)]; let path = [here]; let unvisited = []; for (let j = 0; j<x+2; j++) { unvisited[j] = []; for (let 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) { let potential = [[here[0]+1, here[1]], [here[0],here[1]+1], [here[0]-1, here[1]], [here[0],here[1]-1]]; let neighbors = []; for (let 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; let 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(); } resolve({x: x, y: y, horiz: horiz, verti: verti}); } }); }

/**

* A mere way of generating text.
* The text (Since it can be large) is generated in a non-blocking way.
* @param {Object} m Maze object.
* @param {Stream} writeTo Optinally, include here a function to write to.
* @returns {Promise} finished when the text is generated.
*/

function display(m, writeTo) { return new Promise((resolve, reject) => { let text = []; for (let j= 0; j<m.x*2+1; j++) { let line = []; if (0 == j%2) for (let 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 (let 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'); } const OUTPUT = text.join(); if (typeof writeTo === 'function') writeTo(OUTPUT); resolve(OUTPUT); }); }

module.exports = {

 maze: maze,
 display: display

} </lang>

Example use:

Image that you have a main.js file, to run then invoke in your shell node main.js Here is a basic example of what your main file should contain:

<lang javascript> 'use strict';

const maze = require('./maze.js'); const X = 20,

 Y = 20;

console.log(`Generating a maze of ${X} x ${Y}...`); const origin = new Date().getTime();

maze.maze(X, Y).then((m) => {

 const time = new Date().getTime() - origin;
 console.log(`Done in ${time <= 1000 ? time+'ms' : Math.round(time/1000)+'s'}!`);
 maze.display(m, console.log); //Here you can pass a given stream (ie: stream) and it's write function;
 //An example could be: maze.display(m, stream.write);

}, (err) => console.error(err));

</lang>

Sample Output:

$ node main.js
Generating a maze of 10 x 10...
Done in 3ms!
+   +---+---+---+---+---+---+---+---+---+
|                       |               |
+   +---+---+   +---+   +   +---+   +   +
|   |   |       |       |       |   |   |
+   +   +   +---+   +---+---+   +   +   +
|   |   |   |   |           |   |   |   |
+   +   +   +   +---+---+   +   +   +---+
|       |   |           |   |   |       |
+---+   +   +   +---+---+   +---+---+   +
|       |   |       |       |       |   |
+---+---+   +---+   +   +---+   +   +   +
|           |   |   |   |       |   |   |
+   +---+---+   +   +   +   +---+   +   +
|               |       |   |           |
+---+---+---+---+   +---+   +---+---+   +
|           |       |               |   |
+   +---+   +   +---+---+---+---+   +   +
|       |   |   |                   |   |
+---+   +   +   +---+   +---+---+---+   +
|       |               |
+---+---+---+---+---+---+---+---+---+---+

Julia

Works with: Julia version >0.6

Generating functions <lang julia>check(bound::Vector) = cell -> all([1, 1] .≤ cell .≤ bound) neighbors(cell::Vector, bound::Vector, step::Int=2) =

   filter(check(bound), map(dir -> cell + step * dir, [[0, 1], [-1, 0], [0, -1], [1, 0]]))

function walk(maze::Matrix, nxtcell::Vector, visited::Vector=[])

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

end function maze(w::Int, h::Int)

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

end</lang>

Printing functions <lang julia>pprint(matrix) = for i = 1:size(matrix, 1) println(join(matrix[i, :])) end function printmaze(maze)

   walls = split("╹ ╸ ┛ ╺ ┗ ━ ┻ ╻ ┃ ┓ ┫ ┏ ┣ ┳ ╋")
   h, w = size(maze)
   f = cell -> 2 ^ ((3cell[1] + cell[2] + 3) / 2)
   wall(i, j) = if maze[i,j] == 0 " " else
       walls[Int(sum(f, filter(x -> maze[x...] != 0, neighbors([i, j], [h, w], 1)) .- i, j))]
   end
   mazewalls = collect(wall(i, j) for i in 1:2:h, j in 1:w)
   pprint(mazewalls)

end

printmaze(maze(10, 10)) </lang>

Output:

