Maze generation
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.
Ada
mazes.ads: <lang Ada>generic
Height : Positive; Width : Positive;
package Mazes is
type Maze_Grid is private;
procedure Initialize (Maze : in out Maze_Grid);
procedure Put (Item : Maze_Grid);
private
type Directions is (North, South, West, East);
type Cell_Walls is array (Directions) of Boolean;
type Cells is record
Walls : Cell_Walls := (others => True);
Visited : Boolean := False;
end record;
subtype Height_Type is Positive range 1 .. Height; subtype Width_Type is Positive range 1 .. Width;
type Maze_Grid is array (Height_Type, Width_Type) of Cells;
end Mazes;</lang>
mazes.adb: <lang Ada>with Ada.Numerics.Discrete_Random; with Ada.Text_IO;
package body Mazes is
package RNG is new Ada.Numerics.Discrete_Random (Positive); package Random_Direction is new Ada.Numerics.Discrete_Random (Directions);
Generator : RNG.Generator; Dir_Generator : Random_Direction.Generator;
function "-" (Dir : Directions) return Directions;
procedure Depth_First_Algorithm
(Maze : in out Maze_Grid;
Row : Height_Type;
Column : Width_Type);
function Has_Unvisited_Neighbours
(Maze : Maze_Grid;
Row : Height_Type;
Column : Width_Type)
return Boolean;
procedure Move
(Row : in out Height_Type;
Column : in out Width_Type;
Direction : Directions;
Valid_Move : out Boolean);
function "-" (Dir : Directions) return Directions is
begin
case Dir is
when North =>
return South;
when South =>
return North;
when East =>
return West;
when West =>
return East;
end case;
end "-";
procedure Depth_First_Algorithm
(Maze : in out Maze_Grid;
Row : Height_Type;
Column : Width_Type)
is
Next_Row : Height_Type;
Next_Column : Width_Type;
Next_Direction : Directions;
Valid_Direction : Boolean;
begin
-- mark as visited
Maze (Row, Column).Visited := True;
-- continue as long as there are unvisited neighbours left
while Has_Unvisited_Neighbours (Maze, Row, Column) loop
-- use random direction
Next_Direction := Random_Direction.Random (Dir_Generator);
Next_Row := Row;
Next_Column := Column;
Move (Next_Row, Next_Column, Next_Direction, Valid_Direction);
if Valid_Direction then
-- connect the two cells
if not Maze (Next_Row, Next_Column).Visited then
Maze (Row, Column).Walls (Next_Direction) :=
False;
Maze (Next_Row, Next_Column).Walls (-Next_Direction) :=
False;
Depth_First_Algorithm (Maze, Next_Row, Next_Column);
end if;
end if;
end loop;
end Depth_First_Algorithm;
function Has_Unvisited_Neighbours
(Maze : Maze_Grid;
Row : Height_Type;
Column : Width_Type)
return Boolean
is
Neighbour_Row : Height_Type;
Neighbour_Column : Width_Type;
Is_Valid : Boolean;
begin
for Dir in Directions loop
Neighbour_Row := Row;
Neighbour_Column := Column;
Move
(Row => Neighbour_Row,
Column => Neighbour_Column,
Direction => Dir,
Valid_Move => Is_Valid);
if Is_Valid
and then not Maze (Neighbour_Row, Neighbour_Column).Visited
then
return True;
end if;
end loop;
return False;
end Has_Unvisited_Neighbours;
procedure Initialize (Maze : in out Maze_Grid) is
Row, Column : Positive;
begin
-- initialize random generators
RNG.Reset (Generator);
Random_Direction.Reset (Dir_Generator);
-- choose starting cell
Row := RNG.Random (Generator) mod Height + 1;
Column := RNG.Random (Generator) mod Width + 1;
Ada.Text_IO.Put_Line
("Starting generation at " &
Positive'Image (Row) &
" x" &
Positive'Image (Column));
Depth_First_Algorithm (Maze, Row, Column);
end Initialize;
procedure Move
(Row : in out Height_Type;
Column : in out Width_Type;
Direction : Directions;
Valid_Move : out Boolean)
is
begin
Valid_Move := False;
case Direction is
when North =>
if Row > Height_Type'First then
Valid_Move := True;
Row := Row - 1;
end if;
when East =>
if Column < Width_Type'Last then
Valid_Move := True;
Column := Column + 1;
end if;
when West =>
if Column > Width_Type'First then
Valid_Move := True;
Column := Column - 1;
end if;
when South =>
if Row < Height_Type'Last then
Valid_Move := True;
Row := Row + 1;
end if;
end case;
end Move;
procedure Put (Item : Maze_Grid) is
begin
for Row in Item'Range (1) loop
if Row = Item'First (1) then
for Col in Item'Range (2) loop
if Col = Item'First (2) then
Ada.Text_IO.Put ('+');
end if;
if Item (Row, Col).Walls (North) then
Ada.Text_IO.Put ("---");
else
Ada.Text_IO.Put (" ");
end if;
Ada.Text_IO.Put ('+');
end loop;
Ada.Text_IO.New_Line;
end if;
for Col in Item'Range (2) loop
if Col = Item'First (2) then
if Item (Row, Col).Walls (West) then
Ada.Text_IO.Put ('|');
else
Ada.Text_IO.Put (' ');
end if;
elsif Item (Row, Col).Walls (West)
