Maze generation: Difference between revisions
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=={{header|Julia}}== |
=={{header|Julia}}== |
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String API has changed in julia versions > 0.4. One must import the library LegacyStrings for the following code to work. |
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<lang julia>function walk(maze, cell, visited = Any[]) |
<lang julia>function walk(maze, cell, visited = Any[]) |
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push!(visited, cell) |
push!(visited, cell) |
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Revision as of 21:21, 1 October 2016
You are encouraged to solve this task according to the task description, using any language you may know.
| This page uses content from Wikipedia. The original article was at Maze generation algorithm. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
- Task
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.
- Related tasks
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 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + + +---+ + + +---+---+---+ + | | | | | | | + +---+---+ +---+---+ + + + +---+ | | | | | | | | + +---+---+---+---+ +---+ + + + + | | | | | | | + + +---+ + + + +---+---+---+ + | | | | | | | + + +---+---+---+---+---+ +---+ + + | | | | | | +---+ + +---+---+---+ +---+---+---+ + | | | | | + +---+ +---+---+ +---+---+---+---+---+ | | +---+---+---+---+---+---+---+---+---+---+---+
Aime
<lang aime>void grid_maze(data b, integer N) {
data d;
integer i, j;
j = N;
while (j) {
b_suffix(d, "+---"); j -= 1;
}
{
b_suffix(d, "+\n");
}
j = N;
while (j) {
b_suffix(d, "| * "); j -= 1;
}
{
b_suffix(d, "|\n");
}
i = N;
while (i) {
b_extend(b, d);
i -= 1;
}
b_size(d, N * 4 + 2);
{
b_extend(b, d);
}
}
void walk_cell(data b, integer N, integer line_size, integer x, integer y, list x_offsets, list y_offsets) {
integer i, r;
b_replace(b, y + x, ' ');
r = drand(3);
i = 0;
while (i < 4) {
integer p, q;
p = x + l_q_integer(x_offsets, (r + i) & 3); q = y + l_q_integer(y_offsets, (r + i) & 3);
if (-1 < p && p < line_size && -1 < q && q < line_size * (N * 2 + 1)) { if (b_text(b, q + p) == '*') { walk_cell(b, N, line_size, p, q, x_offsets, y_offsets); b_replace(b, (q + y) / 2 + (p + x) / 2, ' '); if (p == x) { b_replace(b, (q + y) / 2 + p - 1, ' '); b_replace(b, (q + y) / 2 + p + 1, ' '); } } }
i += 1;
}
}
void walk_maze(data b, integer N) {
integer line_size, x, y; list x_offsets, y_offsets; line_size = N * 4 + 1 + 1; lb_p_integer(x_offsets, 4); lb_p_integer(y_offsets, 0); lb_p_integer(x_offsets, 0); lb_p_integer(y_offsets, line_size * 2); lb_p_integer(x_offsets, -4); lb_p_integer(y_offsets, 0); lb_p_integer(x_offsets, 0); lb_p_integer(y_offsets, line_size * -2); x = drand(N - 1) * 4 + 2; y = line_size * (drand(N - 1) * 2 + 1); walk_cell(b, N, line_size, x, y, x_offsets, y_offsets);
}
integer main(void) {
data b; integer N; N = 10; grid_maze(b, N); walk_maze(b, N); o_text(b_string(b)); return 0;
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+ | | | + +---+---+---+---+ + +---+---+ + | | | | | | | + + + + + + + + +---+ + | | | | | | | | | + +---+---+ +---+---+---+ + + + | | | | | | +---+---+---+---+---+---+ + + + + | | | | | + +---+---+---+---+ + + +---+---+ | | | | | | + +---+---+---+ + + +---+ + + | | | | | | | + + + + + +---+---+ +---+ + | | | | | | | +---+---+---+ +---+---+---+---+ + + | | | | | + +---+---+---+ + + + +---+ + | | | | +---+---+---+---+---+---+---+---+---+---+
AutoHotkey
For a challenge, this maze generation is entirely string based. That is to say, all operations including the wall removal and retrieval of cell states are done on the output string. <lang AHK>; Initially build the board Width := 11 Height := 8 Loop % height*2+1 { Outer := A_Index Loop % Width maze .= Outer & 1 ? "+-" : "|0" maze .= (Outer & 1 ? "+" : "|") "`n" } StringTrimRight, maze, maze, 1 ; removes trailing newline Clipboard := Walk(maze)
Walk(S, x=0, y=0){ If !x{ ; --Start at a random cell... StringReplace, junk, S, `n,,UseErrorLevel ; Calculate rows Random, y, 1, ErrorLevel//2 Random, x, 1, InStr(S, "`n")//2-1 ; Calculate height }
; --Obtain a list of its neighbors... neighbors := x "," y+1 "`n" x "," y-1 "`n" x+1 "," y "`n" x-1 "," y ; --Randomize the list... Sort neighbors, random
; --Then for each neighbor... Loop Parse, neighbors, `n { pC := InStr(A_LoopField, ","), x2 := SubStr(A_LoopField, 1, pC-1), y2 := SubStr(A_LoopField, pC+1) ; If it has not been visited... If GetChar(S, 2*x2, 2*y2) = "0"{ ; Mark it as visited... S := ChangeChar(s, 2*x2, 2*y2, " ") ; Remove the wall between this cell and the neighbor... S := ChangeChar(S, x+x2, y+y2, " ") ; Then recurse with the neighbor as the current cell S := Walk(S, x2, y2) } } return S }
- Change a character in a string using x and y coordinates
ChangeChar(s, x, y, c){ Loop Parse, s, `n { If (A_Index = Y) Loop Parse, A_LoopField If (A_Index = x) out .= c Else out .= A_LoopField Else out .= A_LoopField out .= "`n" } StringTrimRight, out, out, 1 return out }
- retrieve a character in a string using x and y coordinates
GetChar(s, x, y, n=1){ x*=n, y*=n Loop Parse, s, `n If (A_Index = Y) return SubStr(A_LoopField, x, 1) }</lang>
- Sample output:
+-+-+-+-+-+-+-+-+-+-+-+ | | | | +-+ +-+-+ +-+ + + +-+-+ | | | | | + +-+ +-+ +-+-+ +-+ + + | | | | | | | | + + +-+-+ + + +-+ +-+ + | | | | | | | + +-+ + +-+-+-+ +-+ + + | | | | | | + +-+-+-+-+-+ +-+-+-+ + | | | | | | + + + + +-+-+-+ + + +-+ | | | | | | | +-+-+-+-+ +-+ + +-+-+ + | | | +-+-+-+-+-+-+-+-+-+-+-+
AWK
<lang awk>#!/usr/bin/awk -f
- 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);
} </lang>
Example output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | +---+ +---+ +---+---+ +---+ +---+---+ +---+ +---+---+ + +---+ + | | | | | | | | | | | | | + +---+ + + +---+---+ +---+---+ + +---+ + + +---+---+---+ + | | | | | | | | | + + + +---+ +---+ + +---+ +---+---+ +---+---+ +---+ +---+ + | | | | | | | | | | | | | | +---+ + + +---+ +---+ + +---+---+ + + + +---+---+---+ +---+ | | | | | | | | | | | + + +---+---+ +---+ +---+---+---+---+ +---+---+ +---+ + +---+ + | | | | | | | | | | | | | + +---+ + + +---+---+ +---+ + + + + +---+ + + + + + | | | | | | | | | | | | | | | + + +---+---+---+ + +---+ + + + +---+---+ + + +---+---+ + | | | | | | | | | | + + +---+---+---+ +---+---+---+ + +---+---+---+ + +---+---+ +---+ | | | | | | | | | | + +---+ +---+---+---+ + +---+---+---+---+ + +---+ + + +---+ + | | | | | | | | | | | | | | + + + + +---+ + + + + + + + + + +---+---+ + +---+ | | | | | | | | | | | | | | + +---+---+---+ + +---+---+---+ + + + + + +---+ + +---+ + | | | | | | | | | | | | +---+ +---+---+---+---+---+ + +---+ +---+---+---+---+ + +---+ + + | | | | | | | | | | | | | + + + +---+ +---+ + +---+ + + +---+ +---+ +---+ + + + | | | | | | | | | | | | + + + +---+---+ +---+---+ + +---+ +---+---+ +---+---+ + +---+ | | | | | | | | | | | | | + + + + + +---+ +---+---+---+---+---+ + +---+---+ + +---+ + | | | | | | | | | +---+---+ + +---+---+---+---+ + +---+---+---+ +---+---+---+---+ + + | | | | | | | | | | + + +---+ +---+---+ + + +---+ + + +---+---+ +---+---+---+ + | | | | | | | | | | | | | + + +---+---+ + +---+ + +---+ +---+ + + +---+---+ + +---+ | | | | | | | | | | | | | + +---+ +---+ + + +---+---+ +---+ +---+ +---+---+ + +---+ + | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
BBC BASIC
<lang bbcbasic> MazeWidth% = 11
MazeHeight% = 9
MazeCell% = 50
VDU 23,22,MazeWidth%*MazeCell%/2+3;MazeHeight%*MazeCell%/2+3;8,16,16,128
VDU 23,23,3;0;0;0; : REM Line thickness
PROCgeneratemaze(Maze&(), MazeWidth%, MazeHeight%, MazeCell%)
END
DEF PROCgeneratemaze(RETURN m&(), w%, h%, s%)
LOCAL x%, y%
DIM m&(w%, h%)
FOR y% = 0 TO h%
LINE 0,y%*s%,w%*s%,y%*s%
NEXT
FOR x% = 0 TO w%
LINE x%*s%,0,x%*s%,h%*s%
NEXT
GCOL 15
PROCcell(m&(), RND(w%)-1, y% = RND(h%)-1, w%, h%, s%)
ENDPROC
DEF PROCcell(m&(), x%, y%, w%, h%, s%)
LOCAL i%, p%, q%, r%
m&(x%,y%) OR= &40 : REM Mark visited
r% = RND(4)
FOR i% = r% TO r%+3
CASE i% MOD 4 OF
WHEN 0: p% = x%-1 : q% = y%
WHEN 1: p% = x%+1 : q% = y%
WHEN 2: p% = x% : q% = y%-1
WHEN 3: p% = x% : q% = y%+1
ENDCASE
IF p% >= 0 IF p% < w% IF q% >= 0 IF q% < h% IF m&(p%,q%) < &40 THEN
IF p% > x% m&(p%,q%) OR= 1 : LINE p%*s%,y%*s%+4,p%*s%,(y%+1)*s%-4
IF q% > y% m&(p%,q%) OR= 2 : LINE x%*s%+4,q%*s%,(x%+1)*s%-4,q%*s%
IF x% > p% m&(x%,y%) OR= 1 : LINE x%*s%,y%*s%+4,x%*s%,(y%+1)*s%-4
IF y% > q% m&(x%,y%) OR= 2 : LINE x%*s%+4,y%*s%,(x%+1)*s%-4,y%*s%
PROCcell(m&(), p%, q%, w%, h%, s%)
ENDIF
NEXT
ENDPROC</lang>
Sample output:
Befunge
Dimensions are specified by the first two values pushed onto the stack - currently 20 (45*) by 16 (28*). Note, however, that the upper limit in a standard Befunge-93 implementation will be around 38 by 40 (1520 cells) due to the constrained page size.
Also note that this requires an interpreter with working read-write memory support, which is suprisingly rare in online implementations. Padding the code page with extra blank lines or spaces can sometimes help. Using smaller dimensions might also be preferable, especially on slower implementations.