┏━━━━━┳━━━━━┳━━━━━━━┓
┃ ╻ ╻ ┃ ╺━┓ ╹ ┏━━━┓ ┃
┣━┛ ┃ ┗━┓ ┗━━━┛ ╻ ┃ ┃
┃ ╺━┻━┓ ┃ ╺━┳━━━┛ ┃ ┃
┃ ╺━┓ ┃ ┗━━━┛ ┏━━━┛ ┃
┣━━━┛ ┣━━━━━┳━┛ ┏━━━┫
┃ ┏━━━┛ ┏━╸ ┃ ╺━┛ ╻ ┃
┣━┛ ┏━━━┛ ╻ ┣━━━━━┛ ┃
┃ ┏━┛ ┏━━━┻━┛ ┏━━━┳━┫
┃ ┃ ╺━┛ ╺━━━━━┛ ╻ ╹ ┃
┗━┻━━━━━━━━━━━━━┻━━━┛

Kotlin

Translation of: Java

<lang scala>import java.util.*

class MazeGenerator(val x: Int, val y: Int) {

   private val maze = Array(x) { IntArray(y) }

   fun generate(cx: Int, cy: Int) {
       Direction.values().shuffle().forEach {
           val nx = cx + it.dx
           val ny = cy + it.dy
           if (between(nx, x) && between(ny, y) && maze[nx][ny] == 0) {
               maze[cx][cy] = maze[cx][cy] or it.bit
               maze[nx][ny] = maze[nx][ny] or it.opposite!!.bit
               generate(nx, ny)
           }
       }
   }

   fun display() {
       for (i in 0..y - 1) {
           // draw the north edge
           for (j in 0..x - 1)
               print(if (maze[j][i] and 1 == 0) "+---" else "+   ")
           println('+')

           // draw the west edge
           for (j in 0..x - 1)
               print(if (maze[j][i] and 8 == 0) "|   " else "    ")
           println('|')
       }

       // draw the bottom line
       for (j in 0..x - 1) print("+---")
       println('+')
   }

   inline private fun <reified T> Array<T>.shuffle(): Array<T> {
       val list = toMutableList()
       Collections.shuffle(list)
       return list.toTypedArray()
   }

   private enum class Direction(val bit: Int, val dx: Int, val dy: Int) {
       N(1, 0, -1), S(2, 0, 1), E(4, 1, 0),W(8, -1, 0);

       var opposite: Direction? = null

       companion object {
           init {
               N.opposite = S
               S.opposite = N
               E.opposite = W
               W.opposite = E
           }
       }
   }

   private fun between(v: Int, upper: Int) = v >= 0 && v < upper

}

fun main(args: Array<String>) {

   val x = if (args.size >= 1) args[0].toInt() else 8
   val y = if (args.size == 2) args[1].toInt() else 8
   with(MazeGenerator(x, y)) {
       generate(0, 0)
       display()
   }

}</lang>

Lua

Works with: Lua version 5.1

<lang Lua> math.randomseed( os.time() )

-- Fisher-Yates shuffle from http://santos.nfshost.com/shuffling.html function shuffle(t)

 for i = 1, #t - 1 do
   local r = math.random(i, #t)
   t[i], t[r] = t[r], t[i]
 end

end

-- builds a width-by-height grid of trues function initialize_grid(w, h)

 local a = {}
 for i = 1, h do
   table.insert(a, {})
   for j = 1, w do
     table.insert(a[i], true)
   end
 end
 return a

end

-- average of a and b function avg(a, b)

 return (a + b) / 2

end

dirs = {

 {x = 0, y = -2}, -- north
 {x = 2, y = 0}, -- east
 {x = -2, y = 0}, -- west
 {x = 0, y = 2}, -- south