and then Item (Row, Col - 1).Walls (East)
then
Ada.Text_IO.Put ('|');
elsif Item (Row, Col).Walls (West)
or else Item (Row, Col - 1).Walls (East)
then
Ada.Text_IO.Put ('>');
else
Ada.Text_IO.Put (' ');
end if;
if Item (Row, Col).Visited then
Ada.Text_IO.Put (" ");
else
Ada.Text_IO.Put ("???");
end if;
if Col = Item'Last (2) then
if Item (Row, Col).Walls (East) then
Ada.Text_IO.Put ('|');
else
Ada.Text_IO.Put (' ');
end if;
end if;
end loop;
Ada.Text_IO.New_Line;
for Col in Item'Range (2) loop
--for Col in Item'Range (2) loop
if Col = Item'First (2) then
Ada.Text_IO.Put ('+');
end if;
if Item (Row, Col).Walls (South) then
Ada.Text_IO.Put ("---");
else
Ada.Text_IO.Put (" ");
end if;
Ada.Text_IO.Put ('+');
--end loop;
end loop;
Ada.Text_IO.New_Line;
end loop;
end Put;
end Mazes;</lang>
Example main.adb: <lang Ada>with Mazes; procedure Main is
package Small_Mazes is new Mazes (Height => 8, Width => 11); My_Maze : Small_Mazes.Maze_Grid;
begin
Small_Mazes.Initialize (My_Maze); Small_Mazes.Put (My_Maze);
end Main;</lang>
Output:
Starting generation at 3 x 7 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + + +---+ + + +---+---+---+ + | | | | | | | + +---+---+ +---+---+ + + + +---+ | | | | | | | | + +---+---+---+---+ +---+ + + + + | | | | | | | + + +---+ + + + +---+---+---+ + | | | | | | | + + +---+---+---+---+---+ +---+ + + | | | | | | +---+ + +---+---+---+ +---+---+---+ + | | | | | + +---+ +---+---+ +---+---+---+---+---+ | | +---+---+---+---+---+---+---+---+---+---+---+
AutoHotkey
For a challenge, this maze generation is entirely string based. That is to say, all operations including the wall removal and retrieval of cell states are done on the output string. <lang AHK>; Initially build the board Width := 11 Height := 8 Loop % height*2+1 { Outer := A_Index Loop % Width maze .= Outer & 1 ? "+-" : "|0" maze .= (Outer & 1 ? "+" : "|") "`n" } StringTrimRight, maze, maze, 1 ; removes trailing newline Clipboard := Walk(maze)
Walk(S, x=0, y=0){ If !x{ ; --Start at a random cell... StringReplace, junk, S, `n,,UseErrorLevel ; Calculate rows Random, y, 1, ErrorLevel//2 Random, x, 1, InStr(S, "`n")//2-1 ; Calculate height }
; --Obtain a list of its neighbors... neighbors := x "," y+1 "`n" x "," y-1 "`n" x+1 "," y "`n" x-1 "," y ; --Randomize the list... Sort neighbors, random
; --Then for each neighbor... Loop Parse, neighbors, `n { pC := InStr(A_LoopField, ","), x2 := SubStr(A_LoopField, 1, pC-1), y2 := SubStr(A_LoopField, pC+1) ; If it has not been visited... If GetChar(S, 2*x2, 2*y2) = "0"{ ; Mark it as visited... S := ChangeChar(s, 2*x2, 2*y2, " ") ; Remove the wall between this cell and the neighbor... S := ChangeChar(S, x+x2, y+y2, " ") ; Then recurse with the neighbor as the current cell S := Walk(S, x2, y2) } } return S }
- Change a character in a string using x and y coordinates
ChangeChar(s, x, y, c){ Loop Parse, s, `n { If (A_Index = Y) Loop Parse, A_LoopField If (A_Index = x) out .= c Else out .= A_LoopField Else out .= A_LoopField out .= "`n" } StringTrimRight, out, out, 1 return out }
- retrieve a character in a string using x and y coordinates
GetChar(s, x, y, n=1){ x*=n, y*=n Loop Parse, s, `n If (A_Index = Y) return SubStr(A_LoopField, x, 1) }</lang> Sample output:
+-+-+-+-+-+-+-+-+-+-+-+ | | | | +-+ +-+-+ +-+ + + +-+-+ | | | | | + +-+ +-+ +-+-+ +-+ + + | | | | | | | | + + +-+-+ + + +-+ +-+ + | | | | | | | + +-+ + +-+-+-+ +-+ + + | | | | | | + +-+-+-+-+-+ +-+-+-+ + | | | | | | + + + + +-+-+-+ + + +-+ | | | | | | | +-+-+-+-+ +-+ + +-+-+ + | | | +-+-+-+-+-+-+-+-+-+-+-+
C
Generation/solver in one. Requires UTF8 locale and unicode capable console. If your console font line-drawing chars are single width, define DOUBLE_SPACE to 0. <lang c>#include <stdio.h>
- 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; }</lang>default output<lang>┌───┬─────┬─────────┬───────┬───┐ │┄┄╮│╭┄┄┄╮│ ╭┄┄┄┄┄╮│ ╭┄┄┄╮│╭┄╮│ │ │┆│┆──┐┆│ │┆──┬─┐┆└──┆┌─┐┆│┆│┆│ │ │┆│╰┄╮│┆│ │╰┄╮│ │╰┄┄┄╯│ │╰┄╯│┆│ │ │┆└──┆│┆└─┼──┆│ └─────┤ └─┬─┘┆│ │ │╰┄┄┄╯│╰┄╮│╭┄╯│ │ │╭┄╯│ │ └─────┴─┐┆│┆┌─┴───┐ │ │ │ │┆──┤ │ │┆│┆│╭┄┄┄╮│ │ │ │╰┄╮│ │ ──────┐ │┆│┆│┆──┐┆└─┤ ┌─┘ └─┐┆│ │ │ │┆│╰┄╯ │╰┄╮│ │ │┆│ │ ┌─────┘ │┆├─────┴─┐┆│ │ ──┬─┘┆│ │ │ │┆│╭┄┄┄┄┄╮│┆│ │ │╭┄╯│ ├─┤ ──┬─┬─┘┆│┆┌─┬──┆│┆└─┴─┐ │┆┌─┤ │ │ │ │╭┄╯│┆│ │╭┄╯│╰┄┄┄╮│ │┆│ │ │ └── │ │┆──┘┆│ │┆──┴────┆│ │┆│ │ │ │ ╰┄┄┄╯│ ╰┄┄┄┄┄┄┄╯│ ╰┄┄│ └─────┴───────┴───────────┴─────┘</lang>
The very alternative version
Invoke as ./maze [width] [depth] [height], and output is in maze.pgm, which you can print out and cut to fold into a cuboid. Sample output with 15, 10 and 20 sizes.
