Maze generation
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(Redirected from Maze)
You are encouraged to solve this task according to the task description, using any language you may know.
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Generate and show a maze, using the simple Depth-first search algorithm.
- Start at a random cell.
- Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor:
- If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell.
See also Maze solving.
Contents |
[edit] Ada
mazes.ads:
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;
mazes.adb:
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;
Example main.adb:
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;
- Output:
Starting generation at 3 x 7 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + + +---+ + + +---+---+---+ + | | | | | | | + +---+---+ +---+---+ + + + +---+ | | | | | | | | + +---+---+---+---+ +---+ + + + + | | | | | | | + + +---+ + + + +---+---+---+ + | | | | | | | + + +---+---+---+---+---+ +---+ + + | | | | | | +---+ + +---+---+---+ +---+---+---+ + | | | | | + +---+ +---+---+ +---+---+---+---+---+ | | +---+---+---+---+---+---+---+---+---+---+---+
[edit] Aime
void
grid_maze(data b, integer N)
{
data d;
integer i, j;
j = N;
while (j) {
b_suffix(d, "+---");
j -= 1;
}
{
b_suffix(d, "+\n");
}
j = N;
while (j) {
b_suffix(d, "| * ");
j -= 1;
}
{
b_suffix(d, "|\n");
}
i = N;
while (i) {
b_extend(b, d);
i -= 1;
}
b_size(d, N * 4 + 2);
{
b_extend(b, d);
}
}
void
walk_cell(data b, integer N, integer line_size, integer x, integer y,
list x_offsets, list y_offsets)
{
integer i, r;
b_replace(b, y + x, ' ');
r = drand(3);
i = 0;
while (i < 4) {
integer p, q;
p = x + l_q_integer(x_offsets, (r + i) & 3);
q = y + l_q_integer(y_offsets, (r + i) & 3);
if (-1 < p && p < line_size
&& -1 < q && q < line_size * (N * 2 + 1)) {
if (b_text(b, q + p) == '*') {
walk_cell(b, N, line_size, p, q, x_offsets, y_offsets);
b_replace(b, (q + y) / 2 + (p + x) / 2, ' ');
if (p == x) {
b_replace(b, (q + y) / 2 + p - 1, ' ');
b_replace(b, (q + y) / 2 + p + 1, ' ');
}
}
}
i += 1;
}
}
void
walk_maze(data b, integer N)
{
integer line_size, x, y;
list x_offsets, y_offsets;
line_size = N * 4 + 1 + 1;
lb_p_integer(x_offsets, 4);
lb_p_integer(y_offsets, 0);
lb_p_integer(x_offsets, 0);
lb_p_integer(y_offsets, line_size * 2);
lb_p_integer(x_offsets, -4);
lb_p_integer(y_offsets, 0);
lb_p_integer(x_offsets, 0);
lb_p_integer(y_offsets, line_size * -2);
x = drand(N - 1) * 4 + 2;
y = line_size * (drand(N - 1) * 2 + 1);
walk_cell(b, N, line_size, x, y, x_offsets, y_offsets);
}
integer
main(void)
{
data b;
integer N;
N = 10;
grid_maze(b, N);
walk_maze(b, N);
o_text(b_string(b));
return 0;
}
- Output:
+---+---+---+---+---+---+---+---+---+---+ | | | + +---+---+---+---+ + +---+---+ + | | | | | | | + + + + + + + + +---+ + | | | | | | | | | + +---+---+ +---+---+---+ + + + | | | | | | +---+---+---+---+---+---+ + + + + | | | | | + +---+---+---+---+ + + +---+---+ | | | | | | + +---+---+---+ + + +---+ + + | | | | | | | + + + + + +---+---+ +---+ + | | | | | | | +---+---+---+ +---+---+---+---+ + + | | | | | + +---+---+---+ + + + +---+ + | | | | +---+---+---+---+---+---+---+---+---+---+
[edit] 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.
; 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)
}
- Sample output:
+-+-+-+-+-+-+-+-+-+-+-+ | | | | +-+ +-+-+ +-+ + + +-+-+ | | | | | + +-+ +-+ +-+-+ +-+ + + | | | | | | | | + + +-+-+ + + +-+ +-+ + | | | | | | | + +-+ + +-+-+-+ +-+ + + | | | | | | + +-+-+-+-+-+ +-+-+-+ + | | | | | | + + + + +-+-+-+ + + +-+ | | | | | | | +-+-+-+-+ +-+ + +-+-+ + | | | +-+-+-+-+-+-+-+-+-+-+-+
[edit] AWK
#!/usr/bin/awk -f
# 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();
}
# 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)
}
}
}
# 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
}
# 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;
}
# 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;
}
# 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;
}
# 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;
}
# 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);
}
# 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);
}
# 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);
}
# 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);
}
# Plunk a cell into the maze.
function setCell(x, y, cell, idx) {
if (!isGoodXY(x, y)) return;
maze[x, y] = cell
}
# Get a cell from the maze.
function getCell(x, y, idx) {
if (!isGoodXY(x, y)) return -1; # Bad cell marker.
return maze[x, y];