}

function make_maze(w, h)

 w = w or 16
 h = h or 8

 local map = initialize_grid(w*2+1, h*2+1)

 function walk(x, y)
   map[y][x] = false

   local d = { 1, 2, 3, 4 }
   shuffle(d)
   for i, dirnum in ipairs(d) do
     local xx = x + dirs[dirnum].x
     local yy = y + dirs[dirnum].y
     if map[yy] and map[yy][xx] then
       map[avg(y, yy)][avg(x, xx)] = false
       walk(xx, yy)
     end
   end
 end

 walk(math.random(1, w)*2, math.random(1, h)*2)

 local s = {}
 for i = 1, h*2+1 do
   for j = 1, w*2+1 do
     if map[i][j] then
       table.insert(s, '#')
     else
       table.insert(s, ' ')
     end
   end
   table.insert(s, '\n')
 end
 return table.concat(s)

end

print(make_maze()) </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 shuffle lst =
    let nl = List.map (fun c -> (Random.bits (), c)) lst in
    List.map snd (List.sort compare nl) 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 (shuffle (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':

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

Ol

<lang scheme>

maze generation

(import (otus random!)) (define WIDTH 30) (define HEIGHT 8)

(define maze

  (map (lambda (?)
        (repeat #b01111 WIDTH)) ; 0 - unvisited, 1111 - all walls exists
     (iota HEIGHT)))

(define (at x y)

  (list-ref (list-ref maze y) x))

(define (unvisited? x y)

  (if (and (< -1 x WIDTH) (< -1 y HEIGHT))
     (zero? (band (at x y) #b10000))))

(define neighbors '((-1 . 0) (0 . -1) (+1 . 0) (0 . +1))) (define walls '( #b10111 #b11011 #b11101 #b11110)) (define antiwalls '( #b11101 #b11110 #b10111 #b11011))

(let loop ((x (rand! WIDTH)) (y (rand! HEIGHT)))

  (list-set! (list-ref maze y) x (bor (at x y) #b10000))
  (let try ()
     (if (or
           (unvisited? (- x 1) y) ; left
           (unvisited? x (- y 1)) ; top
           (unvisited? (+ x 1) y) ; right
           (unvisited? x (+ y 1))) ; bottom
        (let*((p (rand! 4))
              (neighbor (list-ref neighbors p)))
           (let ((nx (+ x (car neighbor)))
                 (ny (+ y (cdr neighbor))))
           (if (unvisited? nx ny)
              (let ((ncell (at nx ny)))
                 (list-set! (list-ref maze y) x (band (at x y) (list-ref walls p)))
                 (list-set! (list-ref maze ny) nx (band ncell (list-ref antiwalls p)))
                 (loop nx ny)))
           (try))))))

</lang> <lang scheme>

maze printing

(display "+") (for-each (lambda (?) (display "--+")) (iota WIDTH)) (print) (for-each (lambda (l)

           ; left wall (always)
           (display "|")
           ; draw right wall
           (for-each (lambda (x)
                       (display "  ")
                       (display (if (zero? (band x #b10)) " " "|")))
              l)
           (print)
           (display "+")
           ; draw bottom wall
           (for-each (lambda (x)
                       (display (if (zero? (band x #b01)) "  " "--"))
                       (display "+"))
              l)
           (print))
  maze)

(print) </lang>

Sample 30 x 8 output:

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

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

Works with: rakudo version 2015-09-22

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 Sym (mapping.map: *.key); my @ch = 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, $[ flat ES, -N, (ESW, EW) xx $X - 1, SW ];
   push @maze, $[ flat (NS, TODO) xx $X, NS ];
   for 1 ..^ $Y {

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

   }
   push @maze, $[ flat 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.rotor(2) -> ($w, $c) { print @ch[abs $w]; if $c >= 0 { print @ch[$c] x 3 } else { print ' ', @ch[abs $c], ' ' } } say @ch[@y[*-1]];

   }

}

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

Output:

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

Phix

Adapted a couple of techniques from the excellent D submission
(however this holds the grid as an array of complete lines) <lang Phix>-- -- grid is eg for w=3,h=2: {"+---+---+---+", -- ("wall") -- "| ? | ? | ? |", -- ("cell") -- "+---+---+---+", -- ("wall") -- "| ? | ? | ? |", -- ("cell") -- "+---+---+---+", -- ("wall") -- ""} -- (for a trailing \n) -- -- note those ?(x,y) are at [y*2][x*4-1], and we navigate -- using y=2..2*h (+/-2), x=3..w*4-1 (+/-4) directly. -- constant w = 11, h = 8

sequence wall = join(repeat("+",w+1),"---")&"\n",

        cell = join(repeat("|",w+1)," ? ")&"\n",
        grid = split(join(repeat(wall,h+1),cell),'\n')

procedure amaze(integer x, integer y)

   grid[y][x] = ' '                        -- mark cell visited
   sequence p = shuffle({{x-4,y},{x,y+2},{x+4,y},{x,y-2}})
   for i=1 to length(p) do
       integer {nx,ny} = p[i]
       if nx>1 and nx<w*4 and ny>1 and ny<=2*h and grid[ny][nx]='?' then
           integer mx = (x+nx)/2
           grid[(y+ny)/2][mx-1..mx+1] = ' ' -- knock down wall
           amaze(nx,ny)
       end if
   end for

end procedure

function heads()

   return rand(2)=1 -- 50:50 true(1)/false(0)

end function

integer {x,y} = {(rand(w)*4)-1,rand(h)*2} amaze(x,y) -- mark start pos grid[y][x] = '*' -- add a random door (heads=rhs/lhs, tails=top/btm) if heads() then

   grid[rand(h)*2][heads()*w*4-1] = ' '

else

   x = rand(w)*4-1
   grid[heads()*h*2+1][x-1..x+1] = ' '

end if puts(1,join(grid,'\n'))</lang>

Output:

+---+---+---+---+---+---+---+---+---+---+---+
|   |                                   |   |
+   +   +---+---+---+---+---+---+   +   +   +
|   |       |   | *             |   |       |
+   +---+   +   +---+---+---+   +   +---+---+
|   |       |               |   |           |
+   +   +---+   +---+   +---+   +---+---+   +
|   |       |   |   |       |   |           |
+   +---+   +   +   +---+   +   +   +---+---+
|   |       |       |       |       |       |
+   +   +---+---+---+   +---+---+---+---+   +
|   |               |           |           |
+   +---+---+---+   +---+   +   +   +---+   +
|       |       |           |       |       |
+   +---+   +   +---+---+---+---+---+   +---+
            |                               |
+---+---+---+---+---+---+---+---+---+---+---+

PHP

Code inspired by the D and Python solutions (with the implementation of backtracking, or sometimes it wouldn't work). Could have been done procedurally or fully OO (with cells as class too). A debug flag has been provided to allow following the inner workings. Works on PHP > 5.6. <lang php><?php class Maze {

   protected $width;
   protected $heigth;
   protected $grid;
   protected $path;
   protected $horWalls;
   protected $vertWalls;
   protected $dirs;
   protected $isDebug;

   public function __construct($x, $y, $debug = false)
   {
       $this->width = $x;
       $this->height = $y;
       $this->path = [];        
       $this->dirs = [ [0, -1], [0, 1], [-1, 0], [1, 0]]; // array of coordinates of N,S,W,E
       $this->horWalls = []; // list of removed horizontal walls (---+)        
       $this->vertWalls = [];// list of removed vertical walls (|)        
       $this->isDebug = $debug; // debug flag

       // generate the maze:
       $this->generate();
   }

   protected function generate()
   {        
       $this->initMaze(); // init the stack and an unvisited grid
       // start from a random cell and then proceed recursively
       $this->walk(mt_rand(0, $this->width-1), mt_rand(0, $this->height-1));
   }

   /**
   * Actually prints the Maze, on stdOut. Put in a separate method to allow extensibility
   * For simplicity sake doors are positioned on the north wall and east wall
   */
   public function printOut()
   {
       $this->log("Horizontal walls: %s", json_encode($this->horWalls));
       $this->log("Vertical walls: %s", json_encode($this->vertWalls));        
       
       $northDoor = mt_rand(0,$this->width-1);
       $eastDoor = mt_rand(0, $this->height-1);