<lang befunge>45*28*10p00p020p030p006p0>20g30g00g*+::"P"%\"P"/6+gv>$\1v@v1::\+g02+*g00+g03-\< 0_ 1!%4+1\-\0!::\-\2%2:p<pv0<< v0p+6/"P"\%"P":\+4%4<^<v-<$>+2%\1-*20g+\1+4%::v^
- | +2%\1-*30g+\1\40g1-:v0+v2?1#<v>+:00g%!55+*>:#0>#,_^>:!|>\#%"P"v#:*+*g00g0<>1
02!:++`\0\`-1g01:\+`\< !46v3<^$$<^1,g2+1%2/2,g1+1<v%g00:\<*g01,<>:30p\:20p:v^3g 0#$g#<1#<-#<`#<\#<0#<^#_^/>#1+#4<>"P"%\"P"/6+g:2%^!>,1-:#v_$55+^|$$ "JH" $$>#<0
- "P"%\"P"/6+g40p\40g+\:#^"P"%#\<^ ::$_,#!0#:<*"|"<^," _"<:g000 <> /6+g4/2%+#^_
</lang>
- Output:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |_ | _ _ |_ _ _| _ _ _ _ |_ | | |_ _| _|_ |_|_ | _| | _|_ |_ | | | |_ _ | | |_ _ _| | _ _ _|_ | | |_ |_| _|_ _|_ |_ _| _|_ | _| | | |_ _ _ | | _ _| | _ | | | | _| | _ _ |_| | | | _ _| |_| _| _|_ _| | | | | _| _|_ _|_ |_ _ | | | | _ _ | |_ |_ _ _| _ _ |_ _ |_ _| | |_ | | | | |_ _ _ _ _| |_ _ _ _| | |_ | | | | |_ | _ _ _|_ _ _ _ _ | |_ |_ _| | | | _|_ _|_ _ _ | _ _|_ |_ _ _| | | | _ _ _ | | _|_|_ _ _ |_ |_ _ | | | _| _ | | |_ _ _ _ _ _ _| | | | | |_ |_ | _|_| | _ |_| _ _ _| | | | | | | | |_| _ _| | | _| _| | _|_| | |_ _ _|_ _ _ _ _|_ _|_ _ _ _ _|_|_ _ _ _|
C
Generation/solver in one. Requires UTF8 locale and unicode capable console. If your console font line-drawing chars are single width, define DOUBLE_SPACE to 0. <lang c>#include <stdio.h>
- 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>
- Sample output:
┌───┬─────┬─────────┬───────┬───┐ │┄┄╮│╭┄┄┄╮│ ╭┄┄┄┄┄╮│ ╭┄┄┄╮│╭┄╮│ │ │┆│┆──┐┆│ │┆──┬─┐┆└──┆┌─┐┆│┆│┆│ │ │┆│╰┄╮│┆│ │╰┄╮│ │╰┄┄┄╯│ │╰┄╯│┆│ │ │┆└──┆│┆└─┼──┆│ └─────┤ └─┬─┘┆│ │ │╰┄┄┄╯│╰┄╮│╭┄╯│ │ │╭┄╯│ │ └─────┴─┐┆│┆┌─┴───┐ │ │ │ │┆──┤ │ │┆│┆│╭┄┄┄╮│ │ │ │╰┄╮│ │ ──────┐ │┆│┆│┆──┐┆└─┤ ┌─┘ └─┐┆│ │ │ │┆│╰┄╯ │╰┄╮│ │ │┆│ │ ┌─────┘ │┆├─────┴─┐┆│ │ ──┬─┘┆│ │ │ │┆│╭┄┄┄┄┄╮│┆│ │ │╭┄╯│ ├─┤ ──┬─┬─┘┆│┆┌─┬──┆│┆└─┴─┐ │┆┌─┤ │ │ │ │╭┄╯│┆│ │╭┄╯│╰┄┄┄╮│ │┆│ │ │ └── │ │┆──┘┆│ │┆──┴────┆│ │┆│ │ │ │ ╰┄┄┄╯│ ╰┄┄┄┄┄┄┄╯│ ╰┄┄│ └─────┴───────┴───────────┴─────┘
C++
<lang cpp>
- 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;
} //-------------------------------------------------------------------------------------------------- </lang>
C#
<lang csharp>using System; using System.Collections.Generic; using System.Diagnostics; using System.Linq; using System.Text; using System.Drawing;
namespace MazeGeneration {
public static class Extensions
{
public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> source, Random rng)
{
var e = source.ToArray();
for (var i = e.Length - 1; i >= 0; i--)
{
var swapIndex = rng.Next(i + 1);
yield return e[swapIndex];
e[swapIndex] = e[i];
}
}
public static CellState OppositeWall(this CellState orig)
{
return (CellState)(((int) orig >> 2) | ((int) orig << 2)) & CellState.Initial;
}
public static bool HasFlag(this CellState cs,CellState flag)
{
return ((int)cs & (int)flag) != 0;
}
}
[Flags]
public enum CellState
{
Top = 1,
Right = 2,
Bottom = 4,
Left = 8,
Visited = 128,
Initial = Top | Right | Bottom | Left,
}
public struct RemoveWallAction
{
public Point Neighbour;
public CellState Wall;
}
public class Maze
{
private readonly CellState[,] _cells;
private readonly int _width;
private readonly int _height;
private readonly Random _rng;
public Maze(int width, int height)
{
_width = width;
_height = height;
_cells = new CellState[width, height];
for(var x=0; x<width; x++)
for(var y=0; y<height; y++)
_cells[x, y] = CellState.Initial;
_rng = new Random();
VisitCell(_rng.Next(width), _rng.Next(height));
}
public CellState this[int x, int y]
{
get { return _cells[x,y]; }
set { _cells[x,y] = value; }
}
public IEnumerable<RemoveWallAction> GetNeighbours(Point p)
{
if (p.X > 0) yield return new RemoveWallAction {Neighbour = new Point(p.X - 1, p.Y), Wall = CellState.Left};
if (p.Y > 0) yield return new RemoveWallAction {Neighbour = new Point(p.X, p.Y - 1), Wall = CellState.Top};
if (p.X < _width-1) yield return new RemoveWallAction {Neighbour = new Point(p.X + 1, p.Y), Wall = CellState.Right};
if (p.Y < _height-1) yield return new RemoveWallAction {Neighbour = new Point(p.X, p.Y + 1), Wall = CellState.Bottom};
}
public void VisitCell(int x, int y)
{
this[x,y] |= CellState.Visited;
foreach (var p in GetNeighbours(new Point(x, y)).Shuffle(_rng).Where(z => !(this[z.Neighbour.X, z.Neighbour.Y].HasFlag(CellState.Visited))))
{
this[x, y] -= p.Wall;
this[p.Neighbour.X, p.Neighbour.Y] -= p.Wall.OppositeWall();
VisitCell(p.Neighbour.X, p.Neighbour.Y);
}
}
public void Display()
{
var firstLine = string.Empty;
for (var y = 0; y < _height; y++)
{
var sbTop = new StringBuilder();
var sbMid = new StringBuilder();
for (var x = 0; x < _width; x++)
{
sbTop.Append(this[x, y].HasFlag(CellState.Top) ? "+--" : "+ ");
sbMid.Append(this[x, y].HasFlag(CellState.Left) ? "| " : " ");
}
if (firstLine == string.Empty)
firstLine = sbTop.ToString();
Debug.WriteLine(sbTop + "+");
Debug.WriteLine(sbMid + "|");
Debug.WriteLine(sbMid + "|");
}
Debug.WriteLine(firstLine);
}
}
class Program
{
static void Main(string[] args)
{
var maze = new Maze(20, 20);
maze.Display();
}
}
} </lang> Sample output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | | | | | | | | | | | | | | | | | | + +--+ + + + + +--+ + +--+ + + + + +--+ + +--+ | | | | | | | | | | | | | | | | | | | | | | | | | | + +--+ + +--+--+--+--+--+--+ + +--+--+ + + +--+--+ + | | | | | | | | | | | | | | | | | | | | + + +--+--+ + +--+--+ +--+--+--+ + +--+ +--+--+ + + | | | | | | | | | | | | | | | | | | | | | | + + +--+--+--+ + + +--+ +--+ + +--+ +--+ + +--+--+ | | | | | | | | | | | | | | | | | | | | | | | | | | + + + +--+ +--+--+ + + + + +--+ + + +--+--+--+ + | | | | | | | | | | | | | | | | | | | | | | | | | | | | + + + + +--+--+ + +--+ +--+--+--+--+ + + + + + + | | | | | | | | | | | | | | | | | | | | | | | | | | + +--+--+ + +--+--+--+ +--+--+ + +--+--+ +--+ + +--+ | | | | | | | | | | | | | | | | | | +--+--+--+ +--+ + +--+--+ + +--+ + +--+--+--+--+--+ + | | | | | | | | | | | | | | | | | | + +--+--+--+--+ +--+--+ +--+ +--+--+ + +--+ +--+--+--+ | | | | | | | | | | | | | | | | | | | | | | | | + +--+ + + +--+--+ +--+ +--+--+ + +--+ +--+ + + + | | | | | | | | | | | | | | | | | | | | | | | | +--+ + + +--+--+ +--+ +--+--+ + +--+ +--+ + +--+ + | | | | | | | | | | | | | | | | | | | | | | + +--+ +--+--+ +--+ +--+ +--+ +--+ +--+ + +--+--+ + | | | | | | | | | | | | | | | | | | | | | | +--+ + +--+ + +--+--+ +--+ +--+--+ + + +--+ +--+--+ | | | | | | | | | | | | | | | | | | | | | | | | + + + + + +--+ +--+ + +--+ + +--+--+--+ +--+--+ + | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +--+--+ + + +--+ +--+--+--+ + + + + +--+--+ + + | | | | | | | | | | | | | | | | | | | | | | +--+--+--+--+--+ + +--+--+ +--+--+ + + +--+--+ + + + | | | | | | | | | | | | | | | | | | | | + + + + + + +--+ + +--+ +--+--+--+--+--+ +--+--+ + | | | | | | | | | | | | | | | | | | | | | | | | | | + +--+--+ +--+ + +--+--+--+ + + + + + +--+--+ + + | | | | | | | | | | | | | | | | | | | | | | | | +--+ + +--+ + +--+--+--+ +--+--+ + + + +--+--+--+ + | | | | | | | | | | | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--
Common Lisp
The remove-wall function has been written so as to be as close as possible to the specification. The walls are made from a single unicode character, specified by the block keyword, e. g. (maze 20 6 :block #\X). The BOX_DRAWINGS_LIGHT_DIAGONAL_CROSS character is used by default. <lang lisp>(defun shuffle (list) ;; Z not uniform
(sort list '> :key (lambda(x) (random 1.0))))
(defun neighbors (x y maze)
(remove-if-not
(lambda (x-y) (and (< -1 (first x-y) (array-dimension maze 0))
(< -1 (second x-y) (array-dimension maze 1))))
`((,x ,(+ y 2)) (,(- x 2) ,y) (,x ,(- y 2)) (,(+ x 2) ,y))))
(defun remove-wall (maze x y &optional visited)
(labels ((walk (maze x y)
(push (list x y) visited)
(loop for (u v) in (shuffle (neighbors x y maze))
unless (member (list u v) visited :test 'equal)
do (setf (aref maze u v) #\space
(aref maze (/ (+ x u) 2) (/ (+ y v) 2)) #\space)
(walk maze u v))))
(setf (aref maze x y) #\space)
(walk maze x y)))
(defun draw-maze (width height &key (block #\BOX_DRAWINGS_LIGHT_DIAGONAL_CROSS))
(let ((maze (make-array (list (1+ (* 2 height)) (1+ (* 2 width)))
:element-type 'character :initial-element block)))
(remove-wall maze (1+ (* 2 (random height))) (1+ (* 2 (random width))))
(loop for i below (array-dimension maze 0)
do (fresh-line)
(loop for j below (array-dimension maze 1)
do (princ (aref maze i j))))))
(draw-maze 20 6)</lang>
- Output:
╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳╳╳╳╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳╳╳ ╳ ╳╳╳ ╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳ ╳╳╳ ╳╳╳ ╳ ╳╳╳╳╳ ╳╳╳╳╳ ╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳╳╳ ╳╳╳ ╳╳╳╳╳╳╳ ╳ ╳ ╳╳╳╳╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳ ╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳╳
Another solution using unicode line drawing chars. Assumes they are single width on console. Code pretty horribly unreadable. <lang lisp>(setf *random-state* (make-random-state t))
(defun 2d-array (w h)
(make-array (list h w) :initial-element 0))
(defmacro or-and (v a b c)
`(if (or ,a (and ,b (= 1 ,c))) 0 ,v))
(defun make-maze (w h)
(let ((vis (2d-array w h))
(ver (2d-array w h)) (hor (2d-array w h)))
(labels
((walk (y x)
(setf (aref vis y x) 1) (loop (let (x2 y2) (loop for (dx dy) in '((-1 0) (1 0) (0 -1) (0 1)) with cnt = 0 do (let ((xx (+ x dx)) (yy (+ y dy))) (if (and (array-in-bounds-p vis yy xx) (zerop (aref vis yy xx)) (zerop (random (incf cnt)))) (setf x2 xx y2 yy)))) (if (not x2) (return-from walk)) (if (= x x2) (setf (aref hor (min y y2) x) 1) (setf (aref ver y (min x x2)) 1)) (walk y2 x2))))