}
# 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;
}
# 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.
}
}
}
# 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);
}
Example output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | +---+ +---+ +---+---+ +---+ +---+---+ +---+ +---+---+ + +---+ + | | | | | | | | | | | | | + +---+ + + +---+---+ +---+---+ + +---+ + + +---+---+---+ + | | | | | | | | | + + + +---+ +---+ + +---+ +---+---+ +---+---+ +---+ +---+ + | | | | | | | | | | | | | | +---+ + + +---+ +---+ + +---+---+ + + + +---+---+---+ +---+ | | | | | | | | | | | + + +---+---+ +---+ +---+---+---+---+ +---+---+ +---+ + +---+ + | | | | | | | | | | | | | + +---+ + + +---+---+ +---+ + + + + +---+ + + + + + | | | | | | | | | | | | | | | + + +---+---+---+ + +---+ + + + +---+---+ + + +---+---+ + | | | | | | | | | | + + +---+---+---+ +---+---+---+ + +---+---+---+ + +---+---+ +---+ | | | | | | | | | | + +---+ +---+---+---+ + +---+---+---+---+ + +---+ + + +---+ + | | | | | | | | | | | | | | + + + + +---+ + + + + + + + + + +---+---+ + +---+ | | | | | | | | | | | | | | + +---+---+---+ + +---+---+---+ + + + + + +---+ + +---+ + | | | | | | | | | | | | +---+ +---+---+---+---+---+ + +---+ +---+---+---+---+ + +---+ + + | | | | | | | | | | | | | + + + +---+ +---+ + +---+ + + +---+ +---+ +---+ + + + | | | | | | | | | | | | + + + +---+---+ +---+---+ + +---+ +---+---+ +---+---+ + +---+ | | | | | | | | | | | | | + + + + + +---+ +---+---+---+---+---+ + +---+---+ + +---+ + | | | | | | | | | +---+---+ + +---+---+---+---+ + +---+---+---+ +---+---+---+---+ + + | | | | | | | | | | + + +---+ +---+---+ + + +---+ + + +---+---+ +---+---+---+ + | | | | | | | | | | | | | + + +---+---+ + +---+ + +---+ +---+ + + +---+---+ + +---+ | | | | | | | | | | | | | + +---+ +---+ + + +---+---+ +---+ +---+ +---+---+ + +---+ + | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
[edit] BBC BASIC
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
Sample output:
[edit] 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.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <locale.h>
#define DOUBLE_SPACE 1
#if DOUBLE_SPACE
# define SPC " "
#else
# define SPC " "
#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;
#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;
}
- Sample output:
┌───┬─────┬─────────┬───────┬───┐ │┄┄╮│╭┄┄┄╮│ ╭┄┄┄┄┄╮│ ╭┄┄┄╮│╭┄╮│ │ │┆│┆──┐┆│ │┆──┬─┐┆└──┆┌─┐┆│┆│┆│ │ │┆│╰┄╮│┆│ │╰┄╮│ │╰┄┄┄╯│ │╰┄╯│┆│ │ │┆└──┆│┆└─┼──┆│ └─────┤ └─┬─┘┆│ │ │╰┄┄┄╯│╰┄╮│╭┄╯│ │ │╭┄╯│ │ └─────┴─┐┆│┆┌─┴───┐ │ │ │ │┆──┤ │ │┆│┆│╭┄┄┄╮│ │ │ │╰┄╮│ │ ──────┐ │┆│┆│┆──┐┆└─┤ ┌─┘ └─┐┆│ │ │ │┆│╰┄╯ │╰┄╮│ │ │┆│ │ ┌─────┘ │┆├─────┴─┐┆│ │ ──┬─┘┆│ │ │ │┆│╭┄┄┄┄┄╮│┆│ │ │╭┄╯│ ├─┤ ──┬─┬─┘┆│┆┌─┬──┆│┆└─┴─┐ │┆┌─┤ │ │ │ │╭┄╯│┆│ │╭┄╯│╰┄┄┄╮│ │┆│ │ │ └── │ │┆──┘┆│ │┆──┴────┆│ │┆│ │ │ │ ╰┄┄┄╯│ ╰┄┄┄┄┄┄┄╯│ ╰┄┄│ └─────┴───────┴───────────┴─────┘
[edit] The very alternative version
Invoke as ./maze [width] [depth] [height], and output is in maze.pgm, which you can print out and cut to fold into a cuboid. Sample output with 15, 10 and 20 sizes.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define CW 10 /* cell width. This decides how big the output is */
typedef struct cell_t cell_t, *cell;
enum { N, E, S, W, V };
struct cell_t {
unsigned int flags;
cell prev, next, nei[4]; /* neighbors */
};
int sx, sy, sz, w, h;
#define C(y, x) c[(y) * w + x]
#define P(y, x) pix[(y) * w2 + x]
void draw_maze(cell *c)
{
#define FOR(a, b) for(a = 0; a < b; a++)
FILE *fp;
int w2 = w * CW + 8, h2 = h * CW + 7;
char *pix = malloc(w2 * h2);
memset(pix, 200, w2 * h2);
void draw_face(int x, int y, int ww, int hh, int px, int py) {
int i, j, k, l;
cell t;
px += 2, py += 2;
for (i = py; i <= py + hh * CW; i++)
memset(&P(i, px), 0, ww * CW+1);
px++, py++;
# define mark(y, x) P(py + CW*i + y, px + CW*j + x) = 255
FOR (i, hh) FOR (j, ww) {
FOR(k, CW - 1) FOR(l, CW - 1) mark(k, l);
t = C(y + i, x + j);
if (t->flags & (1 << N))
FOR (l, CW - 1) mark(-1, l);
if (t->flags & (1 << S))
FOR (l, CW - 1) mark(CW - 1, l);
if (t->flags & (1 << E))
FOR (l, CW - 1) mark(l, CW - 1);
if (t->flags & (1 << W))
FOR (l, CW - 1) mark(l, -1);
}
}
draw_face(0, 0, sx, sy, 0, 0);
draw_face(0, sy, sx, sz, 0, CW*sy + 1);
draw_face(sx, sy, sy, sz, CW*sx + 1, CW*sy + 1);
draw_face(sx + sy, sy, sx, sz, CW*(sx + sy) + 2, CW*sy + 1);
draw_face(sx + sy + sx, sy, sy, sz, CW*(sx + sy + sx) + 3, CW*sy + 1);
draw_face(sx + sy, sy + sz, sx, sy, CW*(sx + sy) + 2, CW*(sy + sz) + 2);
fp = fopen("maze.pgm", "w+");
fprintf(fp, "P5\n%d %d\n255\n", w2, h2);
fwrite(pix, 1, w2 * h2, fp);
fclose(fp);
}
cell rand_neighbor(cell x)
{
cell r = 0;
int i, c = 1;
for (i = N; i <= W; i++) {
if (!x->nei[i] || (x->nei[i]->flags & (1 << V)))
continue;
if (rand() % c++ == 0)
r = x->nei[i];
}
return r;
}
void link_cells(cell a, cell b)
{
int i;
for (i = N; i <= W; i++) {
if (a->nei[i] != b) continue;
a->flags |= 1 << i;
break;
}
for (i = N; i <= W; i++) {
if (b->nei[i] != a) continue;
b->flags |= 1 << i;
break;
}
}
void walk(cell head)
{
cell tail = head, p, n;