       $str = '+';
       for ($i=0;$i<$this->width;$i++) {
           $str .= ($northDoor == $i) ? '   +' : '---+';
       }
       $str .= PHP_EOL;
       for ($i=0; $i<$this->height; $i++) {
           
           for ($j=0; $j<$this->width; $j++) {
               $str .= (!empty($this->vertWalls[$j][$i]) ? $this->vertWalls[$j][$i] : '|   ');
           }
           $str .= ($i == $eastDoor ? '  ' : '|').PHP_EOL.'+';
           for ($j=0; $j<$this->width; $j++) {
               $str .= (!empty($this->horWalls[$j][$i]) ? $this->horWalls[$j][$i] : '---+');
           }
           $str .= PHP_EOL;
       }
       echo $str;
   }

   /**
   * Logs to stdOut if debug flag is enabled
   */
   protected function log(...$params)
   {
       if ($this->isDebug) {
           echo vsprintf(array_shift($params), $params).PHP_EOL;
       }
   }

   private function walk($x, $y)
   {
       $this->log('Entering cell %d,%d', $x, $y);
       // mark current cell as visited     
       $this->grid[$x][$y] = true; 
       // add cell to path
       $this->path[] = [$x, $y];
       // get list of all neighbors
       $neighbors = $this->getNeighbors($x, $y);       
       $this->log("Valid neighbors: %s", json_encode($neighbors));

       if(empty($neighbors)) {
           // Dead end, we need now to backtrack, if there's still any cell left to be visited
           $this->log("Start backtracking along path: %s", json_encode($this->path));
           array_pop($this->path);
           if (!empty($this->path)) {
               $next = array_pop($this->path);
               return $this->walk($next[0], $next[1]);
           }
       } else {            
           // randomize neighbors, as per request
           shuffle($neighbors);

           foreach ($neighbors as $n) {
               $nextX = $n[0];
               $nextY = $n[1];
               if ($nextX == $x) {
                   $wallY = max($nextY, $y);
                   $this->log("New cell is on the same column (%d,%d), removing %d, (%d-1) horizontal wall", $nextX, $nextY, $x, $wallY);
                   $this->horWalls[$x][min($nextY, $y)] = "   +";
               }
               if ($nextY == $y) {
                   $wallX = max($nextX, $x);
                   $this->log("New cell is on the same row (%d,%d), removing %d,%d vertical wall", $nextX, $nextY, $wallX, $y);
                   $this->vertWalls[$wallX][$y] = "    ";              
               }
               return $this->walk($nextX, $nextY);
           }
       }
   }
   
   /**
   * Initialzie an empty grid of $width * $height dimensions
   */
   private function initMaze()
   {
       for ($i=0;$i<$this->width;$i++) {
           for ($j = 0;$j<$this->height;$j++) {
               $this->grid[$i][$j] = false;
           }
       }
   }

   /**
   * @param int $x
   * @param int $y
   * @return array
   */
   private function getNeighbors($x, $y) 
   {       
       $neighbors = [];
       foreach ($this->dirs as $dir) {
           $nextX = $dir[0] + $x;
           $nextY = $dir[1] + $y;
           if (($nextX >= 0 && $nextX < $this->width && $nextY >= 0 && $nextY < $this->height) && !$this->grid[$nextX][$nextY]) {
               $neighbors[] = [$nextX, $nextY];
           }
       }
       return $neighbors;
   }

}

$maze = new Maze(10,10); $maze->printOut();</lang>

Output:

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

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

Translation of: REXX

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

mgg: Proc Options(main);
/* REXX ***************************************************************
* 04.09.2013 Walter Pachl translated from REXX version 3
**********************************************************************/
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))

   s = ""
   for (a, b) in zip(hor, ver):
       s += .join(a + ['\n'] + b + ['\n'])
   return s

if __name__ == '__main__':

   print(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   invocations and
some other instructions were added to increase the horizontal dimension (cell size). <lang rexx>/*REXX program generates and displays a rectangular solvable maze (of any size). */ parse arg rows cols seed . /*allow user to specify the maze size. */ if rows= | rows==',' then rows= 19 /*No rows given? Then use the default.*/ if cols= | cols==',' then cols= 19 /* " cols "  ? " " " " */ if datatype(seed, 'W') then call random ,,seed /*use a random seed for repeatability.*/ ht=0; @.=0 /*HT= # rows in grid; @.: default cell*/ call makeRow '┌'copies('~┬', cols - 1)'~┐' /*construct the top edge of the maze. */