<lang c>#include <stdio.h>
- 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; }</lang>
Common Lisp
Uses unicode line drawing chars. Assumes they are single width on console. Code pretty horribly unreadable. <lang lisp>(setf *random-state* (make-random-state t))
(defun 2d-array (w h)
(make-array (list h w) :initial-element 0))
(defmacro or-and (v a b c)
`(if (or ,a (and ,b (= 1 ,c))) 0 ,v))
(defun make-maze (w h)
(let ((vis (2d-array w h))
(ver (2d-array w h)) (hor (2d-array w h)))
(labels
((walk (y x)
(setf (aref vis y x) 1) (loop (let (x2 y2) (loop for (dx dy) in '((-1 0) (1 0) (0 -1) (0 1)) with cnt = 0 do (let ((xx (+ x dx)) (yy (+ y dy))) (if (and (array-in-bounds-p vis yy xx) (zerop (aref vis yy xx)) (zerop (random (incf cnt)))) (setf x2 xx y2 yy)))) (if (not x2) (return-from walk)) (if (= x x2) (setf (aref hor (min y y2) x) 1) (setf (aref ver y (min x x2)) 1)) (walk y2 x2))))
(show ()
(let ((g " │││─┘┐┤─└┌├─┴┬┼")) (loop for i from 0 to h do (loop for j from 0 to w do (format t "~c~a" (char g (+ (or-and 1 (= i 0) (> j 0) (aref ver (1- i) (1- j))) (or-and 2 (= i h) (> j 0) (aref ver i (1- j))) (or-and 4 (= j 0) (> i 0) (aref hor (1- i) (1- j))) (or-and 8 (= j w) (> i 0) (aref hor (1- i) j )))) (if (and (< j w) (or (= i 0) (= 0 (aref hor (1- i) j)))) "───" " "))) (terpri) (when (< i h) (loop for j from 0 below w do (format t (if (or (= j 0) (= 0 (aref ver i (1- j)))) "│ " " "))) (format t "│~%"))))))
(walk (random h) (random w))
(show))))
(make-maze 20 20)</lang>output<lang>┼───┴───┼───┴───┴───┼───┴───┴───┼ │ │ │ │ ┼──── │ │ │ │ ┌───┐ ├ │ │ │ │ │ │ │ │ ┤ ┌───┘ │ │ │ │ │ ├ │ │ │ │ │ │ │ ┤ │ ┌───┘ ├───────┤ │ ├ │ │ │ │ │ │ ┤ │ │ ────┤ │ │ ────┼ │ │ │ │ │ │ ┤ ────┼───┐ │ │ └───┐ ├ │ │ │ │ │ │ ┼───┐ │ └───────┼───┐ └───┼ │ │ │ │ │ ┤ └──────────── │ └───┐ ├ │ │ │ ┼───┬───┬───┬───┬───┬───┬───┼───┼</lang>
D
<lang d>import std.stdio,std.random,std.algorithm,std.array,std.typecons;
void main() {
enum int W = 11, H = 8;
auto hWalls = new bool[][](W, H),
vWalls = new bool[][](W, H),
seen = new bool[][](W, H);
alias Tuple!(uint,"x", uint,"y") P;
void visit(int x, int y) {
seen[x][y] = true;
P[] D = [P(x-1,y), P(x+1,y), P(x,y-1), P(x,y+1)];
P[] ns = array(filter!((p){ return p.x<W && p.y<H; })(D));
while (ns.length) {
P n = ns[uniform(0, ns.length)];
if (!seen[n.x][n.y]) {
if (x != n.x) hWalls[min(x, n.x)][y] = true;
else vWalls[x][min(y, n.y)] = true;
visit(n.tupleof);
}
ns = array(filter!((x){ return x != n; })(ns));
}
}
visit(uniform(0, W), uniform(0, H));
writeln("+", "--+".replicate(W));
foreach (y; 0 .. H) {
string s = "|";
foreach (x; 0 .. W)
s ~= hWalls[x][y] ? " " : " |";
s ~= "\n+";
foreach (x; 0 .. W)
s ~= vWalls[x][y] ? " +" : "--+";
writeln(s);
}
}</lang> Output example:
+--+--+--+--+--+--+--+--+--+--+--+ | | | | | + + + + + +--+--+ + + + + | | | | | | | | | | + +--+ +--+--+ + +--+ + + + | | | | | | | + +--+--+--+--+ +--+ + + +--+ | | | | | | + + + + +--+--+--+--+--+--+ + | | | | | | +--+--+ + +--+--+ + + + + + | | | | | | | | | + + + +--+ +--+--+ + + +--+ | | | | | | | | + +--+--+ +--+ +--+--+--+ + + | | | +--+--+--+--+--+--+--+--+--+--+--+
Alternative version
See Maze_solving#D
F#
Using mutable state in the form of 2D arrays: <lang fsharp>let rnd : int -> int =
let gen = new System.Random() fun max -> gen.Next(max)
// randomly choose an element of a list let choose (xs:_ list) = xs.[rnd xs.Length]
type Maze(width, height) =
// (x,y) -> have we been here before?
let visited = Array2D.create width height false
// (x,y) -> is there a wall between (x,y) and (x+1,y)?
let horizWalls = Array2D.create width height true
// (x,y) -> is there a wall between (x,y) and (x,y+1)?
let vertWalls = Array2D.create width height true
let isLegalPoint (x,y) =
x >= 0 && x < width && y >= 0 && y < height
let neighbours (x,y) =
[(x-1,y);(x+1,y);(x,y-1);(x,y+1)] |> List.filter isLegalPoint
let removeWallBetween (x1,y1) (x2,y2) =
if x1 <> x2 then
horizWalls.[min x1 x2, y1] <- false
else
vertWalls.[x1, min y1 y2] <- false
let rec visit (x,y as p) =
let rec loop ns =
let (nx,ny) as n = choose ns
if not visited.[nx,ny] then
removeWallBetween p n
visit n
match List.filter ((<>) n) ns with
| [] -> ()
| others -> loop others
visited.[x,y] <- true loop (neighbours p)
do visit (rnd width, rnd height)
member x.Print() =
("+" + (String.replicate width "-+")) ::
[for y in 0..(height-1) do
yield "\n|"
for x in 0..(width-1) do
yield if horizWalls.[x,y] then " |" else " "
yield "\n+"
for x in 0..(width-1) do
yield if vertWalls.[x,y] then "-+" else " +"
]
|> String.concat ""
|> printfn "%s"
let m = new Maze(10,10) m.Print()</lang> Output example:
+-+-+-+-+-+-+-+-+-+-+ | | | | + +-+-+-+-+ +-+ + + + | | | | | | + +-+-+ + +-+-+ +-+ + | | | | | +-+ +-+ +-+-+ +-+-+ + | | | | | + +-+ +-+ +-+-+-+ +-+ | | | | | | + + +-+ +-+ +-+ +-+ + | | | | | | | | + + +-+ + +-+-+-+ + + | | | | | +-+ + +-+-+-+-+-+-+ + | | | | | + +-+-+ +-+ +-+-+ + + | | | | | | + +-+ +-+ +-+-+ +-+-+ | | | +-+-+-+-+-+-+-+-+-+-+
Haskell
<lang haskell>import Control.Monad import Control.Monad.ST import Data.Array import Data.Array.ST import Data.STRef import System.Random
rand :: Random a => (a, a) -> STRef s StdGen -> ST s a rand range gen = do
(a, g) <- liftM (randomR range) $ readSTRef gen gen `writeSTRef` g return a
data Maze = Maze {rightWalls, belowWalls :: Array (Int, Int) Bool}
maze :: Int -> Int -> StdGen -> ST s Maze maze width height gen = do
visited <- mazeArray False
rWalls <- mazeArray True