while (head) {
for (p = head; p; p = n) {
p->flags |= 1 << V;
n = rand_neighbor(p);
if (!n) break;
tail->next = n;
n->prev = tail;
tail = n;
link_cells(p, n);
}
while (head && !rand_neighbor(head)) head = head->next;
}
}
void make_maze(void)
{
int i, j;
int n = (sx * sy + sx * sz + sy * sz) * 2;
cell t, *c;
cell_t * cells;
w = 2 * sx + 2 * sy, h = sy * 2 + sz;
cells = calloc(sizeof(cell_t), n);
c = calloc(sizeof(cell), w * h);
for (i = 0; i < sy; i++)
for (j = 0; j < sx; j++)
C(i, j) = cells + --n;
for (; i < sy + sz; i++)
for (j = 0; j < w; j++)
C(i, j) = cells + --n;
for (; i < h; i++)
for (j = sx + sy; j < w - sy; j++)
C(i, j) = cells + --n;
for (i = 0; i < h; i++) {
for (j = 0; j < w; j++) {
t = C(i, j);
if (!t) continue;
if (i) t->nei[N] = C(i - 1, j);
if (i < h - 1) t->nei[S] = C(i + 1, j);
if (j) t->nei[W] = C(i, j - 1);
if (j < w - 1) t->nei[E] = C(i, j + 1);
}
}
for (j = 0; j < sx; j++) {
C(0, j)->nei[N] = C(sy, w - sy - j - 1);
C(sy, w - sy - j - 1)->nei[N] = C(0, j);
C(h - sy - 1, j)->nei[S] = C(h - 1, w - sy - j - 1);
C(h - 1, w - sy - j - 1)->nei[S] = C(h - sy - 1, j);
}
for (i = sy; i < sy + sz; i++) {
C(i, 0)->nei[W] = C(i, w - 1);
C(i, w - 1)->nei[E] = C(i, 0);
}
for (i = 0; i < sy; i++) {
C(i, 0)->nei[W] = C(sy, w - sy + i);
C(sy, w - sy + i)->nei[N] = C(i, 0);
C(i, sx - 1)->nei[E] = C(sy, sx + sy - i - 1);
C(sy, sx + sy - i - 1)->nei[N] = C(i, sx - 1);
C(h - sy - 1, sx + i)->nei[S] = C(h - 1 - i, sx + sy);
C(h - 1 - i, sx + sy)->nei[W] = C(h - sy - 1, sx + i);
C(sy + sz + i, w - sy - 1)->nei[E] = C(sy + sz - 1, w - sy + i);
C(sy + sz - 1, w - sy + i)->nei[S] = C(sy + sz + i, w - sy - 1);
}
walk(C(0, 0));
draw_maze(c);
}
int main(int c, char **v)
{
if (c < 2 || (sx = atoi(v[1])) <= 0) sx = 10;
if (c < 3 || (sy = atoi(v[2])) <= 0) sy = sx;
if (c < 4 || (sz = atoi(v[3])) <= 0) sz = sy;
make_maze();
return 0;
}
[edit] C++
#include <windows.h>
#include <iostream>
#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;
}
//--------------------------------------------------------------------------------------------------
[edit] 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.
(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)
- Output:
╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳╳╳╳╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳ ╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳╳╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳ ╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳
Another solution using unicode line drawing chars. Assumes they are single width on console. Code pretty horribly unreadable.
(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)
- Output:
┼───┴───┼───┴───┴───┼───┴───┴───┼ │ │ │ │ ┼──── │ │ │ │ ┌───┐ ├ │ │ │ │ │ │ │ │ ┤ ┌───┘ │ │ │ │ │ ├ │ │ │ │ │ │ │ ┤ │ ┌───┘ ├───────┤ │ ├ │ │ │ │ │ │ ┤ │ │ ────┤ │ │ ────┼ │ │ │ │ │ │ ┤ ────┼───┐ │ │ └───┐ ├ │ │ │ │ │ │ ┼───┐ │ └───────┼───┐ └───┼ │ │ │ │ │ ┤ └──────────── │ └───┐ ├ │ │ │ ┼───┬───┬───┬───┬───┬───┬───┼───┼
[edit] D
import std.stdio, std.algorithm, std.range, std.random;
alias R = std.array.replicate;
void main() {
enum int w = 14, h = 10;
auto vis = new bool[][](h, w),
hor = iota(h + 1).map!(_ => ["+---"].R(w)).array,
ver = h.iota.map!(_ => ["| "].R(w) ~ "|").array;
void walk(in int x, in int y) /*nothrow*/ {
vis[y][x] = true;
static struct P { immutable uint x, y; } // Will wrap-around.
auto d = [P(x-1, y), P(x, y+1), P(x+1, y), P(x, y-1)];
foreach (p; d.randomCover(unpredictableSeed.Random)) {
if (p.x >= w || p.y >= h || vis[p.y][p.x]) continue;
if (p.x == x) hor[max(y, p.y)][x] = "+ ";
if (p.y == y) ver[y][max(x, p.x)] = " ";
walk(p.tupleof);
}
}
walk(uniform(0, w), uniform(0, h));
foreach (a, b; hor.zip(ver ~ []))
join(a ~ ["+\n"] ~ b).writeln;
}
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+---+ + +---+ + +---+---+---+ + + | | | | | | | | +---+---+---+---+---+---+---+ +---+ +---+ + +---+ | | | | | | + +---+---+---+ + + +---+ +---+---+ +---+---+ | | | | | | | | | +---+ + + + + +---+---+---+ + +---+ + + | | | | | | | | | + +---+ + +---+---+ + +---+---+---+ +---+ + | | | | | | + +---+---+ + +---+---+---+---+---+ +---+---+ + | | | | | | | | +---+ + +---+---+ + +---+ + + +---+---+ + | | | | | | | | + +---+---+---+ + +---+ +---+ + + +---+---+ | | | | | | | | | + + +---+---+---+---+ +---+ + +---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+
[edit] 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
- Output example (for 10x10 maze):
+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+---+---+ +---+ + + + | | | | | | | | + +---+ + + + + + +---+ + | | | | | | | | + + +---+ + +---+ + + +---+ | | | | | | | | + +---+---+ + + +---+ +---+---+ | | | | | | | + + +---+---+ + + + + + + | | | | | | | | | + + + + +---+ + +---+---+ + | | | | | | | + +---+ +---+---+---+ + + + + | | | | | | + +---+ +---+ + +---+ +---+ + | | | | | | | +---+ +---+ +---+---+---+---+ + + | | | +---+---+---+---+---+---+---+---+---+---+
[edit] F#
Using mutable state in the form of 2D arrays:
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()
- Output example:
+-+-+-+-+-+-+-+-+-+-+ | | | | + +-+-+-+-+ +-+ + + + | | | | | | + +-+-+ + +-+-+ +-+ + | | | | | +-+ +-+ +-+-+ +-+-+ + | | | | | + +-+ +-+ +-+-+-+ +-+ | | | | | | + + +-+ +-+ +-+ +-+ + | | | | | | | | + + +-+ + +-+-+-+ + + | | | | | +-+ + +-+-+-+-+-+-+ + | | | | | + +-+-+ +-+ +-+-+ + + | | | | | | + +-+ +-+ +-+-+ +-+-+ | | | +-+-+-+-+-+-+-+-+-+-+
[edit] 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)
}
- Output:
+---+---+---+---+---+---+ | | | | + + + +---+ +---+ | | | | | + + +---+---+---+ + | | | | + + + +---+---+ + | | | +---+---+---+---+---+---+
[edit] Haskell
import Control.Monad
import Control.Monad.ST
import Data.Array
import Data.Array.ST
import Data.STRef
import System.Random
rand :: Random a => (a, a) -> STRef s StdGen -> ST s a
rand range gen = do
(a, g) <- liftM (randomR range) $ readSTRef gen
gen `writeSTRef` g
return a
data Maze = Maze {rightWalls, belowWalls :: Array (Int, Int) Bool}
maze :: Int -> Int -> StdGen -> ST s Maze
maze width height gen = do
visited <- mazeArray False
rWalls <- mazeArray True
bWalls <- mazeArray True
gen <- newSTRef gen
liftM2 (,) (rand (0, maxX) gen) (rand (0, maxY) gen) >>=
visit gen visited rWalls bWalls
liftM2 Maze (freeze rWalls) (freeze bWalls)
where visit gen visited rWalls bWalls here = do
writeArray visited here True
let ns = neighbors here
i <- rand (0, length ns - 1) gen
forM_ (ns !! i : take i ns ++ drop (i + 1) ns) $ \there -> do
seen <- readArray visited there
unless seen $ do
removeWall here there
visit gen visited rWalls bWalls there
where removeWall (x1, y1) (x2, y2) = writeArray
(if x1 == x2 then bWalls else rWalls)
(min x1 x2, min y1 y2)
False
neighbors (x, y) =
(if x == 0 then [] else [(x - 1, y )]) ++
(if x == maxX then [] else [(x + 1, y )]) ++
(if y == 0 then [] else [(x, y - 1)]) ++
(if y == maxY then [] else [(x, y + 1)])
maxX = width - 1
maxY = height - 1
mazeArray = newArray ((0, 0), (maxX, maxY))
:: Bool -> ST s (STArray s (Int, Int) Bool)
printMaze :: Maze -> IO ()
printMaze (Maze rWalls bWalls) = do
putStrLn $ '+' : (concat $ replicate (maxX + 1) "---+")
forM_ [0 .. maxY] $ \y -> do
putStr "|"
forM_ [0 .. maxX] $ \x -> do
putStr " "
putStr $ if rWalls ! (x, y) then "|" else " "
putStrLn ""
forM_ [0 .. maxX] $ \x -> do
putStr "+"
putStr $ if bWalls ! (x, y) then "---" else " "
putStrLn "+"
where maxX = fst (snd $ bounds rWalls)
maxY = snd (snd $ bounds rWalls)
main = getStdGen >>= stToIO . maze 11 8 >>= printMaze
- Sample output:
+---+---+---+---+---+---+---+---+---+---+---+ | | | + +---+---+---+ +---+---+---+---+---+ + | | | | | | + +---+---+ +---+---+ + + + + + | | | | | | | | + + + +---+---+---+---+ +---+ + + | | | | | | +---+---+ + +---+---+---+---+ +---+---+ | | | | | | + + + + +---+---+---+ +---+ + + | | | | | | | + +---+---+ + +---+---+---+ +---+ + | | | | | + +---+---+---+---+ + +---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+---+
[edit] Icon and Unicon
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
$define BORDER 30 # border size in pixels
record mazeinfo(window,maze,filename) # keepers
procedure DisplayMaze(maze) #: show it off
if CELL < 8 then runerr(205,CELL) # too small
wh := (ch := (mh := *maze ) * CELL) + 2 * BORDER # win, cell, maze height
ww := (cw := (mw := *maze[1]) * CELL) + 2 * BORDER # win, cell, maze width
wparms := [ sprintf("Maze %dx%d",*maze,*maze[1]), # window parameters
"g","bg=white","canvas=hidden",
sprintf("size=%d,%d",ww,wh),
sprintf("dx=%d",BORDER),
sprintf("dy=%d",BORDER)]
&window := open!wparms | stop("Unable to open Window")
Fg("black") # Draw full grid
every DrawLine(x := 0 to cw by CELL,0,x,ch+1) # . verticals
every DrawLine(0,y := 0 to ch by CELL,cw+1,y) # . horizontals
Fg("white") # Set to erase lines
every y := CELL*((r := 1 to mh)-1) & x := CELL*((c := 1 to mw)-1) do {
WAttrib("dx="||x+BORDER,"dy="||y+BORDER) # position @ cell r,c
if iand(maze[r,c],NORTH) > 0 then DrawLine(2,0,CELL-1,0)
if iand(maze[r,c],EAST) > 0 then DrawLine(CELL,2,CELL,CELL-1)
if iand(maze[r,c],SOUTH) > 0 then DrawLine(2,CELL,CELL-1,CELL)
if iand(maze[r,c],WEST) > 0 then DrawLine(0,2,0,CELL-1)
}
return mazeinfo(&window,maze,sprintf("maze-%dx%d-%d.gif",r,c,&now))
end
Note: The underlying maze structure (matrix) is uni-directional from the start
printf.icn provides formatting
[edit] J
This algorithm allows almost no parallelism. So, while it might be "simple", generating very large mazes this way will not be necessarily efficient to implement on future (highly parallel) systems. That said, perhaps mazes with millions of cells are not very likely to be needed to be generated quickly.
But without any relevant grid support:
maze=:4 :0
assert.0<:n=.<:x*y
horiz=. 0$~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
)
The result of maze is a pair of arrays: one for open "doors" in the horizontal direction and the other for open "doors" in the vertical direction. The entry and exit doors are not represented by maze -- they are implicitly defined and are implemented in display.