                                                /* [↓]  construct the maze's grid.     */
     do    r=1  for rows;   _=;     __=;      hp= "|";              hj= '├'
        do c=1  for cols;   _= _ || hp'1';    __= __ || hj"~";      hj= '┼';      hp= "│"
        end   /*c*/
                       call makeRow  _'│'       /*construct the right edge of the cells*/
     if r\==rows  then call makeRow __'┤'       /*    "      "    "     "   "  "  maze.*/
     end      /*r*/                             /* [↑]  construct the maze's grid.     */

call makeRow '└'copies("~┴", cols - 1)'~┘' /*construct the bottom edge of the maze*/ 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  /*¬freecell?*/
 call ?;        @._r._c= 0                      /*get the (next) maze direction to go. */
 ro= r!;        co= c!;     r!= _r;    c!= _c   /*save original maze cell coordinates. */
 ?.zr= ?.zr % 2;            ?.zc= ?.zc % 2      /*get the maze row and cell directions.*/
 rw= ro + ?.zr;             cw= co + ?.zc       /*calculate the next row and column.   */
 @.rw.cw= .                                     /*mark the maze cell as being visited. */
 end   /*forever*/
                                                /* [↓]  display maze to the terminal.  */
        do     r=1  for ht;            _=
            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 ht;           _= @.#           /*display the maze to the terminal.    */
     call makeNice                              /*prettify cell corners and dead─ends. */
     _=  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 the screen.  */
     end   /*#*/
     end   /*#*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a maze cell. */ makeRow: parse arg z; ht= ht+1; do c=1 for length(z); @.ht.c=substr(z,c,1); end; return hood: parse arg rh,ch; return @(rh+2,ch) + @(rh-2,ch) + @(rh,ch-2) + @(rh,ch+2) /*──────────────────────────────────────────────────────────────────────────────────────*/ ?: 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*/

/*──────────────────────────────────────────────────────────────────────────────────────*/ fCell: do r=1 for rows; rr= r + r

              do c=1  for cols;                         cc= c + c
              if hood(rr,cc)==1  then do;  r!= rr;  c!= cc;   @.r!.c!= 0;  return 1;  end
              end   /*c*/                       /* [↑]  r! and c!  are used by invoker.*/
          end       /*r*/;       return 0

/*──────────────────────────────────────────────────────────────────────────────────────*/ makeNice: width= length(_); old= # - 1; new= # + 1; old_= @.old; new_= @.new

         if left(_, 2)=='├.'  then _= translate(_, "|", '├')
         if right(_,2)=='.┤'  then _= translate(_, "|", '┤')

            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 #==ht;        z= substr(_, k, 1) /*maze bot row.*/
            if z\=='┴'                  then iterate
            if substr(old_, k, 1)=='\'  then _= overlay("═", _, k)
            end   /*k*/

            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   6

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

simpler version of above

The above REXX version had a quite of bit of code to "dress up" the maze presentation,   so a slimmed-down version
was included here for easier reading and understanding of the program's logic. <lang rexx>/*REXX program generates and displays a rectangular solvable maze (of any size). */ parse arg rows cols seed . /*allow user to specify the maze size. */ if rows= | rows=="," then rows= 19 /*No rows given? Then use the default.*/ if cols= | cols=="," then cols= 19 /* " cols "  ? " " " " */ if datatype(seed, 'W') then call random ,,seed /*use a random seed for repeatability.*/ ht=0; @.=0 /*HT= # rows in grid; @.: default cell*/ call makeRow '┌'copies("─┬", cols-1)'─┐' /*construct the top edge of the maze.*/

     do    r=1  for rows;   _=;     __=;      hp= "|";              hj= '├'
        do c=1  for cols;   _= _ || hp'1';    __= __ || hj"─";      hj= '┼';      hp= "│"
        end   /*c*/
                       call makeRow  _'│'       /*construct the right edge of the cells*/
     if r\==rows  then call makeRow __'┤'       /*    "      "    "     "   "  "  maze.*/
     end      /*r*/                             /* [↑]  construct the maze's grid.     */