bWalls <- mazeArray True
gen <- newSTRef gen
liftM2 (,) (rand (0, maxX) gen) (rand (0, maxY) gen) >>=
visit gen visited rWalls bWalls
liftM2 Maze (freeze rWalls) (freeze bWalls)
where visit gen visited rWalls bWalls here = do
writeArray visited here True
let ns = neighbors here
i <- rand (0, length ns - 1) gen
forM_ (ns !! i : take i ns ++ drop (i + 1) ns) $ \there -> do
seen <- readArray visited there
unless seen $ do
removeWall here there
visit gen visited rWalls bWalls there
where removeWall (x1, y1) (x2, y2) = writeArray
(if x1 == x2 then bWalls else rWalls)
(min x1 x2, min y1 y2)
False
neighbors (x, y) =
(if x == 0 then [] else [(x - 1, y )]) ++
(if x == maxX then [] else [(x + 1, y )]) ++
(if y == 0 then [] else [(x, y - 1)]) ++
(if y == maxY then [] else [(x, y + 1)])
maxX = width - 1
maxY = height - 1
mazeArray = newArray ((0, 0), (maxX, maxY))
:: Bool -> ST s (STArray s (Int, Int) Bool)
printMaze :: Maze -> IO () printMaze (Maze rWalls bWalls) = do
putStrLn $ '+' : (concat $ replicate (maxX + 1) "---+")
forM_ [0 .. maxY] $ \y -> do
putStr "|"
forM_ [0 .. maxX] $ \x -> do
putStr " "
putStr $ if rWalls ! (x, y) then "|" else " "
putStrLn ""
forM_ [0 .. maxX] $ \x -> do
putStr "+"
putStr $ if bWalls ! (x, y) then "---" else " "
putStrLn "+"
where maxX = fst (snd $ bounds rWalls)
maxY = snd (snd $ bounds rWalls)
main = getStdGen >>= stToIO . maze 11 8 >>= printMaze</lang>
Sample output:
+---+---+---+---+---+---+---+---+---+---+---+ | | | + +---+---+---+ +---+---+---+---+---+ + | | | | | | + +---+---+ +---+---+ + + + + + | | | | | | | | + + + +---+---+---+---+ +---+ + + | | | | | | +---+---+ + +---+---+---+---+ +---+---+ | | | | | | + + + + +---+---+---+ +---+ + + | | | | | | | + +---+---+ + +---+---+---+ +---+ + | | | | | + +---+---+---+---+ + +---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+---+
Icon and Unicon
<lang Icon>link printf
procedure main(A) # generate rows x col maze
/mh := \A[1] | 12 # or take defaults 12 x 16 /mw := \A[2] | 16 mz := DisplayMaze(GenerateMaze(mh,mw)) WriteImage(mz.filename) # save file WAttrib(mz.window,"canvas=normal") # show maze in hidden window until Event() == &lpress # wait for left mouse press close(mz.window)
end
$define FINISH 64 # exit $define START 32 # entrance $define PATH 128 $define SEEN 16 # bread crumbs for generator $define NORTH 8 # sides ... $define EAST 4 $define SOUTH 2 $define WEST 1 $define EMPTY 0 # like new
procedure GenerateMaze(r,c) #: Depth First Maze Generation static maze,h,w,rd
if /maze then { # BEGING - No maze yet
/h := integer(1 < r) | runerr(r,205) # valid size 2x2 or better
/w := integer(1 < c) | runerr(r,205)
every !(maze := list(h)) := list(w,EMPTY) # shinny new empty maze
start := [?h,?w,?4-1,START] # random [r,c] start & finish
finish := [?h,?w,(start[3]+2)%4,FINISH] # w/ opposite side exponent
every x := start | finish do {
case x[3] := 2 ^ x[3] of { # get side from exponent and
NORTH : x[1] := 1 # project r,c to selected edge
EAST : x[2] := w
SOUTH : x[1] := h
WEST : x[2] := 1
}
maze[x[1],x[2]] +:= x[3] + x[4] # transcribe s/f to maze
}
rd := [NORTH, EAST, SOUTH, WEST] # initial list of directions
GenerateMaze(start[1],start[2]) # recurse through maze
return 1(.maze,maze := &null) # return maze, reset for next
}
else { # ----------------------- recursed to clear insize of maze
if iand(maze[r,c],SEEN) = 0 then { # in bounds and not SEEN yet?
maze[r,c] +:= SEEN # Mark current cell as visited
every !rd :=: ?rd # randomize list of directions
every d := !rd do
case d of { # try all, succeed & clear wall
NORTH : maze[r,c] +:= ( GenerateMaze(r-1,c), NORTH)
EAST : maze[r,c] +:= ( GenerateMaze(r,c+1), EAST)
SOUTH : maze[r,c] +:= ( GenerateMaze(r+1,c), SOUTH)
WEST : maze[r,c] +:= ( GenerateMaze(r,c-1), WEST)
}
return # signal success to caller
}
}
end
$define CELL 20 # cell size in pixels $define BORDER 30 # border size in pixels
record mazeinfo(window,maze,filename) # keepers
procedure DisplayMaze(maze) #: show it off if CELL < 8 then runerr(205,CELL) # too small
wh := (ch := (mh := *maze ) * CELL) + 2 * BORDER # win, cell, maze height ww := (cw := (mw := *maze[1]) * CELL) + 2 * BORDER # win, cell, maze width
wparms := [ sprintf("Maze %dx%d",*maze,*maze[1]), # window parameters
"g","bg=white","canvas=hidden",
sprintf("size=%d,%d",ww,wh),
sprintf("dx=%d",BORDER),
sprintf("dy=%d",BORDER)]
&window := open!wparms | stop("Unable to open Window")
Fg("black") # Draw full grid every DrawLine(x := 0 to cw by CELL,0,x,ch+1) # . verticals every DrawLine(0,y := 0 to ch by CELL,cw+1,y) # . horizontals
Fg("white") # Set to erase lines every y := CELL*((r := 1 to mh)-1) & x := CELL*((c := 1 to mw)-1) do {
WAttrib("dx="||x+BORDER,"dy="||y+BORDER) # position @ cell r,c
if iand(maze[r,c],NORTH) > 0 then DrawLine(2,0,CELL-1,0)
if iand(maze[r,c],EAST) > 0 then DrawLine(CELL,2,CELL,CELL-1)
if iand(maze[r,c],SOUTH) > 0 then DrawLine(2,CELL,CELL-1,CELL)
if iand(maze[r,c],WEST) > 0 then DrawLine(0,2,0,CELL-1)
}
return mazeinfo(&window,maze,sprintf("maze-%dx%d-%d.gif",r,c,&now)) end</lang>
Note: The underlying maze structure (matrix) is uni-directional from the start
printf.icn provides formatting
J
This algorithm allows almost no parallelism. So, while it might be "simple", generating very large mazes this way will not be necessarily efficient to implement on future (highly parallel) systems. That said, perhaps mazes with millions of cells are not very likely to be needed to be generated quickly.