- Example use (with ascii box drawing enabled):
display 8 maze 11
+ +---+---+---+---+---+---+---+---+---+---+
| | | | |
+ + + + +---+ + +---+---+ + +
| | | | | | | |
+ +---+---+ + +---+---+---+ + + +
| | | | | | |
+---+ +---+ + + +---+ + +---+---+
| | | | | | |
+ + +---+---+ +---+ + +---+---+ +
| | | | | | | | |
+ +---+ + + + + +---+---+ + +
| | | | |
+ +---+---+---+---+---+---+---+ +---+ +
| | | | | | | | |
+ + + + + + + + +---+ + +
| | | | |
+---+---+---+---+---+---+---+---+---+---+---+
[edit] Java
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();
}
}
- Output:
+---+---+---+---+---+---+---+---+---+---+ | | | | + +---+---+ +---+---+ + + +---+ | | | | | | | +---+---+ + + + +---+ +---+ + | | | | | | | + +---+---+ +---+ + +---+ + + | | | | | | | + + + +---+ +---+---+---+ + + | | | | | | + + +---+ + +---+---+ +---+---+ | | | | | | | + +---+ + +---+ +---+---+ + + | | | | | | +---+ + +---+ + +---+---+---+ + | | | | | | | + + +---+ + +---+---+ +---+ + | | | | | | | | + +---+ + +---+---+ + + + + | | | | +---+---+---+---+---+---+---+---+---+---+
[edit] JavaScript
function maze(x,y) {
var n=x*y-1;
if (n<0) {alert("illegal maze dimensions");return;}
var horiz=[]; for (var j= 0; j<x+1; j++) horiz[j]= [];
var verti=[]; for (var j= 0; j<y+1; j++) verti[j]= [];
var here= [Math.floor(Math.random()*x), Math.floor(Math.random()*y)];
var path= [here];
var unvisited= [];
for (var j= 0; j<x+2; j++) {
unvisited[j]= [];
for (var k= 0; k<y+1; k++)
unvisited[j].push(j>0 && j<x+1 && k>0 && (j != here[0]+1 || k != here[1]+1));
}
while (0<n) {
var potential= [[here[0]+1, here[1]], [here[0],here[1]+1],
[here[0]-1, here[1]], [here[0],here[1]-1]];
var neighbors= [];
for (var j= 0; j < 4; j++)
if (unvisited[potential[j][0]+1][potential[j][1]+1])
neighbors.push(potential[j]);
if (neighbors.length) {
n= n-1;
next= neighbors[Math.floor(Math.random()*neighbors.length)];
unvisited[next[0]+1][next[1]+1]= false;
if (next[0] == here[0])
horiz[next[0]][(next[1]+here[1]-1)/2]= true;
else
verti[(next[0]+here[0]-1)/2][next[1]]= true;
path.push(here= next);
} else
here= path.pop();
}
return ({x: x, y: y, horiz: horiz, verti: verti});
}
function display(m) {
var text= [];
for (var j= 0; j<m.x*2+1; j++) {
var line= [];
if (0 == j%2)
for (var k=0; k<m.y*4+1; k++)
if (0 == k%4)
line[k]= '+';
else
if (j>0 && m.verti[j/2-1][Math.floor(k/4)])
line[k]= ' ';
else
line[k]= '-';
else
for (var k=0; k<m.y*4+1; k++)
if (0 == k%4)
if (k>0 && m.horiz[(j-1)/2][k/4-1])
line[k]= ' ';
else
line[k]= '|';
else
line[k]= ' ';
if (0 == j) line[1]= line[2]= line[3]= ' ';
if (m.x*2-1 == j) line[4*m.y]= ' ';
text.push(line.join('')+'\r\n');
}
return text.join('');
}
Variable meanings in function maze:
-
x,y— dimensions of maze -
n— number of openings to be generated -
horiz— two dimensional array of locations of horizontal openings (true means wall is open) -
verti— two dimensional array of locations of vertical openings (true means wall is open) -
here— current location under consideration -
path— history (stack) of locations that might need to be revisited -
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) -
potential— locations adjacent tohere -
neighbors— unvisited locations adjacent tohere
Variable meanings in function display:
-
m— maze to be drawn -
text— lines of text representing maze -
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:
<html><head><title></title></head><body><pre id="out"></pre></body></html>
<script type="text/javascript">
/* ABOVE CODE GOES HERE */
document.getElementById('out').innerHTML= display(maze(8,11));
</script>
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:
function step() {
if (0<n) {
And replace the closing brace for this while loop with:
document.getElementById('out').innerHTML= display({x: x, y: y, horiz: horiz, verti: verti, here: here});
setTimeout(step, 100);
}
}
step();
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
if (m.here && m.here[0]*2+1 == j && m.here[1]*4+2 == k)
line[k]= '#'
else if (0 == k%4) {
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:
here= next;
if (1 < neighbors.length)
path.push(here);
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.
[edit] HTML Table
Using HTML, CSS and table cells for maze.
<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><table id='maze'/></body></html>
[edit] 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]
- Output:
[edit] Graph
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.
MazeGraph[m_, n_] :=
Block[{$RecursionLimit = Infinity, grid = GridGraph[{m, n}],
visited = {}},
Graph[Range[m n], Reap[{AppendTo[visited, #];
Do[
If[FreeQ[visited, neighbor],
Sow[# <-> neighbor]; #0@neighbor], {neighbor,
RandomSample@AdjacencyList[grid, #]}]} &@
RandomChoice@VertexList@grid][[2, 1]],
GraphLayout -> {"GridEmbedding", "Dimension" -> {m, n}}]];
maze = MazeGraph[13, 21]
- Output:
[edit] 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;
[edit] OCaml
let seen = Hashtbl.create 7Output from 'ocaml gen_maze.ml 10 10':
let mark t = Hashtbl.add seen t true
let marked t = Hashtbl.mem seen t
let walls = Hashtbl.create 7
let ord a b = if a <= b then (a,b) else (b,a)
let join a b = Hashtbl.add walls (ord a b) true
let joined a b = Hashtbl.mem walls (ord a b)
let () =
let nx = int_of_string Sys.argv.(1) in
let ny = int_of_string Sys.argv.(2) in
let rec random_order = function
| [] -> []
| [a] -> [a]
| x -> let i = Random.int (List.length x) in
let rec del i = function
| [] -> failwith "del"
| h::t -> if i = 0 then t else h :: del (i-1) t in
(List.nth x i) :: random_order (del i x) in
let get_neighbours (x,y) =
let lim n k = (0 <= k) && (k < n) in
let bounds (x,y) = lim nx x && lim ny y in
List.filter bounds [(x-1,y);(x+1,y);(x,y-1);(x,y+1)] in
let rec visit cell =
mark cell;
let check k =
if not (marked k) then (join cell k; visit k) in
List.iter check (random_order (get_neighbours cell)) in
let print_maze () =
begin
for i = 1 to nx do print_string "+---";done; print_endline "+";
let line n j k l s t u =
for i = 0 to n do print_string (if joined (i,j) (i+k,j+l) then s else t) done;
print_endline u in
for j = 0 to ny-2 do
print_string "| ";
line (nx-2) j 1 0 " " "| " "|";
line (nx-1) j 0 1 "+ " "+---" "+";
done;
print_string "| ";
line (nx-2) (ny-1) 1 0 " " "| " "|";
for i = 1 to nx do print_string "+---";done; print_endline "+";
end in
Random.self_init();
visit (Random.int nx, Random.int ny);
print_maze ();
+---+---+---+---+---+---+---+---+---+---+ | | | | + +---+ +---+ + +---+ +---+ + | | | | | | + + +---+ +---+---+ +---+---+ + | | | | | | + + +---+ + +---+ +---+---+---+ | | | | | | | +---+---+ + + +---+---+ +---+ + | | | | | + +---+---+ +---+---+---+---+ +---+ | | | | | + +---+---+---+ + +---+ +---+ + | | | | | | +---+---+---+ +---+---+ +---+ + + | | | | | | + +---+ +---+ + + + +---+ + | | | | | | | +---+ + +---+ +---+---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+
[edit] Perl
use List::Util 'max';
my ($w, $h) = @ARGV;
$w ||= 26;
$h ||= 127;
my $avail = $w * $h;
# 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;
}
Run as maze.pl [width] [height] or use default dimensions.