(show ()
(let ((g " │││─┘┐┤─└┌├─┴┬┼")) (loop for i from 0 to h do (loop for j from 0 to w do (format t "~c~a" (char g (+ (or-and 1 (= i 0) (> j 0) (aref ver (1- i) (1- j))) (or-and 2 (= i h) (> j 0) (aref ver i (1- j))) (or-and 4 (= j 0) (> i 0) (aref hor (1- i) (1- j))) (or-and 8 (= j w) (> i 0) (aref hor (1- i) j )))) (if (and (< j w) (or (= i 0) (= 0 (aref hor (1- i) j)))) "───" " "))) (terpri) (when (< i h) (loop for j from 0 below w do (format t (if (or (= j 0) (= 0 (aref ver i (1- j)))) "│ " " "))) (format t "│~%"))))))
(walk (random h) (random w))
(show))))
(make-maze 20 20)</lang>
- Output:
┼───┴───┼───┴───┴───┼───┴───┴───┼ │ │ │ │ ┼──── │ │ │ │ ┌───┐ ├ │ │ │ │ │ │ │ │ ┤ ┌───┘ │ │ │ │ │ ├ │ │ │ │ │ │ │ ┤ │ ┌───┘ ├───────┤ │ ├ │ │ │ │ │ │ ┤ │ │ ────┤ │ │ ────┼ │ │ │ │ │ │ ┤ ────┼───┐ │ │ └───┐ ├ │ │ │ │ │ │ ┼───┐ │ └───────┼───┐ └───┼ │ │ │ │ │ ┤ └──────────── │ └───┐ ├ │ │ │ ┼───┬───┬───┬───┬───┬───┬───┼───┼
D
<lang d>void main() @safe {
import std.stdio, std.algorithm, std.range, std.random;
enum uint w = 14, h = 10;
auto vis = new bool[][](h, w),
hor = iota(h + 1).map!(_ => ["+---"].replicate(w)).array,
ver = h.iota.map!(_ => ["| "].replicate(w) ~ "|").array;
void walk(in uint x, in uint y) /*nothrow*/ @safe /*@nogc*/ {
vis[y][x] = true;
//foreach (immutable p; [[x-1,y], [x,y+1], [x+1,y], [x,y-1]].randomCover) {
foreach (const p; [[x-1, y], [x, y+1], [x+1, y], [x, y-1]].randomCover) {
if (p[0] >= w || p[1] >= h || vis[p[1]][p[0]]) continue;
if (p[0] == x) hor[max(y, p[1])][x] = "+ ";
if (p[1] == y) ver[y][max(x, p[0])] = " ";
walk(p[0], p[1]);
}
}
walk(uniform(0, w), uniform(0, h));
foreach (const a, const b; hor.zip(ver ~ []))
join(a ~ "+\n" ~ b).writeln;
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+---+ + +---+ + +---+---+---+ + + | | | | | | | | +---+---+---+---+---+---+---+ +---+ +---+ + +---+ | | | | | | + +---+---+---+ + + +---+ +---+---+ +---+---+ | | | | | | | | | +---+ + + + + +---+---+---+ + +---+ + + | | | | | | | | | + +---+ + +---+---+ + +---+---+---+ +---+ + | | | | | | + +---+---+ + +---+---+---+---+---+ +---+---+ + | | | | | | | | +---+ + +---+---+ + +---+ + + +---+---+ + | | | | | | | | + +---+---+---+ + +---+ +---+ + + +---+---+ | | | | | | | | | + + +---+---+---+---+ +---+ + +---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+
EGL
<lang EGL>program MazeGen
// First and last columns/rows are "dead" cells. Makes generating // a maze with border walls much easier. Therefore, a visible // 20x20 maze has a maze size of 22. mazeSize int = 22;
south boolean[][]; west boolean[][]; visited boolean[][];
function main()
initMaze();
generateMaze();
drawMaze();
end
private function initMaze()
visited = createBooleanArray(mazeSize, mazeSize, false);
// Initialize border cells as already visited
for(col int from 1 to mazeSize)
visited[col][1] = true;
visited[col][mazeSize] = true;
end
for(row int from 1 to mazeSize)
visited[1][row] = true;
visited[mazeSize][row] = true;
end
// Initialize all walls as present
south = createBooleanArray(mazeSize, mazeSize, true);
west = createBooleanArray(mazeSize, mazeSize, true);
end
private function createBooleanArray(col int in, row int in, initialState boolean in) returns(boolean[][])
newArray boolean[][] = new boolean[0][0];
for(i int from 1 to col)
innerArray boolean[] = new boolean[0];
for(j int from 1 to row)
innerArray.appendElement(initialState);
end
newArray.appendElement(innerArray);
end
return(newArray);
end
private function createIntegerArray(col int in, row int in, initialValue int in) returns(int[][])
newArray int[][] = new int[0][0];
for(i int from 1 to col)
innerArray int[] = new int[0];
for(j int from 1 to row)
innerArray.appendElement(initialValue);
end
newArray.appendElement(innerArray);
end
return(newArray);
end
private function generate(col int in, row int in)
// Mark cell as visited
visited[col][row] = true;
// Keep going as long as there is an unvisited neighbor
while(!visited[col][row + 1] || !visited[col + 1][row] ||
!visited[col][row - 1] || !visited[col - 1][row])
while(true)
r float = MathLib.random(); // Choose a random direction
case
when(r < 0.25 && !visited[col][row + 1]) // Go south
south[col][row] = false; // South wall down
generate(col, row + 1);
exit while;
when(r >= 0.25 && r < 0.50 && !visited[col + 1][row]) // Go east
west[col + 1][row] = false; // West wall of neighbor to the east down
generate(col + 1, row);
exit while;
when(r >= 0.5 && r < 0.75 && !visited[col][row - 1]) // Go north
south[col][row - 1] = false; // South wall of neighbor to the north down
generate(col, row - 1);
exit while;
when(r >= 0.75 && r < 1.00 && !visited[col - 1][row]) // Go west
west[col][row] = false; // West wall down
generate(col - 1, row);
exit while;
end
end
end
end
private function generateMaze()
// Pick random start position (within the visible maze space)
randomStartCol int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
randomStartRow int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
generate(randomStartCol, randomStartRow);
end
private function drawMaze()
line string;
// Iterate over wall arrays (skipping dead border cells as required).
// Construct a line at a time and output to console.
for(row int from 1 to mazeSize - 1)
if(row > 1)
line = "";
for(col int from 2 to mazeSize)
if(west[col][row])
line ::= "| ";
else
line ::= " ";
end
end
Syslib.writeStdout(line);
end
line = "";
for(col int from 2 to mazeSize - 1)
if(south[col][row])
line ::= "+---";
else
line ::= "+ ";
end
end
line ::= "+";
SysLib.writeStdout(line);
end
end
end</lang>
- Output example (for 10x10 maze):
+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+---+---+ +---+ + + + | | | | | | | | + +---+ + + + + + +---+ + | | | | | | | | + + +---+ + +---+ + + +---+ | | | | | | | | + +---+---+ + + +---+ +---+---+ | | | | | | | + + +---+---+ + + + + + + | | | | | | | | | + + + + +---+ + +---+---+ + | | | | | | | + +---+ +---+---+---+ + + + + | | | | | | + +---+ +---+ + +---+ +---+ + | | | | | | | +---+ +---+ +---+---+---+---+ + + | | | +---+---+---+---+---+---+---+---+---+---+
Elixir
<lang elixir>defmodule Maze do
def generate(w, h) do
maze = (for i <- 1..w, j <- 1..h, into: Map.new, do: {{:vis, i, j}, true})
|> walk(:rand.uniform(w), :rand.uniform(h))
print(maze, w, h)
maze
end
defp walk(map, x, y) do
Enum.shuffle( [[x-1,y], [x,y+1], [x+1,y], [x,y-1]] )
|> Enum.reduce(Map.put(map, {:vis, x, y}, false), fn [i,j],acc ->
if acc[{:vis, i, j}] do
{k, v} = if i == x, do: {{:hor, x, max(y, j)}, "+ "},
else: {{:ver, max(x, i), y}, " "}
walk(Map.put(acc, k, v), i, j)
else
acc
end
end)
end
defp print(map, w, h) do
Enum.each(1..h, fn j ->
IO.puts Enum.map_join(1..w, fn i -> Map.get(map, {:hor, i, j}, "+---") end) <> "+"
IO.puts Enum.map_join(1..w, fn i -> Map.get(map, {:ver, i, j}, "| ") end) <> "|"
end)
IO.puts String.duplicate("+---", w) <> "+"
end
end
Maze.generate(20, 10)</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | | + +---+ + +---+ +---+ +---+---+---+---+ + + +---+---+ + +---+ | | | | | | | | | | | + + +---+---+ +---+---+---+---+ +---+---+ + + + + + + + + | | | | | | | | | | | | | | | | + + + + +---+---+ + + +---+ + + +---+ + +---+ + + + | | | | | | | | | | | | + + + + +---+---+---+---+---+---+---+ +---+---+---+ +---+---+---+ + | | | | | | | | | | | + + +---+---+---+---+ + + + + +---+ + + + + +---+ + + | | | | | | | | | | | | | + +---+---+---+---+ + + + + +---+ + + +---+---+---+ +---+ + | | | | | | | | | | | | + +---+---+---+---+ + +---+---+ +---+---+ + + + + +---+ +---+ | | | | | | | | | | | | + +---+ + +---+---+---+---+ +---+ +---+---+---+ + +---+ + + + | | | | | | | | | | | | + + + +---+ + +---+---+ + +---+---+---+---+---+---+ + + + + | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Elm
<lang elm>import Maybe as M import Result as R import Matrix import Mouse import Random exposing (Seed) import Matrix.Random import Time exposing (Time, every, second) import Set exposing (Set, fromList) import List exposing (..) import String exposing (join) import Html exposing (Html, br, input, h1, h2, text, div, button) import Html.Events as HE import Html.Attributes as HA import Html.App exposing (program) import Json.Decode as JD import Svg import Svg.Attributes exposing (version, viewBox, cx, cy, r, x, y, x1, y1, x2, y2, fill,points, style, width, height, preserveAspectRatio)
minSide = 10 maxSide = 40 w = 700 h = 700 dt = 0.001
type alias Direction = Int down = 0 right = 1
type alias Door = (Matrix.Location, Direction)
type State = Initial | Generating | Generated | Solved
type alias Model =
{ rows : Int
, cols : Int
, animate : Bool
, boxes : Matrix.Matrix Bool
, doors : Set Door
, current : List Matrix.Location
, state : State
, seedStarter : Int
, seed : Seed
}
initdoors : Int -> Int -> Set Door initdoors rows cols =
let pairs la lb = List.concatMap (\at -> List.map ((,) at) lb) la downs = pairs (pairs [0..rows-2] [0..cols-1]) [down] rights = pairs (pairs [0..rows-1] [0..cols-2]) [right] in downs ++ rights |> fromList
initModel : Int -> Int -> Bool -> State -> Int -> Model initModel rows cols animate state starter =
let rowGenerator = Random.int 0 (rows-1)
colGenerator = Random.int 0 (cols-1)
locationGenerator = Random.pair rowGenerator colGenerator
(c, s)= Random.step locationGenerator (Random.initialSeed starter)
in { rows = rows
, cols = cols
, animate = animate
, boxes = Matrix.matrix rows cols (\location -> state == Generating && location == c)
, doors = initdoors rows cols
, current = if state == Generating then [c] else []
, state = state
, seedStarter = starter -- updated every Tick until maze generated.