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

                                                /* [↓]  traipse through the maze.      */
 do forever;        n= hood(r!, c!)             /*number of free maze cells.           */
 if n==0  then if \fCell()  then leave          /*if no free maze cells left, then done*/
 call ?;            @._r._c= 0                  /*get the (next) maze direction to go. */
 ro= r!;            co= c!;    r!= _r;   c!= _c /*save the original cell coordinates.  */
 ?.zr= ?.zr % 2;    ?.zc= ?.zc % 2              /*get the maze row and cell directions.*/
 rw= ro + ?.zr;     cw= co + ?.zc               /*calculate the next maze row and col. */
 @.rw.cw=.                                      /*mark the maze cell as being visited. */
 end   /*forever*/
                                                /* [↓]  display maze to the terminal.  */
        do     r=1  for ht;           _=
            do c=1  for cols*2 + 1;   _= _ || @.r.c;   end  /*c*/
        if \(r//2)  then _= translate(_, '\',.) /*translate a  period  to a  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 the screen.  */
        end   /*r*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a maze cell. */ makeRow: parse arg z; ht= ht+1; do c=1 for length(z); @.ht.c=substr(z,c,1); end; return hood: parse arg rh,ch; return @(rh+2,ch) + @(rh-2,ch) + @(rh,ch-2) + @(rh,ch+2) /*──────────────────────────────────────────────────────────────────────────────────────*/ ?: 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*/

/*──────────────────────────────────────────────────────────────────────────────────────*/ fCell: do r=1 for rows; rr= r + r

              do c=1  for cols;                         cc= c + c
              if hood(rr,cc)==1  then do;  r!= rr;  c!= cc;   @.r!.c!= 0;  return 1;  end
              end   /*c*/                       /* [↑]  r! and c!  are used by invoker.*/
          end       /*r*/;       return 0</lang>

output   when using input:     10  10

┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│                                   │   │
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└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

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

Translation of: Perl

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

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 d = [[-1, 0], [0, 1], [1, 0], [0, -1]]
   while (!d.is_empty) {
       var i = d.pop_rand
       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)
   }

}

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

for i in (0 .. h) {

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

}</lang>

Output:

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

SuperCollider

<lang SuperCollider> // some useful functions ( ~grid = { 0 ! 60 } ! 60;

~at = { |coord| var col = ~grid.at(coord[0]); if(col.notNil) { col.at(coord[1]) } }; ~put = { |coord, value| var col = ~grid.at(coord[0]); if(col.notNil) { col.put(coord[1], value) } };

~coord = ~grid.shape.rand; ~next = { |p| var possible = [p] + [[0, 1], [1, 0], [-1, 0], [0, -1]]; possible = possible.select { |x| var c = ~at.(x); c.notNil and: { c == 0 } }; possible.choose }; ~walkN = { |p, scale| var next = ~next.(p); if(next.notNil) { ~put.(next, 1); Pen.lineTo(~topoint.(next, scale)); ~walkN.(next, scale); ~walkN.(next, scale); Pen.moveTo(~topoint.(p, scale)); }; };

~topoint = { |c, scale| (c + [1, 1] * scale).asPoint };

)

// do the drawing ( var b, w;

b = Rect(100, 100, 700, 700); w = Window("so-a-mazing", b); w.view.background_(Color.black);

w.drawFunc = { var p = ~grid.shape.rand; var scale = b.width / ~grid.size * 0.98; Pen.moveTo(~topoint.(p, scale)); ~walkN.(p, scale); Pen.width = scale / 4; Pen.color = Color.white; Pen.stroke; }; w.front.refresh; ) </lang>