- Sample 4 x 1 output:
+--+--+--+--+ | | +--+--+--+--+
[edit] Perl 6
Supply a width and height and optionally the x,y grid coords for the starting cell. If no starting cell is supplied, a random one will be selected automatically. 0,0 is the top left corner.
constant mapping = :OPEN(' '),
:N< ╵ >,
:E< ╶ >,
:NE< └ >,
:S< ╷ >,
:NS< │ >,
:ES< ┌ >,
:NES< ├ >,
:W< ╴ >,
:NW< ┘ >,
:EW< ─ >,
:NEW< ┴ >,
:SW< ┐ >,
:NSW< ┤ >,
:ESW< ┬ >,
:NESW< ┼ >,
:TODO< x >,
:TRIED< · >;
enum Code (mapping.map: *.key);
my @code = mapping.map: *.value;
enum Direction <DeadEnd Up Right Down Left>;
sub gen_maze ( $X,
$Y,
$start_x = (^$X).pick * 2 + 1,
$start_y = (^$Y).pick * 2 + 1 )
{
my @maze;
push @maze, [ ES, -N, (ESW, EW) xx $X - 1, SW ];
push @maze, [ (NS, TODO) xx $X, NS ];
for 1 ..^ $Y {
push @maze, [ NES, EW, (NESW, EW) xx $X - 1, NSW ];
push @maze, [ (NS, TODO) xx $X, NS ];
}
push @maze, [ NE, (EW, NEW) xx $X - 1, -NS, NW ];
@maze[$start_y][$start_x] = OPEN;
my @stack;
my $current = [$start_x, $start_y];
loop {
if my $dir = pick_direction( $current ) {
@stack.push: $current;
$current = move( $dir, $current );
}
else {
last unless @stack;
$current = @stack.pop;
}
}
return @maze;
sub pick_direction([$x,$y]) {
my @neighbors =
(Up if @maze[$y - 2][$x]),
(Down if @maze[$y + 2][$x]),
(Left if @maze[$y][$x - 2]),
(Right if @maze[$y][$x + 2]);
@neighbors.pick or DeadEnd;
}
sub move ($dir, @cur) {
my ($x,$y) = @cur;
given $dir {
when Up { @maze[--$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y--][$x+1] -= W; }
when Down { @maze[++$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y++][$x+1] -= W; }
when Left { @maze[$y][--$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x--] -= N; }
when Right { @maze[$y][++$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x++] -= N; }
}
@maze[$y][$x] = 0;
[$x,$y];
}
}
sub display (@maze) {
for @maze -> @y {
for @y -> $w, $c {
print @code[abs $w];
if $c >= 0 { print @code[$c] x 3 }
else { print ' ', @code[abs $c], ' ' }
}
say @code[@y[*-1]];
}
}
display gen_maze( 29, 19 );
- Output:
┌ ╵ ────────────────────────────┬───────────────────────────────────────────┬───────────┬───────────────────────────┐ │ │ │ │ │ │ ╶───────────┬───────────┐ │ ┌───────────────────────╴ ┌───────┐ ├───╴ ╷ │ ┌───────────┬───┬───╴ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───────┐ ╵ ┌───┐ ├───┘ │ ┌───────────┬───────────┤ ╶───┤ │ ╶───┴───┤ │ ┌───┐ │ │ ╶───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ └───────┤ │ ╵ ┌───┘ │ ╷ ╶───┤ ┌───┐ │ ╷ │ ├───────╴ │ ╵ │ │ │ └───┐ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┬───────┐ │ ├───────┤ ╶───┤ └───┐ ╵ │ │ ╵ │ ╵ │ ┌───┐ └───┬───┘ │ │ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╶───┤ ╷ ╵ │ ╵ ╷ └───┐ ├───┐ ├───────┤ └───────┴───────┘ │ └───┐ └───╴ │ ╵ ├───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───╴ │ ├───────┴───┐ ├───╴ │ │ │ ╵ ╷ └───┐ ╶───┬───────┬───┘ ┌───┴───────╴ │ ┌───┘ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╷ │ │ ╶───┐ └───┤ ╷ │ │ └───────┴───┐ └───╴ │ ╷ ╵ ╷ ╵ ╶───────┬───┤ │ ┌───┴───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╷ ├───╴ ╵ │ │ │ ┌───────┐ └───────────┤ └───┬───┴───────────┐ ╵ │ │ ╵ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───┘ │ ┌───────┴───┘ │ ╵ ┌───┴───────╴ ╷ ├───┐ │ ╶───────┐ └───┐ │ └───┬───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───┘ │ ┌───┘ │ ┌───┬───────┼───╴ │ ╶───┬───────┤ ╵ │ └───┬───╴ ├───┐ │ └───┐ │ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───────┘ ├───────┤ │ ╵ ╷ │ ┌───┴───┐ │ ╶───┘ ┌───┴───╴ │ ┌───┘ │ │ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ ╷ │ ╷ │ └───┐ │ ╵ │ ╷ ╵ ├───────┐ │ ╶───────┤ └───┐ │ └───┤ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────────┤ │ │ └───╴ │ └───────┤ └───────┘ ╷ └───┴───┬───╴ ├───╴ │ └───┐ │ │ ╶───┴───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───╴ │ │ ├───╴ ┌───┴───────┬───┴───┐ ┌───────┴───────┐ ╵ ┌───┤ ╶───┤ ╷ │ ╵ └───┬───╴ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╶───┘ │ │ ╶───┤ ╶───┐ ╵ ╷ │ └───╴ ┌───╴ └───────┘ ├───╴ │ ├───┴───────┬───┘ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┬───┘ ├───────┴───┐ ├───────┤ └───────────┤ ┌───────────┐ │ ┌───┘ │ ╶───┐ ╵ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ │ ╷ │ ╶───┐ ╵ │ ╷ └───────────┐ │ │ ┌───┐ └───┘ │ ╶───┴───┐ └───────┴───────┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────╴ │ └───┴───╴ └───────┴───┴───────────╴ │ └───┘ ╵ └───────────┴───╴ ╷ └───────────────┐ │ │ │ │ │ │ │ └───────────┴───────────────────────────────────────────┴───────────────────────────────────┴───────────────────┴ │ ┘
[edit] PicoLisp
This solution uses 'grid' from "lib/simul.l" to generate the two-dimensional structure.