, seed = s
}
view model =
let borderLineStyle = style "stroke:green;stroke-width:0.3" wallLineStyle = style "stroke:green;stroke-width:0.1"
x1Min = x1 <| toString 0 y1Min = y1 <| toString 0 x1Max = x1 <| toString model.cols y1Max = y1 <| toString model.rows x2Min = x2 <| toString 0 y2Min = y2 <| toString 0 x2Max = x2 <| toString model.cols y2Max = y2 <| toString model.rows
borders = [ Svg.line [ x1Min, y1Min, x2Max, y2Min, borderLineStyle ] []
, Svg.line [ x1Max, y1Min, x2Max, y2Max, borderLineStyle ] []
, Svg.line [ x1Max, y1Max, x2Min, y2Max, borderLineStyle ] []
, Svg.line [ x1Min, y1Max, x2Min, y2Min, borderLineStyle ] []
]
doorToLine door =
let (deltaX1, deltaY1) = if (snd door == right) then (1,0) else (0,1)
(row, column) = fst door
in Svg.line [ x1 <| toString (column + deltaX1)
, y1 <| toString (row + deltaY1)
, x2 <| toString (column + 1)
, y2 <| toString (row + 1)
, wallLineStyle ] []
doors = (List.map doorToLine <| Set.toList model.doors )
circleInBox (row,col) color =
Svg.circle [ r "0.25"
, fill (color)
, cx (toString (toFloat col + 0.5))
, cy (toString (toFloat row + 0.5))
] []
showUnvisited location box =
if box then [] else [ circleInBox location "yellow" ]
unvisited = model.boxes
|> Matrix.mapWithLocation showUnvisited
|> Matrix.flatten
|> concat
current =
case head model.current of
Nothing -> []
Just c -> [circleInBox c "black"]
maze =
if model.animate || model.state /= Generating
then [ Svg.g [] <| doors ++ borders ++ unvisited ++ current ]
else [ Svg.g [] <| borders ]
in
div
[]
[ h2 [centerTitle] [text "Maze Generator"]
, div
[floatLeft]
( slider "rows" minSide maxSide model.rows SetRows
++ [ br [] [] ]
++ slider "cols" minSide maxSide model.cols SetCols
++ [ br [] [] ]
++ checkbox "Animate" model.animate SetAnimate
++ [ br [] [] ]
++ [ button
[ HE.onClick Generate ]
[ text "Generate"]
] )
, div
[floatLeft]
[ Svg.svg
[ version "1.1"
, width (toString w)
, height (toString h)
, viewBox (join " "
[ 0 |> toString
, 0 |> toString
, model.cols |> toString
, model.rows |> toString ])
]
maze
]
]
checkbox label checked msg =
[ input
[ HA.type' "checkbox"
, HA.checked checked
, HE.on "change" (JD.map msg HE.targetChecked)
]
[]
, text label
]
slider name min max current msg =
[ input [ HA.value (if current >= min then current |> toString else "") , HE.on "input" (JD.map msg HE.targetValue ) , HA.type' "range" , HA.min <| toString min , HA.max <| toString max ] [] , text <| name ++ "=" ++ (current |> toString) ]
floatLeft = HA.style [ ("float", "left") ] centerTitle = HA.style [ ( "text-align", "center") ]
unvisitedNeighbors : Model -> Matrix.Location -> List Matrix.Location unvisitedNeighbors model (row,col) =
[(row, col-1), (row-1, col), (row, col+1), (row+1, col)] |> List.filter (\l -> fst l >= 0 && snd l >= 0 && fst l < model.rows && snd l < model.cols) |> List.filter (\l -> (Matrix.get l model.boxes) |> M.withDefault False |> not)
updateModel' : Model -> Int -> Model updateModel' model t =
case head model.current of
Nothing -> {model | state = Generated, seedStarter = t }
Just prev ->
let neighbors = unvisitedNeighbors model prev
in if (length neighbors) > 0 then
let (neighborIndex, seed) = Random.step (Random.int 0 (length neighbors-1)) model.seed
next = head (drop neighborIndex neighbors) |> M.withDefault (0,0)
boxes = Matrix.set next True model.boxes
dir = if fst prev == fst next then right else down
doorCell = if ( (dir == down) && (fst prev < fst next))
|| (dir == right ) && (snd prev < snd next) then prev else next
doors = Set.remove (doorCell, dir) model.doors
in {model | boxes=boxes, doors=doors, current=next :: model.current, seed=seed, seedStarter = t}
else
let tailCurrent = tail model.current |> M.withDefault []
in updateModel' {model | current = tailCurrent} t
updateModel : Msg -> Model -> Model updateModel msg model =
let stringToCellCount s =
let v' = String.toInt s |> R.withDefault minSide
in if v' < minSide then minSide else v'
in case msg of
Tick tf ->
let t = truncate tf
in
if (model.state == Generating) then updateModel' model t
else { model | seedStarter = t }
Generate ->
initModel model.rows model.cols model.animate Generating model.seedStarter
SetRows countString ->
initModel (stringToCellCount countString) model.cols model.animate Initial model.seedStarter
SetCols countString ->
initModel model.rows (stringToCellCount countString) model.animate Initial model.seedStarter
SetAnimate b ->
{ model | animate = b }
NoOp -> model
type Msg = NoOp | Tick Time | Generate | SetRows String | SetCols String | SetAnimate Bool
subscriptions model = every (dt * second) Tick
main =
let
update msg model = (updateModel msg model, Cmd.none)
init = (initModel 21 36 False Initial 0, Cmd.none)
in program
{ init = init
, view = view
, update = update
, subscriptions = subscriptions
}</lang>
Link to live demo: http://dc25.github.io/mazeGenerationElm/
Erlang
Erlang is single assignment. To get mutability I use processes. The code is over-enginered for this task, but the extra is used for Maze_solving. Also, Erlang starts counting at 1, not 0, so the co-ordinate of the lower left corner is 1,1.
Using multiple processes
<lang Erlang> -module( maze ).
-export( [cell_accessible_neighbours/1, cell_content/1, cell_content_set/2, cell_pid/3, cell_position/1, display/1, generation/2, stop/1, task/0] ).
-record( maze, {dict, max_x, max_y, start} ). -record( state, {content=" ", controller, is_dug=false, max_x, max_y, neighbours=[], position, walls=[north, south, east, west], walk_done} ).
cell_accessible_neighbours( Pid ) -> read( Pid, accessible_neighbours ).
cell_content( Pid ) -> read( Pid, content ).
cell_content_set( Pid, Content ) -> Pid ! {content, Content, erlang:self()}.
cell_pid( X, Y, Maze ) -> dict:fetch( {X, Y}, Maze#maze.dict ).
cell_position( Pid ) -> read( Pid, position ).
display( #maze{dict=Dict, max_x=Max_x, max_y=Max_y} ) -> Position_pids = dict:to_list( Dict ), display( Max_x, Max_y, reads(Position_pids, content), reads(Position_pids, walls) ).
generation( Max_x, Max_y ) ->
Controller = erlang:self(),
Position_pids = cells_create( Controller, Max_x, Max_y ),
Pids = [Y || {_X, Y} <- Position_pids],
[X ! {position_pids, Position_pids} || X <- Pids],
{Position, Pid} = lists:nth( random:uniform(Max_x * Max_y), Position_pids ),
Pid ! {dig, Controller},
receive
{dig_done} -> ok
end,
#maze{dict=dict:from_list(Position_pids), max_x=Max_x, max_y=Max_y, start=Position}.
stop( #maze{dict=Dict} ) ->
Controller = erlang:self(),
Pids = [Y || {_X, Y} <- dict:to_list(Dict)],
[X ! {stop, Controller} || X <- Pids],
ok.
task() ->
Maze = generation( 16, 8 ),
io:fwrite( "Starting at ~p~n", [Maze#maze.start] ),
display( Maze ),
stop( Maze ).
cells_create( Controller, Max_x, Max_y ) -> [{{X, Y}, cell_create(Controller, Max_x, Max_y, {X, Y})} || X <- lists:seq(1, Max_x), Y<- lists:seq(1, Max_y)].
cell_create( Controller, Max_x, Max_y, {X, Y} ) -> erlang:spawn_link( fun() -> random:seed( X*1000, Y*1000, (X+Y)*1000 ), loop( #state{controller=Controller, max_x=Max_x, max_y=Max_y, position={X, Y}} ) end ).
display( Max_x, Max_y, Position_contents, Position_walls ) ->
All_rows = [display_row( Max_x, Y, Position_contents, Position_walls ) || Y <- lists:seq(Max_y, 1, -1)],
[io:fwrite("~s+~n~s|~n", [North, West]) || {North, West} <- All_rows],
io:fwrite("~s+~n", [lists:flatten(lists:duplicate(Max_x, display_row_north(true)))] ).
display_row( Max_x, Y, Position_contents, Position_walls ) -> North_wests = [display_row_walls(proplists:get_value({X,Y}, Position_contents), proplists:get_value({X,Y}, Position_walls)) || X <- lists:seq(1, Max_x)], North = lists:append( [North || {North, _West} <- North_wests] ), West = lists:append( [West || {_X, West} <- North_wests] ), {North, West}.
display_row_walls( Content, Walls ) -> {display_row_north( lists:member(north, Walls) ), display_row_west( lists:member(west, Walls), Content )}.
display_row_north( true ) -> "+---"; display_row_north( false ) -> "+ ".
display_row_west( true, Content ) -> "| " ++ Content ++ " "; display_row_west( false, Content ) -> " " ++ Content ++ " ".
loop( State ) ->
receive
{accessible_neighbours, Pid} ->
Pid ! {accessible_neighbours, loop_accessible_neighbours( State#state.neighbours, State#state.walls ), erlang:self()},
loop( State );
{content, Pid} ->
Pid ! {content, State#state.content, erlang:self()},
loop( State );
{content, Content, _Pid} ->
loop( State#state{content=Content} );
{dig, Pid} ->
Not_dug_neighbours = loop_not_dug( State#state.neighbours ), New_walls = loop_dig( Not_dug_neighbours, lists:delete( loop_wall_from_pid(Pid, State#state.neighbours), State#state.walls), Pid ), loop( State#state{is_dug=true, walls=New_walls, walk_done=Pid} );
{dig_done} ->
Not_dug_neighbours = loop_not_dug( State#state.neighbours ), New_walls = loop_dig( Not_dug_neighbours, State#state.walls, State#state.walk_done ), loop( State#state{walls=New_walls} );
{is_dug, Pid} ->
Pid ! {is_dug, State#state.is_dug, erlang:self()},
loop( State );
{position, Pid} ->
Pid ! {position, State#state.position, erlang:self()},
loop( State );
{position_pids, Position_pids} ->
{_My_position, Neighbours} = lists:foldl( fun loop_neighbours/2, {State#state.position, []}, Position_pids ),
erlang:garbage_collect(), % Shrink process after using large Pid_positions. For memory starved systems.