Anyways, based on the picolisp implementation, except without any relevant grid support:
<lang j>maze=:4 :0
assert.0<:n=.<:x*y
horiz=. 0$~x,y-1
verti=. 0$~(x-1),y
path=.,:here=. ?x,y
unvisited=.0 (<here+1)} 0,0,~|:0,0,~1$~y,x
while.n do.
neighbors=. here+"1 (,-)=0 1
neighbors=. neighbors #~ (<"1 neighbors+1) {unvisited
if.#neighbors do.
n=.n-1
next=. ({~ ?@#) neighbors
unvisited=.0 (<next+1)} unvisited
if.{.next=here
do. horiz=.1 (<-:here+next-0 1)} horiz
else. verti=. 1 (<-:here+next-1 0)} verti end.
path=.path,here=.next
else.
here=.{:path
path=.}:path
end.
end.
horiz;verti
)
display=:3 :0
size=. >.&$&>/y
text=. (}:1 3$~2*1+{:size)#"1":size$<' '
'hdoor vdoor'=. 2 4&*&.>&.> (#&,{@;&i./@$)&.> y
' ' (a:-.~0 1;0 2; 0 3;(2 1-~$text);(1 4&+&.> hdoor),,vdoor+&.>"0/2 1;2 2;2 3)} text
)</lang>
The result of maze is a pair of arrays: one for open "doors" in the horizontal direction and the other for open "doors" in the vertical direction. The entry and exit doors are not represented by maze -- they are implicitly defined and are implemented in display.
Example use (with ascii box drawing enabled):
<lang j> display 8 maze 11 + +---+---+---+---+---+---+---+---+---+---+ | | | | | + + + + +---+ + +---+---+ + + | | | | | | | | + +---+---+ + +---+---+---+ + + + | | | | | | | +---+ +---+ + + +---+ + +---+---+ | | | | | | | + + +---+---+ +---+ + +---+---+ + | | | | | | | | | + +---+ + + + + +---+---+ + + | | | | | + +---+---+---+---+---+---+---+ +---+ + | | | | | | | | | + + + + + + + + +---+ + + | | | | | +---+---+---+---+---+---+---+---+---+---+---+</lang>
Java
<lang java>package org.rosettacode;
import java.util.Random; 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; private static final Random rand = new Random();
public MazeGenerator(int x, int y) { this.x = x; this.y = y; maze = new int[this.x][this.y]; generateMaze(0, 0); }
public void display() { for (int i = 0; i < y; i++) { // draw the north edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 1) == 0 ? "+---" : "+ "); } System.out.println("+"); // draw the west edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 8) == 0 ? "| " : " "); } System.out.println("|"); } // draw the bottom line for (int j = 0; j < x; j++) { System.out.print("+---"); } System.out.println("+"); }
private void generateMaze(int cx, int cy) { DIR[] dirs = DIR.values(); Collections.shuffle(Arrays.asList(dirs)); for (DIR dir : dirs) { int nx = cx + dir.dx; int ny = cy + dir.dy; if (between(nx, x) && between(ny, y) && (maze[nx][ny] == 0)) { maze[cx][cy] |= dir.bit; maze[nx][ny] |= dir.opposite.bit; generateMaze(nx, ny); } } }
private static boolean between(int v, int upper) { return (v >= 0) && (v < upper); }
private enum DIR { N(1, 0, -1), S(2, 0, 1), E(4, 1, 0), W(8, -1, 0); private final int bit; private final int dx; private final int dy; private DIR opposite;
// use the static initializer to resolve forward references static { N.opposite = S; S.opposite = N; E.opposite = W; W.opposite = E; }
private DIR(int bit, int dx, int dy) { this.bit = bit; this.dx = dx; this.dy = dy; } };
public static void main(String[] args) { int x = args.length >= 1 ? (Integer.parseInt(args[0])) : 8; int y = args.length == 2 ? (Integer.parseInt(args[1])) : 8; MazeGenerator maze = new MazeGenerator(x, y); maze.display(); }
}</lang> <lang>+---+---+---+---+---+---+---+---+---+---+ | | | | + +---+---+ +---+---+ + + +---+ | | | | | | | +---+---+ + + + +---+ +---+ + | | | | | | | + +---+---+ +---+ + +---+ + + | | | | | | | + + + +---+ +---+---+---+ + + | | | | | | + + +---+ + +---+---+ +---+---+ | | | | | | | + +---+ + +---+ +---+---+ + + | | | | | | +---+ + +---+ + +---+---+---+ + | | | | | | | + + +---+ + +---+---+ +---+ + | | | | | | | | + +---+ + +---+---+ + + + + | | | | +---+---+---+---+---+---+---+---+---+---+</lang>
JavaScript
<lang javascript>function maze(x,y) { var n=x*y-1; if (n<0) {alert("illegal maze dimensions");return;} var horiz=[]; for (var j= 0; j<x+1; j++) horiz[j]= []; var verti=[]; for (var j= 0; j<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();
}</lang>
Variable meanings in function maze:
x,y-- dimensions of mazen-- number of openings to be generatedhoriz-- 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 considerationpath-- history (stack) of locations that might need to be revisitedunvisited-- 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 tohereneighbors-- unvisited locations adjacent tohere
Variable meanings in function display:
m-- maze to be drawntext-- lines of text representing mazeline-- characters of current line
Note that this implementation relies on javascript arrays being treatable as infinite in size with false (null) values springing into existence as needed, to support referenced array locations. (This significantly reduces the bulk of the necessary initialization code.)
Example use:
<lang html><html><head><title></title></head><body>
</body></html>
<script type="text/javascript"> /* ABOVE CODE GOES HERE */ document.getElementById('out').innerHTML= display(maze(8,11)); </script></lang>
produced:
<lang>+ +---+---+---+---+---+---+---+---+---+---+ | | | | +---+---+ + +---+ + +---+---+ + + | | | | | | | | + + + +---+ +---+ +---+---+ + + | | | | | | | + +---+ +---+---+---+---+---+ + + + | | | | | | +---+ +---+ +---+---+ + +---+---+ + | | | | | | | + + + +---+---+---+---+---+ + + + | | | | | | + +---+---+ +---+---+ + +---+---+ + | | | | | | | + + + +---+ +---+---+ + + +---+ | | | | +---+---+---+---+---+---+---+---+---+---+---+</lang>
For an animated presentation of the progress of this maze creation process, you can use display in each iteration of the main loop. You would also need to take steps to make sure you could see each intermediate result.
For example, change replace the line while (0<n) { with:
<lang javascript> function step() { if (0<n) {</lang>
And replace the closing brace for this while loop with:
<lang javascript> document.getElementById('out').innerHTML= display({x: x, y: y, horiz: horiz, verti: verti, here: here}); setTimeout(step, 100); } } step();</lang>
To better see the progress, you might want a marker in place, showing the position being considered. To do that, replace the line which reads if (0 == k%4) { with
<lang javascript> if (m.here && m.here[0]*2+1 == j && m.here[1]*4+2 == k) line[k]= '#' else if (0 == k%4) {</lang>
Note however that this leaves the final '#' in place on maze completion, and that the function maze no longer returns a result which represents a generated maze.