(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) " ")) )
- Output:
: (display (maze 11 8))
+ +---+---+---+---+---+---+---+---+---+---+
8 | | | |
+ + + + + + +---+ +---+---+ +
7 | | | | | | | | |
+---+ +---+---+ + + +---+ + + +
6 | | | | | | | |
+ +---+ +---+ +---+---+---+ + +---+
5 | | | | | |
+---+ +---+ +---+---+---+ +---+---+ +
4 | | | | | | |
+ +---+ +---+ +---+ + + +---+ +
3 | | | | | | | |
+ +---+---+ + + + + +---+ + +
2 | | | | | | | | |
+ + + +---+ + +---+ + +---+ +
1 | | | |
+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j k
[edit] Prolog
Works with SWI-Prolog and XPCE.
:- 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).
- Output:
[edit] 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
#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
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 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+ + +---+ + +---+ + + | | | | | | | | + +---+ +---+---+ +---+ + +---+---+ | | | | | | + + +---+---+ +---+---+---+---+---+ + | | | | | | + +---+ +---+ + +---+ + +---+---+ | | | | | | +---+---+---+ + + +---+---+ +---+ + | | | | | | + +---+---+ +---+ +---+---+ + +---+ | | | | | | | + + + +---+---+---+ + +---+---+ + | | | | +---+---+---+---+---+---+---+---+---+---+---+
[edit] Python
from random import shuffle, randrange
def make_maze(w = 16, h = 8):
vis = [[0] * w + [1] for _ in range(h)] + [[1] * (w + 1)]
ver = [["| "] * w + ['|'] for _ in range(h)] + [[]]
hor = [["+--"] * w + ['+'] for _ in range(h + 1)]
def walk(x, y):
vis[y][x] = 1
d = [(x - 1, y), (x, y + 1), (x + 1, y), (x, y - 1)]
shuffle(d)
for (xx, yy) in d:
if vis[yy][xx]: continue
if xx == x: hor[max(y, yy)][x] = "+ "
if yy == y: ver[y][max(x, xx)] = " "
walk(xx, yy)
walk(randrange(w), randrange(h))
for (a, b) in zip(hor, ver):
print(''.join(a + ['\n'] + b))
make_maze()
- Output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | | | | | | + + + + + + + + +--+--+--+--+--+ +--+ + | | | | | | | | | | +--+ +--+--+ + +--+--+--+ + +--+ +--+--+ + | | | | | | | | | | + +--+ +--+ + + + + + +--+ + + +--+--+ | | | | | | | | | | + +--+ +--+--+ + +--+ +--+--+ +--+--+ + + | | | | | | | | +--+ + + +--+--+--+ +--+--+--+--+--+--+--+ + | | | | | | | | + +--+--+ +--+--+ +--+--+ +--+ +--+ + + + | | | | | | | | + +--+ +--+--+--+ + +--+--+--+--+ +--+ + + | | | | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
[edit] Racket
Maze generator
#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))
Printing out the maze
;; 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))
Example:
-> (define m (build-maze 10 7)) -> (show-maze m) +---+---+---+---+---+---+---+---+---+---+ | | | | | + +---+---+ + + +---+ +---+ + | | | | | | | + + +---+ + +---+ +---+---+ + | | | | | | | + +---+ +---+---+ +---+---+ + + | | | | | | + + +---+---+---+ + + +---+ + | | | | | | | +---+ + +---+ +---+ + + +---+ | | | | | | | + +---+ + +---+ +---+---+---+ + | | | +---+---+---+---+---+---+---+---+---+---+
[edit] Rascal
import IO;
import util::Math;
import List;
public void make_maze(int w, int h){
vis = [[0 | _ <- [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));
}
}
rascal>make_maze(10,10) +--+--+--+--+--+--+--+--+--+--+ | | | | + +--+ +--+ +--+--+--+ + + | | | | | | | + + +--+ +--+--+--+ + + + | | | | | | | + +--+--+ + + +--+--+--+ + | | | | | + +--+--+--+ + + +--+--+--+ | | | | | | + +--+ +--+--+ + + +--+ + | | | | | | + + +--+ +--+--+ +--+--+ + | | | | | | | | +--+ + +--+ +--+ + + + + | | | | | | + + +--+ +--+--+--+--+ + + | | | | | | | | + +--+ +--+ + + + + + + | | | | | +--+--+--+--+--+--+--+--+--+--+ ok
[edit] REXX
In order to preserve the aspect ratio (for most display terminals), several changestr instructions and
some other instructions were added to increase the horizontal dimension (columns).
/*REXX program to generate and display a (rectangular) maze. */
height=0; @.=0 /*default for all cells visited.*/
parse arg rows cols seed . /*allow user to specify maze size*/
if rows='' | rows==',' then rows=19 /*No rows given? Use the default*/
if cols='' | cols==',' then cols=19 /*No cols given? Use the default*/
if seed\=='' then call random ,,seed /*use a seed for repeatability. */
call buildRow '┌'copies('─┬',cols-1)'─┐'
/*(below) build maze's grid & pop*/
do r=1 for rows; _=; __=; hp= '|'; hj='├'
do c=1 for cols; _= _||hp'1'; __=__||hj'─'; hj='┼'; hp='│'
end /*c*/
call buildRow _'│'
if r\==rows then call buildRow __'┤'
end /*r*/
call buildRow '└'copies('─┴',cols-1)'─┘'
r!=random(1,rows)*2; c!=random(1,cols)*2; @.r!.c!=0 /*choose 1st cell*/
do forever; n=hood(r!,c!); if n==0 then if \fcell() then leave
call ?; @._r._c=0
ro=r!; co=c!; r!=_r; c!=_c
?.zr=?.zr%2; ?.zc=?.zc%2
rw=ro+?.zr; cw=co+?.zc
@.rw.cw='·'
end /*forever*/
do r=1 for height; _= /*display the maze. */
do c=1 for cols*2 + 1; _=_ || @.r.c; end
if r//2 then _=translate(_,'-','fa'x) /*translate to minus*/
_=translate(_,'\','fa'x) /*trans to backslash*/
_=changestr(1,_,111) /*these four ────────────────────*/
_=changestr(0,_,000) /*─── statements are ────────────*/
_=changestr('-',_," ") /*──────── used for preserving ──*/
_=changestr('─',_,"───") /*──────────── the aspect ratio. */
say translate(_,'│',"|\10") /*make it presentable for screen.*/
end /*r*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────FCELL subroutine────────────────────*/
fcell: do r=1 for rows; r2=r+r
do c=1 for cols; c2=c+c
if hood(r2,c2)==1 then do; r!=r2; c!=c2; @.r!.c!=0; return 1
end
end /*c*/
end /*r*/
return 0
/*──────────────────────────────────@ subroutine────────────────────────*/
@: parse arg _r,_c; return @._r._c
/*──────────────────────────────────? subroutine────────────────────────*/
?: do forever; ?.=0; ?=random(1,4)
if ?==1 then ?.zc=-2 /*north*/
if ?==2 then ?.zr=+2 /* east*/
if ?==3 then ?.zc=+2 /*south*/
if ?==4 then ?.zr=-2 /* west*/
_r=r!+?.zr; _c=c!+?.zc; if @._r._c==1 then return
end /*forever*/
/*──────────────────────────────────HOOD subroutine─────────────────────*/
hood: parse arg rh,ch; return @(rh+2,ch)+@(rh-2,ch)+@(rh,ch-2)+@(rh,ch+2)
/*──────────────────────────────────BUILDROW subroutine─────────────────*/
buildRow: parse arg z; height=height+1; width=length(z)
do c=1 for width; @.height.c=substr(z,c,1); end; return
Some older REXXes don't have a changestr bif, so one is included here ──► CHANGESTR.REX.