loop( State#state{neighbours=Neighbours} );
{stop, Controller} when Controller =:= State#state.controller ->
ok;
{walls, Pid} ->
Pid ! {walls, State#state.walls, erlang:self()},
loop( State )
end.
loop_accessible_neighbours( Neighbours, Walls ) -> [Pid || {Direction, Pid} <- Neighbours, not lists:member(Direction, Walls)].
loop_dig( [], Walls, Pid ) -> Pid ! {dig_done}, Walls; loop_dig( Not_dug_neighbours, Walls, _Pid ) ->
{Dig_pid, Dig_direction} = lists:nth( random:uniform(erlang:length(Not_dug_neighbours)), Not_dug_neighbours ),
Dig_pid ! {dig, erlang:self()},
lists:delete( Dig_direction, Walls ).
loop_neighbours( {{X, Y}, Pid}, {{X, My_y}, Acc} ) when Y =:= My_y + 1 -> {{X, My_y}, [{north, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{X, My_y}, Acc} ) when Y =:= My_y - 1 -> {{X, My_y}, [{south, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{My_x, Y}, Acc} ) when X =:= My_x + 1 -> {{My_x, Y}, [{east, Pid} | Acc]}; loop_neighbours( {{X, Y}, Pid}, {{My_x, Y}, Acc} ) when X =:= My_x - 1 -> {{My_x, Y}, [{west, Pid} | Acc]}; loop_neighbours( _Position_pid, Acc ) -> Acc.
loop_not_dug( Neighbours ) -> My_pid = erlang:self(), [Pid ! {is_dug, My_pid} || {_Direction, Pid} <- Neighbours], [{Pid, Direction} || {Direction, Pid} <- Neighbours, not read_receive(Pid, is_dug)].
loop_wall_from_pid( Pid, Neighbours ) -> loop_wall_from_pid_result( lists:keyfind(Pid, 2, Neighbours) ). loop_wall_from_pid_result( {Direction, _Pid} ) -> Direction; loop_wall_from_pid_result( false ) -> controller.
read( Pid, Key ) -> Pid ! {Key, erlang:self()}, read_receive( Pid, Key ).
read_receive( Pid, Key ) ->
receive
{Key, Value, Pid} -> Value
end.
reads( Position_pids, Key ) ->
My_pid = erlang:self(),
[Pid ! {Key, My_pid} || {_Position, Pid} <- Position_pids],
[{Position, read_receive(Pid, Key)} || {Position, Pid} <- Position_pids].
</lang>
- Output:
5> maze:task().
Starting at {10,5}
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| | | | | |
+---+ +---+---+ + + + +---+ + + + +---+---+ +
| | | | | | | | | |
+ +---+ + +---+ +---+---+ + +---+---+---+---+ + +
| | | | | | | | |
+ +---+ +---+---+ + +---+---+---+---+ + +---+---+ +
| | | | | | | | | |
+ + + + +---+---+ + +---+---+ +---+ + + +---+
| | | | | | | | | |
+---+ +---+---+ +---+---+---+---+ + + +---+ +---+ +
| | | | | | | | | |
+ + + + +---+---+ + +---+ + + +---+ + + +
| | | | | | | | | | |
+ +---+ + +---+---+ +---+ +---+---+---+ +---+---+ +
| | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Using 2 digraphs
Uses 2 digraph "objects": a) the 'matrix', a fully connected digraph of MxN vertices and b) the 'maze', an unconnected digraph, also MxN, that is populated while walking.
Employs a faux Visitor pattern to populate the maze while traversing the matrix in depth-first order.
Vertices: 0 .. MxN - 1
Rows: 0 .. M - 1
Cols: 0 .. N - 1
Usage: start with generate_default/0. Use generate_MxN() to test other maze sizes. <lang Erlang> -module(maze). -record(maze, {g, m, n}). -export([generate_default/0, generate_MxN/2]).
make_maze(M, N) ->
Maze = #maze{g = digraph:new(), m = M, n = N},
lists:foreach(fun(X) -> digraph:add_vertex(Maze#maze.g, X) end, lists:seq(0, M * N - 1)),
Maze.
row_at(V, Maze) -> trunc(V / Maze#maze.n). col_at(V, Maze) -> V - row_at(V, Maze) * Maze#maze.n. vertex_at(Row, Col, Maze) -> Cell_Exists = cell_exists(Row, Col, Maze), if Cell_Exists -> Row * Maze#maze.n + Col; true -> -1 end. cell_exists(Row, Col, Maze) -> (Row >= 0) and (Row < Maze#maze.m) and (Col >= 0) and (Col < Maze#maze.n).
adjacent_cells(V, Maze) -> % ordered: left, up, right, down
adjacent_cell(cell_left, V, Maze)++adjacent_cell(cell_up, V, Maze)++adjacent_cell(cell_right, V, Maze)++adjacent_cell(cell_down, V, Maze).
adjacent_cell(cell_left, V, Maze) -> case (col_at(V, Maze) == 0) of true -> []; _Else -> [V - 1] end; adjacent_cell(cell_up, V, Maze) -> case (row_at(V, Maze) == 0) of true -> []; _Else -> [V - Maze#maze.n] end; adjacent_cell(cell_right, V, Maze) -> case (col_at(V, Maze) == Maze#maze.n - 1) of true -> []; _Else -> [V + 1] end; adjacent_cell(cell_down, V, Maze) -> case (row_at(V, Maze) == Maze#maze.m - 1) of true -> []; _Else -> [V + Maze#maze.n] end.
connect_all(V, Maze) ->
lists:foreach(fun(X) -> digraph:add_edge(Maze#maze.g, V, X) end, adjacent_cells(V, Maze)).
make_maze(M, N, all_connected) ->
Maze = make_maze(M, N), lists:foreach(fun(X) -> connect_all(X, Maze) end, lists:seq(0, M * N - 1)), Maze.
maze_parts(Maze) ->
SPR = Maze#maze.n + 1, % slots per row is #columns + 1 NPR = (Maze#maze.m * 2) + 1, % # part rows is #(rows * 2) + 1 [make_part(Maze, trunc(Index/SPR), Index - trunc(Index/SPR) * SPR) || Index <- lists:seq(0, (SPR * NPR) - 1)].
draw_part(Part) ->
case Part of
{pwall, pclosed} -> io:format("+---");
{pwall, popen} -> io:format("+ ");
{pwall, pend} -> io:format("+~n");
{phall, pclosed} -> io:format("| ");
{phall, popen} -> io:format(" ");
{phall, pend} -> io:format("|~n")
end.
has_neighbour(Maze, Row, Col, Direction) ->
V = vertex_at(Row, Col, Maze),
if
V >= 0 ->
Adjacent = adjacent_cell(Direction, V, Maze),
if
length(Adjacent) > 0 ->
Neighbours = digraph:out_neighbours(Maze#maze.g, lists:nth(1, Adjacent)),
lists:member(V, Neighbours);
true -> false
end;
true -> false
end.
make_part(Maze, DoubledRow, Col) ->
if
trunc(DoubledRow/2) * 2 == DoubledRow -> % --- (even row) making a wall above the cell
make_part(Maze, trunc(DoubledRow/2), Col, cell_up, pwall);
true -> % ---otherwise (odd row) making a hall through the cell
make_part(Maze, trunc(DoubledRow/2), Col, cell_left, phall)
end.
make_part(Maze, _, Col, _, Part_Type) when Col == Maze#maze.n -> {Part_Type, pend}; make_part(Maze, Row, Col, Direction, Part_Type) ->
Has_Neighbour = has_neighbour(Maze, Row, Col, Direction),
if
Has_Neighbour -> {Part_Type, popen};
true -> {Part_Type, pclosed}
end.
shuffle([], Acc) -> Acc; shuffle(List, Acc) ->
Elem = lists:nth(random:uniform(length(List)), List), shuffle(lists:delete(Elem, List), Acc++[Elem]).
processDepthFirst(Maze) ->
if
Maze#maze.m * Maze#maze.n == 0 -> [{pwall, pend}];
true ->
Visited = array:new([{size, Maze#maze.m * Maze#maze.n},{fixed,true},{default,false}]),
{_, Path} = processDepthFirst(Maze, -1, random:uniform(Maze#maze.m * Maze#maze.n) - 1, {Visited, []}),
Path
end.
processDepthFirst(Maze, Vfrom, V, VandP) ->
{Visited, Path} = VandP,
Was_Visited = array:get(V, Visited),
if
not Was_Visited ->
Walker = fun(X, Acc) -> processDepthFirst(Maze, V, X, Acc) end,
Random_Neighbours = shuffle(digraph:out_neighbours(Maze#maze.g, V), []),
lists:foldl(Walker, {array:set(V, true, Visited), Path++[{Vfrom, V}]}, Random_Neighbours);
true -> VandP
end.
open_wall(_, {-1, _}) -> ok; open_wall(Maze, {V, V2}) ->
case (V2 > V) of true -> digraph:add_edge(Maze#maze.g, V, V2); _Else -> digraph:add_edge(Maze#maze.g, V2, V) end.
generate_MxN(M, N) ->
Maze = make_maze(M, N), Matrix = make_maze(M, N, all_connected), Trail = processDepthFirst(Matrix), lists:foreach(fun(X) -> open_wall(Maze, X) end, Trail), Parts = maze_parts(Maze), lists:foreach(fun(X) -> draw_part(X) end, Parts).
generate_default() ->
generate_MxN(9, 9).
</lang>
- Output:
8> maze:generate_default(). +---+---+---+---+---+---+---+---+---+ | | | + + +---+ +---+---+---+---+ + | | | | | | + +---+ +---+---+ + + + + | | | | | | | + + + + + +---+---+---+ + | | | | | | | | + + +---+ + + + + +---+ | | | | | | + +---+---+---+---+---+---+---+ + | | | | + + +---+---+ +---+---+ + + | | | | | | + +---+---+---+ +---+ +---+ + | | | | | | + + +---+ +---+ +---+ + + | | | | +---+---+---+---+---+---+---+---+---+ ok 9>
F#
Using mutable state in the form of 2D arrays: <lang fsharp>let rnd : int -> int =
let gen = new System.Random() fun max -> gen.Next(max)
// randomly choose an element of a list let choose (xs:_ list) = xs.[rnd xs.Length]
type Maze(width, height) =
// (x,y) -> have we been here before?
let visited = Array2D.create width height false
// (x,y) -> is there a wall between (x,y) and (x+1,y)?
let horizWalls = Array2D.create width height true
// (x,y) -> is there a wall between (x,y) and (x,y+1)?