Note also that this display suggests an optimization. You can replace the line reading path.push(here= next); with:
<lang javascript> here= next; if (1 < neighbors.length) path.push(here);</lang>
And this does indeed save a negligible bit of processing, but the maze algorithm will still be forced to backtrack through a number of locations which have no unvisited neighbors.
HTML Table
Using HTML, CSS and table cells for maze. <lang html><html><head><title>Maze maker</title> <style type="text/css"> table { border-collapse: collapse } td { width: 1em; height: 1em; border: 1px solid } td.s { border-bottom: none } td.n { border-top: none } td.w { border-left: none } td.e { border-right: none } td.v { background: skyblue} </style> <script type="application/javascript"> Node.prototype.add = function(tag, cnt, txt) { for (var i = 0; i < cnt; i++) this.appendChild(ce(tag, txt)); } Node.prototype.ins = function(tag) { this.insertBefore(ce(tag), this.firstChild) } Node.prototype.kid = function(i) { return this.childNodes[i] } Node.prototype.cls = function(t) { this.className += ' ' + t }
NodeList.prototype.map = function(g) { for (var i = 0; i < this.length; i++) g(this[i]); }
function ce(tag, txt) { var x = document.createElement(tag); if (txt !== undefined) x.innerHTML = txt; return x }
function gid(e) { return document.getElementById(e) } function irand(x) { return Math.floor(Math.random() * x) }
function make_maze() { var w = parseInt(gid('rows').value || 8, 10); var h = parseInt(gid('cols').value || 8, 10); var tbl = gid('maze'); tbl.innerHTML = ; tbl.add('tr', h); tbl.childNodes.map(function(x) { x.add('th', 1); x.add('td', w, '*'); x.add('th', 1)}); tbl.ins('tr'); tbl.add('tr', 1); tbl.firstChild.add('th', w + 2); tbl.lastChild.add('th', w + 2); for (var i = 1; i <= h; i++) { for (var j = 1; j <= w; j++) { tbl.kid(i).kid(j).neighbors = [ tbl.kid(i + 1).kid(j), tbl.kid(i).kid(j + 1), tbl.kid(i).kid(j - 1), tbl.kid(i - 1).kid(j) ]; } } walk(tbl.kid(irand(h) + 1).kid(irand(w) + 1)); gid('solve').style.display='inline'; }
function shuffle(x) { for (var i = 3; i > 0; i--) { j = irand(i + 1); if (j == i) continue; var t = x[j]; x[j] = x[i]; x[i] = t; } return x; }
var dirs = ['s', 'e', 'w', 'n']; function walk(c) { c.innerHTML = ' '; var idx = shuffle([0, 1, 2, 3]); for (var j = 0; j < 4; j++) { var i = idx[j]; var x = c.neighbors[i]; if (x.textContent != '*') continue; c.cls(dirs[i]), x.cls(dirs[3 - i]); walk(x); } }
function solve(c, t) { if (c === undefined) { c = gid('maze').kid(1).kid(1); c.cls('v'); } if (t === undefined) t = gid('maze') .lastChild.previousSibling .lastChild.previousSibling;
if (c === t) return 1; c.vis = 1; for (var i = 0; i < 4; i++) { var x = c.neighbors[i]; if (x.tagName.toLowerCase() == 'th') continue; if (x.vis || !c.className.match(dirs[i]) || !solve(x, t)) continue;
x.cls('v'); return 1; } c.vis = null; return 0; }
</script></head> <body><form><fieldset> <label>rows </label><input id='rows' size="3"/> <label>colums </label><input id='cols' size="3"/> <a href="javascript:make_maze()">Generate</a> <a id='solve' style='display:none' href='javascript:solve(); void(0)'>Solve</a>
</fieldset></form>
</body></html></lang>Perl
<lang 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;
}</lang>run as maze.pl [width] [height] or use default dimensions. Sample 4 x 1 output:<lang>+--+--+--+--+
| |
+--+--+--+--+</lang>
Perl 6
Works with Rakudo 2011.01
Supply a width and height and optionally the x,y grid coords for the starting cell. If no starting cell is supplied, a random one will be selected automatically. 0,0 is the top left corner.
<lang perl6>display( gen_maze( 11, 8 ) );
sub gen_maze ( $x_size,
$y_size,
$start_x = (^$x_size).pick,
$start_y = (^$y_size).pick )
{
my %walls;
my @maze;
for ^$y_size -> $x {
@maze[$x] = [ 1 xx $x_size];
%walls{'y'}[$x] = ['|' xx $x_size];
%walls{'x'}[$x] = ['---' xx $x_size];
}
my @stack;
my @current = $start_y, $start_x;
loop {
if my @next = get_unvisited_neighbors( @maze, @current ) {
@stack.push: [@current];
move( @maze, @next, @current, %walls );
@current := @next;
}
else {
last unless @stack;
@current := @stack.pop;
}
}
return %walls;
}
sub get_unvisited_neighbors(@maze, @current) {