output when using the input: 10 10
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐ │ │ │ │ │ ├ ┼ ┼───┼───┼ ┼ ┼───┼───┼ ┼ ┤ │ │ │ │ │ │ │ ├ ┼ ┼ ┼ ┼───┼───┼ ┼ ┼───┼ ┤ │ │ │ │ │ │ │ │ │ ├ ┼ ┼ ┼ ┼───┼ ┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ │ │ ├ ┼ ┼ ┼───┼───┼───┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ ├ ┼───┼───┼───┼───┼ ┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ │ ├───┼ ┼───┼ ┼ ┼───┼ ┼───┼ ┼ ┤ │ │ │ │ │ │ ├ ┼───┼ ┼───┼───┼ ┼───┼───┼───┼ ┤ │ │ │ │ │ ├ ┼ ┼───┼───┼───┼───┼ ┼───┼───┼ ┤ │ │ │ │ │ │ ├ ┼───┼ ┼───┼───┼ ┼ ┼ ┼ ┼───┤ │ │ │ │ │ └───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
[edit] 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[y][x] is true if there is a wall between
# (x,y) and (x+1,y). The additional entry makes printing
# easier.
@vertical_walls = Array.new(height) { Array.new(width, true) }
@horizontal_walls = Array.new(height) { Array.new(width, true) }
# Path for the solved maze.
@path = Array.new(height) { Array.new(width) }
# "Hack" to print the exit.
@horizontal_walls[@end_y][@end_x] = false
reset_visiting_state
# Generate the maze.
generate
end
# Print a nice ASCII maze.
def print
# Special handling: print the top line.
line = "+"
for x in (0...@width)
line.concat(x == @start_x ? " +" : "---+")
end
puts line
# For each cell, print the right and bottom wall, if it exists.
for y in (0...@height)
line = "|"
for x in (0...@width)
line.concat(@path[y][x] ? " o " : " ")
line.concat(@vertical_walls[y][x] ? "|" : " ")
end
puts line
line = "+"
for x in (0...@width)
line.concat(@horizontal_walls[y][x] ? "---+" : " +")
end
puts line
end
end
private
# Reset the VISITED state of all cells.
def reset_visiting_state
@visited = Array.new(@height) { Array.new(@width) }
end
# Check whether the given coordinate is within the valid range.
def coordinate_valid?(x, y)
(x >= 0) && (y >= 0) && (x < @width) && (y < @height)
end
# Is the given coordinate valid and the cell not yet visited?
def move_valid?(x, y)
coordinate_valid?(x, y) && !@visited[y][x]
end
# Generate the maze.
def generate
generate_visit_cell @start_x, @start_y
reset_visiting_state
end
# Depth-first maze generation.
def generate_visit_cell(x, y)
# Mark cell as visited.
@visited[y][x] = true
# Randomly get coordinates of surrounding cells (may be outside
# of the maze range, will be sorted out later).
coordinates = []
for dir in DIRECTIONS.shuffle
coordinates << [ x + dir[0], y + dir[1] ]
end
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 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[ [y1, y2].min ][x1] = false
else
# Cells must be next to each other, remove a vertical
# wall.
@vertical_walls[y1][ [x1, x2].min ] = false
end
end
end
# Demonstration:
maze = Maze.new 20, 10
maze.print
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+ | | | | | | | | + +---+ +---+ + + +---+---+---+ + + +---+ + +---+ +---+ + | | | | | | | | | | | | | | + + + +---+---+ + + +---+ +---+ +---+ +---+---+ + + +---+ | | | | | | | | | | | | + + +---+---+ +---+---+ + +---+---+ + +---+ + + +---+---+ + | | | | | | | | | | + +---+---+ +---+---+ + +---+---+ +---+---+ +---+ +---+---+---+ + | | | | | | | | | | +---+---+ +---+ + + +---+ + + +---+---+---+---+ +---+ + + + | | | | | | | | | | + + +---+ +---+---+---+---+---+ +---+---+ + +---+---+ +---+---+---+ | | | | | | | | | | | + +---+ +---+---+---+---+---+ + +---+ + +---+ + + +---+---+ + | | | | | | | | | | + + +---+---+ + + +---+---+---+---+ +---+ +---+---+ + +---+---+ | | | | | | | | | | + + +---+ +---+ +---+ + +---+---+---+ +---+ +---+---+---+---+ + | | | | | +---+---+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+---+
[edit] Tcl
package require TclOO; # Or Tcl 8.6
# Helper to pick a random number
proc rand n {expr {int(rand() * $n)}}
# Helper to pick a random element of a list
proc pick list {lindex $list [rand [llength $list]]}
# 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]
}
}
# Demonstration
maze create m 11 8
puts [m view]
- Output:
+ +---+---+---+---+---+---+---+---+---+---+ | | | | +---+---+ +---+---+ + +---+ +---+ + | | | | | | + + +---+ +---+---+ +---+ + + + | | | | | | | | + +---+ +---+---+---+ + + + + + | | | | | | | | + + + + +---+---+ + +---+---+ + | | | | | | | | +---+---+---+---+ + +---+ + + +---+ | | | | | | | | + +---+---+ + + + + + +---+ + | | | | | | | | +---+ + +---+---+---+---+ + +---+ + | | +---+---+---+---+---+---+---+---+---+---+---+
[edit] 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 " ");
];
]
Output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| | | |
+ +--+ +--+ +--+--+--+ + +--+ + +--+--+--+--+--+--+ +
| | | | | | | | | | | |
+ + + + +--+ + +--+--+ + +--+--+ +--+--+ +--+ +--+
| | | | | | | | | | |
+ +--+--+ + +--+ + +--+--+--+--+--+--+ + +--+ +--+ +
| | | | | | | | | |
+--+ + +--+--+ + + + +--+--+ + +--+--+--+--+--+--+ +
| | | | | | | | | | | | |
+ + + + +--+--+ + + + + +--+--+ + + + + +--+--+
| | | | | |
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