let vertWalls = Array2D.create width height true
let isLegalPoint (x,y) =
x >= 0 && x < width && y >= 0 && y < height
let neighbours (x,y) =
[(x-1,y);(x+1,y);(x,y-1);(x,y+1)] |> List.filter isLegalPoint
let removeWallBetween (x1,y1) (x2,y2) =
if x1 <> x2 then
horizWalls.[min x1 x2, y1] <- false
else
vertWalls.[x1, min y1 y2] <- false
let rec visit (x,y as p) =
let rec loop ns =
let (nx,ny) as n = choose ns
if not visited.[nx,ny] then
removeWallBetween p n
visit n
match List.filter ((<>) n) ns with
| [] -> ()
| others -> loop others
visited.[x,y] <- true loop (neighbours p)
do visit (rnd width, rnd height)
member x.Print() =
("+" + (String.replicate width "-+")) ::
[for y in 0..(height-1) do
yield "\n|"
for x in 0..(width-1) do
yield if horizWalls.[x,y] then " |" else " "
yield "\n+"
for x in 0..(width-1) do
yield if vertWalls.[x,y] then "-+" else " +"
]
|> String.concat ""
|> printfn "%s"
let m = new Maze(10,10) m.Print()</lang>
- Output example:
+-+-+-+-+-+-+-+-+-+-+ | | | | + +-+-+-+-+ +-+ + + + | | | | | | + +-+-+ + +-+-+ +-+ + | | | | | +-+ +-+ +-+-+ +-+-+ + | | | | | + +-+ +-+ +-+-+-+ +-+ | | | | | | + + +-+ +-+ +-+ +-+ + | | | | | | | | + + +-+ + +-+-+-+ + + | | | | | +-+ + +-+-+-+-+-+-+ + | | | | | + +-+-+ +-+ +-+-+ + + | | | | | | + +-+ +-+ +-+-+ +-+-+ | | | +-+-+-+-+-+-+-+-+-+-+
Go
<lang go>package main
import (
"bytes" "fmt" "math/rand" "time"
)
type maze struct {
c []byte // cell contents h []byte // horizontal walls above cells v []byte // vertical walls to the left of cells c2 [][]byte // cells by row h2 [][]byte // horizontal walls by row (ignore first row) v2 [][]byte // vertical walls by row (ignore first of each column)
}
func newMaze(rows, cols int) *maze {
c := make([]byte, rows*cols) // all cells
h := bytes.Repeat([]byte{'-'}, rows*cols) // all horizontal walls
v := bytes.Repeat([]byte{'|'}, rows*cols) // all vertical walls
c2 := make([][]byte, rows) // cells by row
h2 := make([][]byte, rows) // horizontal walls by row
v2 := make([][]byte, rows) // vertical walls by row
for i := range h2 {
c2[i] = c[i*cols : (i+1)*cols]
h2[i] = h[i*cols : (i+1)*cols]
v2[i] = v[i*cols : (i+1)*cols]
}
return &maze{c, h, v, c2, h2, v2}
}
func (m *maze) String() string {
hWall := []byte("+---")
hOpen := []byte("+ ")
vWall := []byte("| ")
vOpen := []byte(" ")
rightCorner := []byte("+\n")
rightWall := []byte("|\n")
var b []byte
// for all rows
for r, hw := range m.h2 {
// draw h walls
for _, h := range hw {
if h == '-' || r == 0 {
b = append(b, hWall...)
} else {
b = append(b, hOpen...)
}
}
b = append(b, rightCorner...)
// draw v walls
for c, vw := range m.v2[r] {
if vw == '|' || c == 0 {
b = append(b, vWall...)
} else {
b = append(b, vOpen...)
}
// draw cell contents
if m.c2[r][c] != 0 {
b[len(b)-2] = m.c2[r][c]
}
}
b = append(b, rightWall...)
}
// draw bottom edge of maze
for _ = range m.h2[0] {
b = append(b, hWall...)
}
b = append(b, rightCorner...)
return string(b)
}
func (m *maze) gen() {
m.g2(rand.Intn(len(m.c2)), rand.Intn(len(m.c2[0])))
}
const (
up = iota dn rt lf
)
func (m *maze) g2(r, c int) {
m.c2[r][c] = ' '
for _, dir := range rand.Perm(4) {
switch dir {
case up:
if r > 0 && m.c2[r-1][c] == 0 {
m.h2[r][c] = 0
m.g2(r-1, c)
}
case lf:
if c > 0 && m.c2[r][c-1] == 0 {
m.v2[r][c] = 0
m.g2(r, c-1)
}
case dn:
if r < len(m.c2)-1 && m.c2[r+1][c] == 0 {
m.h2[r+1][c] = 0
m.g2(r+1, c)
}
case rt:
if c < len(m.c2[0])-1 && m.c2[r][c+1] == 0 {
m.v2[r][c+1] = 0
m.g2(r, c+1)
}
}
}
}
func main() {
rand.Seed(time.Now().UnixNano()) m := newMaze(4, 6) m.gen() fmt.Print(m)
}</lang>
- Output:
+---+---+---+---+---+---+ | | | | + + + +---+ +---+ | | | | | + + +---+---+---+ + | | | | + + + +---+---+ + | | | +---+---+---+---+---+---+
Haskell
<lang haskell>import Control.Monad import Control.Monad.ST import Data.Array import Data.Array.ST import Data.STRef import System.Random
rand :: Random a => (a, a) -> STRef s StdGen -> ST s a rand range gen = do
(a, g) <- liftM (randomR range) $ readSTRef gen gen `writeSTRef` g return a
data Maze = Maze {rightWalls, belowWalls :: Array (Int, Int) Bool}
maze :: Int -> Int -> StdGen -> ST s Maze maze width height gen = do
visited <- mazeArray False
rWalls <- mazeArray True
bWalls <- mazeArray True
gen <- newSTRef gen
liftM2 (,) (rand (0, maxX) gen) (rand (0, maxY) gen) >>=
visit gen visited rWalls bWalls
liftM2 Maze (freeze rWalls) (freeze bWalls)
where visit gen visited rWalls bWalls here = do
writeArray visited here True
let ns = neighbors here
i <- rand (0, length ns - 1) gen
forM_ (ns !! i : take i ns ++ drop (i + 1) ns) $ \there -> do
seen <- readArray visited there
unless seen $ do
removeWall here there
visit gen visited rWalls bWalls there
where removeWall (x1, y1) (x2, y2) = writeArray
(if x1 == x2 then bWalls else rWalls)
(min x1 x2, min y1 y2)
False
neighbors (x, y) =
(if x == 0 then [] else [(x - 1, y )]) ++
(if x == maxX then [] else [(x + 1, y )]) ++
(if y == 0 then [] else [(x, y - 1)]) ++
(if y == maxY then [] else [(x, y + 1)])
maxX = width - 1
maxY = height - 1
mazeArray = newArray ((0, 0), (maxX, maxY))
:: Bool -> ST s (STArray s (Int, Int) Bool)
printMaze :: Maze -> IO () printMaze (Maze rWalls bWalls) = do
putStrLn $ '+' : (concat $ replicate (maxX + 1) "---+")
forM_ [0 .. maxY] $ \y -> do
putStr "|"
forM_ [0 .. maxX] $ \x -> do
putStr " "
putStr $ if rWalls ! (x, y) then "|" else " "
putStrLn ""
forM_ [0 .. maxX] $ \x -> do
putStr "+"
putStr $ if bWalls ! (x, y) then "---" else " "
putStrLn "+"
where maxX = fst (snd $ bounds rWalls)
maxY = snd (snd $ bounds rWalls)
main = getStdGen >>= stToIO . maze 11 8 >>= printMaze</lang>
- Sample output:
+---+---+---+---+---+---+---+---+---+---+---+ | | | + +---+---+---+ +---+---+---+---+---+ + | | | | | | + +---+---+ +---+---+ + + + + + | | | | | | | | + + + +---+---+---+---+ +---+ + + | | | | | | +---+---+ + +---+---+---+---+ +---+---+ | | | | | | + + + + +---+---+---+ +---+ + + | | | | | | | + +---+---+ + +---+---+---+ +---+ + | | | | | + +---+---+---+---+ + +---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+---+
Icon and Unicon
<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 $define BORDER 30 # border size in pixels
record mazeinfo(window,maze,filename) # keepers
procedure DisplayMaze(maze) #: show it off if CELL < 8 then runerr(205,CELL) # too small
wh := (ch := (mh := *maze ) * CELL) + 2 * BORDER # win, cell, maze height ww := (cw := (mw := *maze[1]) * CELL) + 2 * BORDER # win, cell, maze width
wparms := [ sprintf("Maze %dx%d",*maze,*maze[1]), # window parameters
"g","bg=white","canvas=hidden",
sprintf("size=%d,%d",ww,wh),
sprintf("dx=%d",BORDER),
sprintf("dy=%d",BORDER)]
&window := open!wparms | stop("Unable to open Window")
Fg("black") # Draw full grid every DrawLine(x := 0 to cw by CELL,0,x,ch+1) # . verticals every DrawLine(0,y := 0 to ch by CELL,cw+1,y) # . horizontals
Fg("white") # Set to erase lines every y := CELL*((r := 1 to mh)-1) & x := CELL*((c := 1 to mw)-1) do {
WAttrib("dx="||x+BORDER,"dy="||y+BORDER) # position @ cell r,c
if iand(maze[r,c],NORTH) > 0 then DrawLine(2,0,CELL-1,0)
if iand(maze[r,c],EAST) > 0 then DrawLine(CELL,2,CELL,CELL-1)
if iand(maze[r,c],SOUTH) > 0 then DrawLine(2,CELL,CELL-1,CELL)
if iand(maze[r,c],WEST) > 0 then DrawLine(0,2,0,CELL-1)
}
return mazeinfo(&window,maze,sprintf("maze-%dx%d-%d.gif",r,c,&now)) end</lang> Note: The underlying maze structure (matrix) is uni-directional from the start
printf.icn provides formatting
J
This algorithm allows almost no parallelism. So, while it might be "simple", generating very large mazes this way will not be necessarily efficient to implement on future (highly parallel) systems. That said, perhaps mazes with millions of cells are not very likely to be needed to be generated quickly.
But without any relevant grid library: <lang j>maze=:4 :0
assert.0<:n=.<:x*y
horiz=. 0$~x,y-1
verti=. 0$~(x-1),y
path=.,:here=. ?x,y
unvisited=.0 (<here+1)} 0,0,~|:0,0,~1$~y,x
while.n do.
neighbors=. here+"1 (,-)=0 1
neighbors=. neighbors #~ (<"1 neighbors+1) {unvisited
if.#neighbors do.
n=.n-1
next=. ({~ ?@#) neighbors
unvisited=.0 (<next+1)} unvisited
if.{.next=here
do. horiz=.1 (<-:here+next-0 1)} horiz
else. verti=. 1 (<-:here+next-1 0)} verti end.
path=.path,here=.next
else.
here=.{:path
path=.}:path
end.
end.
horiz;verti
)
display=:3 :0
size=. >.&$&>/y
text=. (}:1 3$~2*1+{:size)#"1":size$<' '
'hdoor vdoor'=. 2 4&*&.>&.> (#&,{@;&i./@$)&.> y
' ' (a:-.~0 1;0 2; 0 3;(2 1-~$text);(1 4&+&.> hdoor),,vdoor+&.>"0/2 1;2 2;2 3)} text
)</lang>
The result of maze is a pair of arrays: one for open "doors" in the horizontal direction and the other for open "doors" in the vertical direction. The entry and exit doors are not represented by maze -- they are implicitly defined and are implemented in display. (The sequences of coordinates in display are the relative coordinates for the doors. For example, 2 1;2 2;2 3 are where we put spaces for each vertical door. The variable text is an ascii representation of the maze grid before the doors are placed.)