Swift

Works with: Swift version 3

<lang Swift>import Foundation

extension Array {

   mutating func shuffle() {
       guard count > 1 else { return }

       for i in 0..<self.count - 1 {
           let j = Int(arc4random_uniform(UInt32(count - i))) + i
           guard i != j else { continue }
           swap(&self[i], &self[j])
       }
   }

}

enum Direction:Int {

   case north = 1
   case south = 2
   case east = 4
   case west = 8

   static var allDirections:[Direction] {
       return [Direction.north, Direction.south, Direction.east, Direction.west]
   }

   var opposite:Direction {
       switch self {
       case .north:
           return .south
       case .south:
           return .north
       case .east:
           return .west
       case .west:
           return .east
       }
   }

   var diff:(Int, Int) {
       switch self {
       case .north:
           return (0, -1)
       case .south:
           return (0, 1)
       case .east:
           return (1, 0)
       case .west:
           return (-1, 0)
       }
   }

   var char:String {
       switch self {
       case .north:
           return "N"
       case .south:
           return "S"
       case .east:
           return "E"
       case .west:
           return "W"
       }
   }

}

class MazeGenerator {

   let x:Int
   let y:Int
   var maze:Int

   init(_ x:Int, _ y:Int) {
       self.x  = x
       self.y = y
       let column = [Int](repeating: 0, count: y)
       self.maze = Int(repeating: column, count: x)
       generateMaze(0, 0)
   }

   private func generateMaze(_ cx:Int, _ cy:Int) {
       var directions = Direction.allDirections
       directions.shuffle()
       for direction in directions {
           let (dx, dy) = direction.diff
           let nx = cx + dx
           let ny = cy + dy
           if inBounds(nx, ny) && maze[nx][ny] == 0 {
               maze[cx][cy] |= direction.rawValue
               maze[nx][ny] |= direction.opposite.rawValue
               generateMaze(nx, ny)
           }
       }
   }

   private func inBounds(_ testX:Int, _ testY:Int) -> Bool {
       return inBounds(value:testX, upper:self.x) && inBounds(value:testY, upper:self.y)
   }

   private func inBounds(value:Int, upper:Int) -> Bool {
       return (value >= 0) && (value < upper)
   }

   func display() {
       let cellWidth = 3
       for j in 0..<y {
           // Draw top edge
           var topEdge = ""
           for i in 0..<x {
               topEdge += "+"
               topEdge += String(repeating: (maze[i][j] & Direction.north.rawValue) == 0 ? "-" : " ", count: cellWidth)
           }
           topEdge += "+"
           print(topEdge)

           // Draw left edge
           var leftEdge = ""
           for i in 0..<x {
               leftEdge += (maze[i][j] & Direction.west.rawValue) == 0 ? "|" : " "
               leftEdge += String(repeating: " ", count: cellWidth)
           }
           leftEdge += "|"
           print(leftEdge)
       }

       // Draw bottom edge
       var bottomEdge = ""
       for _ in 0..<x {
           bottomEdge += "+"
           bottomEdge += String(repeating: "-", count: cellWidth)
       }
       bottomEdge += "+"
       print(bottomEdge)
   }
   
   func displayInts() {
       for j in 0..<y {
           var line = ""
           for i in 0..<x {
               line += String(maze[i][j]) + "\t"
           }
           print(line)
       }
   }

   func displayDirections() {
       for j in 0..<y {
           var line = ""
           for i in 0..<x {
               line += getDirectionsAsString(maze[i][j]) + "\t"
           }
           print(line)
       }
   }

   private func getDirectionsAsString(_ value:Int) -> String {
       var line = ""
       for direction in Direction.allDirections {
           if (value & direction.rawValue) != 0 {
               line += direction.char
           }
       }
       return line
   }

}

let x = 20 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)
    (let ((x (from loc))
          (y (to 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. We also drop use of the TXR pattern extraction language and work purely in TXR Lisp.

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 txrlisp>(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))]))

(defun neigh (loc)

 (let ((x (from loc))
       (y (to 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:

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