my ($x, $y) = @current; my @neighbors; @neighbors.push([ $x-1, $y ]) if $x > 0 and @maze[$x-1][$y]; @neighbors.push([ $x+1, $y ]) if $x < @maze and @maze[$x+1][$y]; @neighbors.push([ $x, $y-1 ]) if $y > 0 and @maze[$x][$y-1]; @neighbors.push([ $x, $y+1 ]) if $y < @maze[0] and @maze[$x][$y+1]; return |@neighbors.roll(1) if @neighbors;
}
sub move ($maze, $next, $current, $walls) {
$maze[$next[0]][$next[1]] = 0;
given () {
when $next[0] < $current[0] { $walls{'x'}[$next[0]][$current[1]] = ' '}
when $next[0] > $current[0] { $walls{'x'}[$current[0]][$current[1]] = ' '}
when $next[1] < $current[1] { $walls{'y'}[$current[0]][$current[1]] = ' ' }
when $next[1] > $current[1] { $walls{'y'}[$current[0]][$next[1]] = ' ' }
}
}
sub display ($walls) {
say '+' ~ ('---' xx $walls{'y'}[0]).join('+') ~ '+';
for ^$walls{'x'} -> $i {
say ~$walls{'y'}[$i].join(' ') ~ ' |';
say '+' ~ $walls{'x'}[$i].join('+') ~ '+';
}
}</lang> Sample Output:
+---+---+---+---+---+---+---+---+---+---+---+ | | | | | +---+---+ + + + +---+---+---+---+ + | | | | | + +---+---+ +---+---+ +---+---+---+---+ | | | | + +---+ +---+ +---+ +---+---+---+ + | | | | | | + +---+---+ +---+ +---+ + +---+---+ | | | | | | | | +---+ + + +---+---+ + +---+ + + | | | | | | | + +---+---+---+ + + + +---+---+ + | | | | | | + + +---+---+---+---+---+---+ +---+ + | | | +---+---+---+---+---+---+---+---+---+---+---+
PicoLisp
This solution uses 'grid' from "lib/simul.l" to generate the two-dimensional structure. <lang PicoLisp>(load "@lib/simul.l")
(de maze (DX DY)
(let Maze (grid DX DY)
(let Fld (get Maze (rand 1 DX) (rand 1 DY))
(recur (Fld)
(for Dir (shuffle '((west . east) (east . west) (south . north) (north . south)))
(with ((car Dir) Fld)
(unless (or (: west) (: east) (: south) (: north))
(put Fld (car Dir) This)
(put This (cdr Dir) Fld)
(recurse This) ) ) ) ) )
(for (X . Col) Maze
(for (Y . This) Col
(set This
(cons
(cons
(: west)
(or
(: east)
(and (= Y 1) (= X DX)) ) )
(cons
(: south)
(or
(: north)
(and (= X 1) (= Y DY)) ) ) ) ) ) )
Maze ) )
(de display (Maze)
(disp Maze 0 '((This) " ")) )</lang>
Output:
: (display (maze 11 8))
+ +---+---+---+---+---+---+---+---+---+---+
8 | | | |
+ + + + + + +---+ +---+---+ +
7 | | | | | | | | |
+---+ +---+---+ + + +---+ + + +
6 | | | | | | | |
+ +---+ +---+ +---+---+---+ + +---+
5 | | | | | |
+---+ +---+ +---+---+---+ +---+---+ +
4 | | | | | | |
+ +---+ +---+ +---+ + + +---+ +
3 | | | | | | | |
+ +---+---+ + + + + +---+ + +
2 | | | | | | | | |
+ + + +---+ + +---+ + +---+ +
1 | | | |
+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j kProlog
Works with SWI-Prolog and XPCE. <lang Prolog>:- dynamic cell/2.
maze(Lig,Col) :- retractall(cell(_,_)),
new(D, window('Maze')),
% creation of the grid forall(between(0,Lig, I), (XL is 50, YL is I * 30 + 50, XR is Col * 30 + 50, new(L, line(XL, YL, XR, YL)), send(D, display, L))),
forall(between(0,Col, I), (XT is 50 + I * 30, YT is 50, YB is Lig * 30 + 50, new(L, line(XT, YT, XT, YB)), send(D, display, L))),
SX is Col * 30 + 100, SY is Lig * 30 + 100, send(D, size, new(_, size(SX, SY))),
% choosing a first cell L0 is random(Lig), C0 is random(Col), assert(cell(L0, C0)), \+search(D, Lig, Col, L0, C0), send(D, open).
search(D, Lig, Col, L, C) :- Dir is random(4), nextcell(Dir, Lig, Col, L, C, L1, C1), assert(cell(L1,C1)), assert(cur(L1,C1)), erase_line(D, L, C, L1, C1), search(D, Lig, Col, L1, C1).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% erase_line(D, L, C, L, C1) :- ( C < C1 -> C2 = C1; C2 = C), XT is C2 * 30 + 50, YT is L * 30 + 51, YR is (L+1) * 30 + 50, new(Line, line(XT, YT, XT, YR)), send(Line, colour, white), send(D, display, Line).
erase_line(D, L, C, L1, C) :- XT is 51 + C * 30, XR is 50 + (C + 1) * 30, ( L < L1 -> L2 is L1; L2 is L), YT is L2 * 30 + 50, new(Line, line(XT, YT, XR, YT)), send(Line, colour, white), send(D, display, Line).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nextcell(Dir, Lig, Col, L, C, L1, C1) :- next(Dir, Lig, Col, L, C, L1, C1); ( Dir1 is (Dir+3) mod 4, next(Dir1, Lig, Col, L, C, L1, C1)); ( Dir2 is (Dir+1) mod 4, next(Dir2, Lig, Col, L, C, L1, C1)); ( Dir3 is (Dir+2) mod 4, next(Dir3, Lig, Col, L, C, L1, C1)).
% 0 => northward next(0, _Lig, _Col, L, C, L1, C) :- L > 0, L1 is L - 1, \+cell(L1, C).
% 1 => rightward next(1, _Lig, Col, L, C, L, C1) :- C < Col - 1, C1 is C + 1, \+cell(L, C1).
% 2 => southward next(2, Lig, _Col, L, C, L1, C) :- L < Lig - 1, L1 is L + 1, \+cell(L1, C).
% 3 => leftward next(2, _Lig, _Col, L, C, L, C1) :- C > 0, C1 is C - 1, \+cell(L, C1).