- Example use (with ascii box drawing enabled):
<lang j> display 8 maze 11 + +---+---+---+---+---+---+---+---+---+---+ | | | | | + + + + +---+ + +---+---+ + + | | | | | | | | + +---+---+ + +---+---+---+ + + + | | | | | | | +---+ +---+ + + +---+ + +---+---+ | | | | | | | + + +---+---+ +---+ + +---+---+ + | | | | | | | | | + +---+ + + + + +---+---+ + + | | | | | + +---+---+---+---+---+---+---+ +---+ + | | | | | | | | | + + + + + + + + +---+ + + | | | | | +---+---+---+---+---+---+---+---+---+---+---+</lang>
Java
<lang java5>package org.rosettacode;
import java.util.Collections; import java.util.Arrays;
/*
* recursive backtracking algorithm * shamelessly borrowed from the ruby at * http://weblog.jamisbuck.org/2010/12/27/maze-generation-recursive-backtracking */
public class MazeGenerator { private final int x; private final int y; private final int[][] maze;
public MazeGenerator(int x, int y) { this.x = x; this.y = y; maze = new int[this.x][this.y]; generateMaze(0, 0); }
public void display() { for (int i = 0; i < y; i++) { // draw the north edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 1) == 0 ? "+---" : "+ "); } System.out.println("+"); // draw the west edge for (int j = 0; j < x; j++) { System.out.print((maze[j][i] & 8) == 0 ? "| " : " "); } System.out.println("|"); } // draw the bottom line for (int j = 0; j < x; j++) { System.out.print("+---"); } System.out.println("+"); }
private void generateMaze(int cx, int cy) { DIR[] dirs = DIR.values(); Collections.shuffle(Arrays.asList(dirs)); for (DIR dir : dirs) { int nx = cx + dir.dx; int ny = cy + dir.dy; if (between(nx, x) && between(ny, y) && (maze[nx][ny] == 0)) { maze[cx][cy] |= dir.bit; maze[nx][ny] |= dir.opposite.bit; generateMaze(nx, ny); } } }
private static boolean between(int v, int upper) { return (v >= 0) && (v < upper); }
private enum DIR { N(1, 0, -1), S(2, 0, 1), E(4, 1, 0), W(8, -1, 0); private final int bit; private final int dx; private final int dy; private DIR opposite;
// use the static initializer to resolve forward references static { N.opposite = S; S.opposite = N; E.opposite = W; W.opposite = E; }
private DIR(int bit, int dx, int dy) { this.bit = bit; this.dx = dx; this.dy = dy; } };
public static void main(String[] args) { int x = args.length >= 1 ? (Integer.parseInt(args[0])) : 8; int y = args.length == 2 ? (Integer.parseInt(args[1])) : 8; MazeGenerator maze = new MazeGenerator(x, y); maze.display(); }
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+ | | | | + +---+---+ +---+---+ + + +---+ | | | | | | | +---+---+ + + + +---+ +---+ + | | | | | | | + +---+---+ +---+ + +---+ + + | | | | | | | + + + +---+ +---+---+---+ + + | | | | | | + + +---+ + +---+---+ +---+---+ | | | | | | | + +---+ + +---+ +---+---+ + + | | | | | | +---+ + +---+ + +---+---+---+ + | | | | | | | + + +---+ + +---+---+ +---+ + | | | | | | | | + +---+ + +---+---+ + + + + | | | | +---+---+---+---+---+---+---+---+---+---+
JavaScript
<lang javascript>function maze(x,y) { var n=x*y-1; if (n<0) {alert("illegal maze dimensions");return;} var horiz =[]; for (var j= 0; j<x+1; j++) horiz[j]= [], verti =[]; for (var j= 0; j<x+1; j++) verti[j]= [], here = [Math.floor(Math.random()*x), Math.floor(Math.random()*y)], path = [here], unvisited = []; for (var j = 0; j<x+2; j++) { unvisited[j] = []; for (var k= 0; k<y+1; k++) unvisited[j].push(j>0 && j<x+1 && k>0 && (j != here[0]+1 || k != here[1]+1)); } while (0<n) { var potential = [[here[0]+1, here[1]], [here[0],here[1]+1], [here[0]-1, here[1]], [here[0],here[1]-1]]; var neighbors = []; for (var j = 0; j < 4; j++) if (unvisited[potential[j][0]+1][potential[j][1]+1]) neighbors.push(potential[j]); if (neighbors.length) { n = n-1; next= neighbors[Math.floor(Math.random()*neighbors.length)]; unvisited[next[0]+1][next[1]+1]= false; if (next[0] == here[0]) horiz[next[0]][(next[1]+here[1]-1)/2]= true; else verti[(next[0]+here[0]-1)/2][next[1]]= true; path.push(here = next); } else here = path.pop(); } return {x: x, y: y, horiz: horiz, verti: verti}; }
function display(m) {
var text= [];
for (var j= 0; j<m.x*2+1; j++) {
var line= [];
if (0 == j%2)
for (var k=0; k<m.y*4+1; k++)
if (0 == k%4)
line[k]= '+';
else
if (j>0 && m.verti[j/2-1][Math.floor(k/4)])
line[k]= ' ';
else
line[k]= '-';
else
for (var k=0; k<m.y*4+1; k++)
if (0 == k%4)
if (k>0 && m.horiz[(j-1)/2][k/4-1])
line[k]= ' ';
else
line[k]= '|';
else
line[k]= ' ';
if (0 == j) line[1]= line[2]= line[3]= ' ';
if (m.x*2-1 == j) line[4*m.y]= ' ';
text.push(line.join()+'\r\n');
}
return text.join();
}</lang>
Variable meanings in function maze:
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 output:
+ +---+---+---+---+---+---+---+---+---+---+ | | | | +---+---+ + +---+ + +---+---+ + + | | | | | | | | + + + +---+ +---+ +---+---+ + + | | | | | | | + +---+ +---+---+---+---+---+ + + + | | | | | | +---+ +---+ +---+---+ + +---+---+ + | | | | | | | + + + +---+---+---+---+---+ + + + | | | | | | + +---+---+ +---+---+ + +---+---+ + | | | | | | | + + + +---+ +---+---+ + + +---+ | | | | +---+---+---+---+---+---+---+---+---+---+---+
For an animated presentation of the progress of this maze creation process, you can use display in each iteration of the main loop. You would also need to take steps to make sure you could see each intermediate result.
For example, change replace the line while (0<n) { with:
<lang javascript> function step() {
if (0<n) {</lang>
And replace the closing brace for this while loop with:
<lang javascript> document.getElementById('out').innerHTML= display({x: x, y: y, horiz: horiz, verti: verti, here: here});
setTimeout(step, 100);
}
}
step();</lang>
To better see the progress, you might want a marker in place, showing the position being considered. To do that, replace the line which reads if (0 == k%4) { with
<lang javascript> if (m.here && m.here[0]*2+1 == j && m.here[1]*4+2 == k)
line[k]= '#'
else if (0 == k%4) {</lang>
Note however that this leaves the final '#' in place on maze completion, and that the function maze no longer returns a result which represents a generated maze.
Note also that this display suggests an optimization. You can replace the line reading path.push(here= next); with:
<lang javascript> here= next;
if (1 < neighbors.length)
path.push(here);</lang>
And this does indeed save a negligible bit of processing, but the maze algorithm will still be forced to backtrack through a number of locations which have no unvisited neighbors.
HTML Table
Using HTML, CSS and table cells for maze. <lang html><html><head><title>Maze maker</title> <style type="text/css"> table { border-collapse: collapse } td { width: 1em; height: 1em; border: 1px solid } td.s { border-bottom: none } td.n { border-top: none } td.w { border-left: none } td.e { border-right: none } td.v { background: skyblue} </style> <script type="application/javascript"> Node.prototype.add = function(tag, cnt, txt) { for (var i = 0; i < cnt; i++) this.appendChild(ce(tag, txt)); } Node.prototype.ins = function(tag) { this.insertBefore(ce(tag), this.firstChild) } Node.prototype.kid = function(i) { return this.childNodes[i] } Node.prototype.cls = function(t) { this.className += ' ' + t }
NodeList.prototype.map = function(g) { for (var i = 0; i < this.length; i++) g(this[i]); }
function ce(tag, txt) { var x = document.createElement(tag); if (txt !== undefined) x.innerHTML = txt; return x }
function gid(e) { return document.getElementById(e) } function irand(x) { return Math.floor(Math.random() * x) }
function make_maze() { var w = parseInt(gid('rows').value || 8, 10); var h = parseInt(gid('cols').value || 8, 10); var tbl = gid('maze'); tbl.innerHTML = ; tbl.add('tr', h); tbl.childNodes.map(function(x) { x.add('th', 1); x.add('td', w, '*'); x.add('th', 1)}); tbl.ins('tr'); tbl.add('tr', 1); tbl.firstChild.add('th', w + 2); tbl.lastChild.add('th', w + 2); for (var i = 1; i <= h; i++) { for (var j = 1; j <= w; j++) { tbl.kid(i).kid(j).neighbors = [ tbl.kid(i + 1).kid(j), tbl.kid(i).kid(j + 1), tbl.kid(i).kid(j - 1), tbl.kid(i - 1).kid(j) ]; } } walk(tbl.kid(irand(h) + 1).kid(irand(w) + 1)); gid('solve').style.display='inline'; }
function shuffle(x) { for (var i = 3; i > 0; i--) { j = irand(i + 1); if (j == i) continue; var t = x[j]; x[j] = x[i]; x[i] = t; } return x; }
var dirs = ['s', 'e', 'w', 'n']; function walk(c) { c.innerHTML = ' '; var idx = shuffle([0, 1, 2, 3]); for (var j = 0; j < 4; j++) { var i = idx[j]; var x = c.neighbors[i]; if (x.textContent != '*') continue; c.cls(dirs[i]), x.cls(dirs[3 - i]); walk(x); } }
function solve(c, t) { if (c === undefined) { c = gid('maze').kid(1).kid(1); c.cls('v'); } if (t === undefined) t = gid('maze') .lastChild.previousSibling .lastChild.previousSibling;
if (c === t) return 1; c.vis = 1; for (var i = 0; i < 4; i++) { var x = c.neighbors[i]; if (x.tagName.toLowerCase() == 'th') continue; if (x.vis || !c.className.match(dirs[i]) || !solve(x, t)) continue;
x.cls('v'); return 1; } c.vis = null; return 0; }
</script></head> <body><form><fieldset> <label>rows </label><input id='rows' size="3"/> <label>colums </label><input id='cols' size="3"/> <a href="javascript:make_maze()">Generate</a> <a id='solve' style='display:none' href='javascript:solve(); void(0)'>Solve</a>
</fieldset></form>
</body></html></lang>Julia
String API has changed in julia versions > 0.4. One must import the library LegacyStrings for the following code to work.
<lang julia>function walk(maze, cell, visited = Any[])
push!(visited, cell)
for neigh in shuffle(neighbors(cell, size(maze)))
if !(neigh in visited)
maze[round(Int,(cell+neigh)/2)...] = 0 # ifloor(n/2) == n >> 1
walk(maze, neigh, visited)
end
end
maze
end
neighbors(c,b,d=2)=filter(check(b),map(m->c+d*m, Any[[0,1],[-1,0],[0,-1],[1,0]]))
check(bound) = cell -> all([1,1] .<= cell .<= [bound...])