</lang>
Output :
PureBasic
<lang PureBasic>Enumeration
;indexes for types of offsets from maze coordinates (x,y) #visited ;used to index visited(x,y) in a given direction from current maze cell #maze ;used to index maze() in a given direction from current maze cell #wall ;used to index walls in maze() in a given direction from current maze cell #numOffsets = #wall ;direction indexes #dir_ID = 0 ;identity value, produces no changes #firstDir #dir_N = #firstDir #dir_E #dir_S #dir_W #numDirs = #dir_W
EndEnumeration
DataSection
;maze(x,y) offsets for visited, maze, & walls for each direction Data.i 1, 1, 0, 0, 0, 0 ;ID Data.i 1, 0, 0, -1, 0, 0 ;N Data.i 2, 1, 1, 0, 1, 0 ;E Data.i 1, 2, 0, 1, 0, 1 ;S Data.i 0, 1, -1, 0, 0, 0 ;W Data.i %00, %01, %10, %01, %10 ;wall values for ID, N, E, S, W
EndDataSection
- cellDWidth = 4
Structure mazeOutput
vWall.s hWall.s
EndStructure
- setup reference values indexed by type and direction from current map cell
Global Dim offset.POINT(#numOffsets, #numDirs) Define i, j For i = 0 To #numDirs
For j = 0 To #numOffsets Read.i offset(j, i)\x: Read.i offset(j, i)\y Next
Next
Global Dim wallvalue(#numDirs) For i = 0 To #numDirs: Read.i wallvalue(i): Next
Procedure makeDisplayMazeRow(Array mazeRow.mazeOutput(1), Array maze(2), y)
;modify mazeRow() to produce output of 2 strings showing the vertical walls above and horizontal walls across a given maze row Protected x, vWall.s, hWall.s Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2) vWall = "": hWall = "" For x = 0 To mazeWidth If maze(x, y) & wallvalue(#dir_N): vWall + "+ ": Else: vWall + "+---": EndIf If maze(x, y) & wallvalue(#dir_W): hWall + " ": Else: hWall + "| ": EndIf Next mazeRow(0)\vWall = Left(vWall, mazeWidth * #cellDWidth + 1) If y <> mazeHeight: mazeRow(0)\hWall = Left(hWall, mazeWidth * #cellDWidth + 1): Else: mazeRow(0)\hWall = "": EndIf
EndProcedure
Procedure displayMaze(Array maze(2))
Protected x, y, vWall.s, hWall.s, mazeHeight = ArraySize(maze(), 2) Protected Dim mazeRow.mazeOutput(0) For y = 0 To mazeHeight makeDisplayMazeRow(mazeRow(), maze(), y) PrintN(mazeRow(0)\vWall): PrintN(mazeRow(0)\hWall) Next
EndProcedure
Procedure generateMaze(Array maze(2), mazeWidth, mazeHeight)
Dim maze(mazeWidth, mazeHeight) ;Each cell specifies walls present above and to the left of it,
;array includes an extra row and column for the right and bottom walls
Dim visited(mazeWidth + 1, mazeHeight + 1) ;Each cell represents a cell of the maze, an extra line of cells are included
;as padding around the representative cells for easy border detection
Protected i
;mark outside border as already visited (off limits)
For i = 0 To mazeWidth
visited(i + offset(#visited, #dir_N)\x, 0 + offset(#visited, #dir_N)\y) = #True
visited(i + offset(#visited, #dir_S)\x, mazeHeight - 1 + offset(#visited, #dir_S)\y) = #True
Next
For i = 0 To mazeHeight
visited(0 + offset(#visited, #dir_W)\x, i + offset(#visited, #dir_W)\y) = #True
visited(mazeWidth - 1 + offset(#visited, #dir_E)\x, i + offset(#visited, #dir_E)\y) = #True
Next
;generate maze
Protected x = Random(mazeWidth - 1), y = Random (mazeHeight - 1), cellCount, nextCell
visited(x + offset(#visited, #dir_ID)\x, y + offset(#visited, #dir_ID)\y) = #True
PrintN("Maze of size " + Str(mazeWidth) + " x " + Str(mazeHeight) + ", generation started at " + Str(x) + " x " + Str(y))
NewList stack.POINT()
Dim unvisited(#numDirs - #firstDir)
Repeat
cellCount = 0
For i = #firstDir To #numDirs
If Not visited(x + offset(#visited, i)\x, y + offset(#visited, i)\y)
unvisited(cellCount) = i: cellCount + 1
EndIf
Next
If cellCount
nextCell = unvisited(Random(cellCount - 1))
visited(x + offset(#visited, nextCell)\x, y + offset(#visited, nextCell)\y) = #True
maze(x + offset(#wall, nextCell)\x, y + offset(#wall, nextCell)\y) | wallvalue(nextCell)
If cellCount > 1
AddElement(stack())
stack()\x = x: stack()\y = y
EndIf
x + offset(#maze, nextCell)\x: y + offset(#maze, nextCell)\y
ElseIf ListSize(stack()) > 0
x = stack()\x: y = stack()\y
DeleteElement(stack())
Else
Break ;end maze generation
EndIf
ForEver
; ;mark random entry and exit point
; x = Random(mazeWidth - 1): y = Random(mazeHeight - 1)
; maze(x, 0) | wallvalue(#dir_N): maze(mazeWidth, y) | wallvalue(#dir_E)
ProcedureReturn
EndProcedure
If OpenConsole()
Dim maze(0, 0) Define mazeWidth = Random(5) + 7: mazeHeight = Random(5) + 3 generateMaze(maze(), mazeWidth, mazeHeight) displayMaze(maze()) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf</lang> The maze is represented by an array of cells where each cell indicates the walls present above (#dir_N) and to its left (#dir_W). Maze generation is done with a additional array marking the visited cells. Neither an entry nor an exit are created, these were not part of the task. A simple means of doing so is included but has been commented out.
Sample output:
Maze of size 11 x 8, generation started at 9 x 3 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+ + +---+ + +---+ + + | | | | | | | | + +---+ +---+---+ +---+ + +---+---+ | | | | | | + + +---+---+ +---+---+---+---+---+ + | | | | | | + +---+ +---+ + +---+ + +---+---+ | | | | | | +---+---+---+ + + +---+---+ +---+ + | | | | | | + +---+---+ +---+ +---+---+ + +---+ | | | | | | | + + + +---+---+---+ + +---+---+ + | | | | +---+---+---+---+---+---+---+---+---+---+---+
Python
<lang python>from random import shuffle, randrange
def make_maze(w = 16, h = 8): vis = [[0] * w + [1] for _ in range(h)] + [[1] * (w + 1)] ver = [["| "] * w + ['|'] for _ in range(h)] + [[]] hor = [["+--"] * w + ['+'] for _ in range(h + 1)]
def walk(x, y): vis[y][x] = 1
d = [(x - 1, y), (x, y + 1), (x + 1, y), (x, y - 1)] shuffle(d) for (xx, yy) in d: if vis[yy][xx]: continue if xx == x: hor[max(y, yy)][x] = "+ " if yy == y: ver[y][max(x, xx)] = " " walk(xx, yy)
walk(randrange(w), randrange(h)) for (a, b) in zip(hor, ver): print(.join(a + ['\n'] + b))
make_maze()</lang>output<lang>+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | | | | | | + + + + + + + + +--+--+--+--+--+ +--+ + | | | | | | | | | | +--+ +--+--+ + +--+--+--+ + +--+ +--+--+ + | | | | | | | | | | + +--+ +--+ + + + + + +--+ + + +--+--+ | | | | | | | | | | + +--+ +--+--+ + +--+ +--+--+ +--+--+ + + | | | | | | | | +--+ + + +--+--+--+ +--+--+--+--+--+--+--+ + | | | | | | | | + +--+--+ +--+--+ +--+--+ +--+ +--+ + + + | | | | | | | | + +--+ +--+--+--+ + +--+--+--+--+ +--+ + + | | | | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+</lang>
Tcl
<lang 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]</lang> Output:
+ +---+---+---+---+---+---+---+---+---+---+ | | | | +---+---+ +---+---+ + +---+ +---+ + | | | | | | + + +---+ +---+---+ +---+ + + + | | | | | | | | + +---+ +---+---+---+ + + + + + | | | | | | | | + + + + +---+---+ + +---+---+ + | | | | | | | | +---+---+---+---+ + +---+ + + +---+ | | | | | | | | + +---+---+ + + + + + +---+ + | | | | | | | | +---+ + +---+---+---+---+ + +---+ + | | +---+---+---+---+---+---+---+---+---+---+---+