maze(w, h) = walk([i%2|j%2 for i=1:2w+1,j=1:2h+1], 2*[rand(1:w),rand(1:h)])
pprint(matrix) = for i = 1:size(matrix,1) println(join(matrix[i,:])) end
function printmaze(maze, wall = convert(UTF32String, "╹╸┛╺┗━┻╻┃┓┫┏┣┳╋"))
h,w = size(maze)
pprint([ maze[i,j] == 0 ? ' ' :
wall[Int(sum(c-> 2.0^.5(3c[1]+c[2]+3),
filter(x -> maze[x...] != 0,
neighbors([i,j],[h,w],1)) .- Anyi,j))]
for i = 1:2:h, j = 1:w])
end </lang>
- Output:
julia> mprint(maze(15,30)) ┏━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━┳━━━━━━━┳━━━┳━━━━━━━━━┳━━━━━┓ ┃ ╺━━━┳━━━┓ ╺━━━┛ ╻ ┏━╸ ┃ ╻ ┃ ╻ ┃ ╻ ╺━┳━┛ ╻ ╹ ╺━┓ ╺━┓ ┗━━━╸ ┃ ┣━━━┓ ╹ ╻ ┣━━━━━━━┫ ┃ ┏━┛ ┃ ╹ ┃ ┃ ┣━┓ ╹ ┏━┻━━━┳━┻━┓ ┗━━━┳━━━┫ ┃ ╺━┻━━━┫ ┃ ╺━┳━╸ ┃ ┗━┛ ┏━┻━┓ ┃ ┃ ┃ ┗━━━┛ ╻ ┏━┛ ╻ ┗━┓ ╻ ╹ ╻ ┃ ┃ ╺━━━┓ ┃ ┃ ┏━┛ ┏━┻━━━━━┫ ╻ ┗━┛ ┃ ┃ ╻ ┏━┳━┛ ┃ ╺━╋━╸ ┃ ┗━┳━┛ ┃ ┣━━━╸ ┃ ╹ ┃ ┃ ╻ ┃ ╺━┓ ╻ ┃ ┗━┳━┓ ┃ ┗━┛ ┃ ╹ ┏━╋━╸ ┃ ╺━╋━━━┛ ┏━┫ ┃ ┏━━━┻━━━┻━┛ ┣━┻━╸ ┃ ┗━┻━┓ ┃ ╹ ┗━━━┳━┛ ┏━┛ ┃ ╺━┻━━━┫ ╺━┳━┛ ┃ ┃ ┗━━━━━┓ ┏━╸ ┃ ╺━┳━┻━┓ ╺━┫ ┗━━━━━━━┛ ┏━┛ ┏━┻━━━━━┓ ┗━┓ ┃ ╺━┫ ┣━━━━━╸ ┃ ┗━━━┻━┓ ┃ ╻ ┗━┓ ┗━━━━━━━┳━━━┫ ╺━┛ ┏━┓ ╺━╋━╸ ┃ ┗━┓ ┃ ┃ ┏━━━┳━┻━┓ ╻ ╺━┛ ╹ ┣━┓ ┣━┓ ╺━━━┳━┛ ╻ ╹ ┏━━━┛ ┗━┓ ┃ ╺━┻━╸ ┃ ┃ ┃ ╹ ╻ ╹ ╻ ┗━┻━━━┳━━━┫ ╹ ╹ ┗━┳━┓ ╹ ┏━┻━━━┫ ╺━┳━╸ ┃ ┗━━━┳━━━┛ ┃ ┣━┳━┻━━━┻━━━━━┓ ╹ ╻ ┗━┳━━━╸ ╹ ┗━━━┛ ┏━╸ ┗━╸ ┃ ┏━┻━┓ ╻ ┗━━━╸ ┃ ┃ ╹ ╻ ╺━━━┳━╸ ┣━━━┻━┓ ┃ ┏━━━┓ ┏━━━━━┻━┳━━━━━┫ ┃ ╻ ╹ ┣━┳━━━╸ ┃ ┃ ╺━╋━━━┓ ┗━━━┫ ╻ ╺━┫ ┃ ┃ ╻ ┗━┛ ┏━━━┓ ╹ ┏━┓ ┗━┫ ┣━━━┫ ╹ ┏━━━┫ ┣━╸ ┗━╸ ┗━━━┓ ╹ ┗━┓ ╹ ┗━┛ ┣━━━━━┛ ╻ ┗━━━┛ ┗━╸ ╹ ┃ ╺━┛ ╺━┛ ╻ ┃ ┗━━━━━━━━━━━┻━━━━━┻━━━━━━━┻━━━━━━━┻━━━━━━━━━━━━━┻━━━━━━━━━┻━┛
Kotlin
<lang scala>import shuffle.shuffle
class Maze_generator(val x: Int, val y: Int) {
fun generate(cx: Int, cy: Int) {
val dirs = arrayOf(*DIR.values()).shuffle()
for (dir in dirs) {
val nx = cx + dir.dx
val ny = cy + dir.dy
if (between(nx, x) && between(ny, y) && maze[nx][ny] == 0) {
maze[cx][cy] = maze[cx][cy] or dir.bit
maze[nx][ny] = maze[nx][ny] or dir.opposite!!.bit
generate(nx, ny)
}
}
}
fun display() {
for (i in 0..y - 1) {
// draw the north edge
for (j in 0..x - 1)
print(if (maze[j][i] and 1 == 0) "+---" else "+ ")
println('+')
// draw the west edge
for (j in 0..x - 1)
print(if (maze[j][i] and 8 == 0) "| " else " ")
println('|')
}
// draw the bottom line
for (j in 0..x - 1) print("+---")
println('+')
}
private enum class DIR(val bit: Int, val dx: Int, val dy: Int) {
N(1, 0, -1), S(2, 0, 1), E(4, 1, 0),W(8, -1, 0);
var opposite: DIR? = null
companion object {
init {
N.opposite = S
S.opposite = N
E.opposite = W
W.opposite = E
}
}
}
private fun between(v: Int, upper: Int) = v >= 0 && v < upper
private val maze = Array(x) { IntArray(y) }
}
fun main(args: Array<String>) {
val x = if (args.size >= 1) args[0].toInt() else 8 val y = if (args.size == 2) args[1].toInt() else 8 val maze = Maze_generator(x, y) maze.generate(0, 0) maze.display()
}</lang>
Lua
<lang Lua> math.randomseed( os.time() )
-- Fisher-Yates shuffle from http://santos.nfshost.com/shuffling.html function shuffle(t)
for i = 1, #t - 1 do local r = math.random(i, #t) t[i], t[r] = t[r], t[i] end
end
-- builds a width-by-height grid of trues function initialize_grid(w, h)
local a = {}
for i = 1, h do
table.insert(a, {})
for j = 1, w do
table.insert(a[i], true)
end
end
return a
end
-- average of a and b function avg(a, b)
return (a + b) / 2
end
dirs = {
{x = 0, y = -2}, -- north
{x = 2, y = 0}, -- east
{x = -2, y = 0}, -- west
{x = 0, y = 2}, -- south
}
function make_maze(w, h)
w = w or 16 h = h or 8
local map = initialize_grid(w*2+1, h*2+1)
function walk(x, y) map[y][x] = false
local d = { 1, 2, 3, 4 }
shuffle(d)
for i, dirnum in ipairs(d) do
local xx = x + dirs[dirnum].x
local yy = y + dirs[dirnum].y
if map[yy] and map[yy][xx] then
map[avg(y, yy)][avg(x, xx)] = false
walk(xx, yy)
end
end
end
walk(math.random(1, w)*2, math.random(1, h)*2)
local s = {}
for i = 1, h*2+1 do
for j = 1, w*2+1 do
if map[i][j] then
table.insert(s, '#')
else
table.insert(s, ' ')
end
end
table.insert(s, '\n')
end
return table.concat(s)
end
print(make_maze()) </lang>
- Output:
################################# # # # # # # # # # ### # # ### ##### # ##### # # # # # # # # # # # # # # # # ########### ### # # ##### # # # # # # # # # # ### ##### # ### # # ####### # # # # # # # # # # # # # # # # ### # # # # # ######### ### # # # # # # # # # # # ### ### # ### ### # ####### # # # # # # # # # # # # # # # ### # ####### ##### # # ### # # # # # # # # # # # # # ### # ####### # # # ### # # # # # # # # # # #################################
Mathematica
<lang mathematica>MazeGraphics[m_, n_] :=
Block[{$RecursionLimit = Infinity,
unvisited = Tuples[Range /@ {m, n}], maze},
maze = Graphics[{Line[{{#, # - {0, 1}}, {#, # - {1, 0}}}] & /@
unvisited,
Line[{{0, n}, {0, 0}, {m, 0}}]}]; {unvisited =
DeleteCases[unvisited, #];
Do[If[MemberQ[unvisited, neighbor],
maze = DeleteCases[
maze, {#,
neighbor - {1, 1}} | {neighbor, # - {1, 1}}, {5}]; #0@
neighbor], {neighbor,
RandomSample@{# + {0, 1}, # - {0, 1}, # + {1, 0}, # - {1,
0}}}]} &@RandomChoice@unvisited; maze];
maze = MazeGraphics[21, 13]</lang>
- Output:
Graph
Here I generate a maze as a graph. Vertices of the graph are cells and edges of the graph are removed walls. This version is mush faster and is convenient to solve. <lang mathematica>MazeGraph[m_, n_] :=
Block[{$RecursionLimit = Infinity, grid = GridGraph[{m, n}],
unvisitedQ}, unvisitedQ[_] := True;
Graph[Range[m n], Reap[{unvisitedQ[#] = False;
Do[
If[unvisitedQ[neighbor],
Sow[# <-> neighbor]; #0@neighbor], {neighbor,
RandomSample@AdjacencyList[grid, #]}]} &@
RandomChoice@VertexList@grid]2, 1,
GraphLayout -> {"GridEmbedding", "Dimension" -> {m, n}}]];
maze = MazeGraph[13, 21]</lang>
- Output:
MATLAB / Octave
<lang Matlab>function M = makeMaze(n)
showProgress = false;
colormap([1,1,1;1,1,1;0,0,0]); set(gcf,'color','w');
NoWALL = 0; WALL = 2; NotVISITED = -1; VISITED = -2;
m = 2*n+3; M = NotVISITED(ones(m)); offsets = [-1, m, 1, -m];
M([1 2:2:end end],:) = WALL; M(:,[1 2:2:end end]) = WALL;
currentCell = sub2ind(size(M),3,3);
M(currentCell) = VISITED;
S = currentCell;
while (~isempty(S))
moves = currentCell + 2*offsets;
unvistedNeigbors = find(M(moves)==NotVISITED);
if (~isempty(unvistedNeigbors))
next = unvistedNeigbors(randi(length(unvistedNeigbors),1));
M(currentCell + offsets(next)) = NoWALL;
newCell = currentCell + 2*offsets(next);
if (any(M(newCell+2*offsets)==NotVISITED))
S = [S newCell];
end
currentCell = newCell;
M(currentCell) = VISITED;
else
currentCell = S(1);
S = S(2:end);
end
if (showProgress)
image(M-VISITED);
axis equal off;
drawnow;
pause(.01);
end
end
image(M-VISITED); axis equal off;</lang>
Nim
<lang nim>import math, sequtils, strutils randomize()
template newSeqWith(len: int, init: expr): expr =
var result {.gensym.} = newSeq[type(init)](len)
for i in 0 .. <len:
result[i] = init
result
iterator randomCover[T](xs: openarray[T]): T =
var js = toSeq 0..xs.high for i in countdown(js.high, 0): let j = random(i + 1) swap(js[i], js[j]) for j in js: yield xs[j]
const
w = 14 h = 10
var
vis = newSeqWith(h, newSeq[bool](w)) hor = newSeqWith(h+1, newSeqWith(w, "+---")) ver = newSeqWith(h, newSeqWith(w, "| ") & "|")
proc walk(x, y) =
vis[y][x] = true for p in [[x-1,y], [x,y+1], [x+1,y], [x,y-1]].randomCover: if p[0] notin 0 .. <w or p[1] notin 0 .. <h or vis[p[1]][p[0]]: continue if p[0] == x: hor[max(y, p[1])][x] = "+ " if p[1] == y: ver[y][max(x, p[0])] = " " walk p[0], p[1]
walk random(0..w), random(0..h) for a,b in zip(hor, ver & @[""]).items:
echo join(a & "+\n" & b)</lang>
Example output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | | | + + + + + + +---+ + + + + + + + | | | | | | | | | | | + + + +---+ +---+ +---+ +---+---+---+---+ + | | | | | | | | +---+ +---+ + + +---+---+---+---+---+ + +---+ | | | | | | | | | +---+---+ + +---+---+ + + + +---+---+ + + | | | | | | | | | | + +---+ +---+ +---+ + + +---+---+ +---+ + | | | | | | | | | | + +---+---+ + + + + +---+ + +---+ + + | | | | | | | | | | + + +---+ + + + +---+---+ +---+ + + + | | | | | | | | | + +---+---+---+---+---+---+ +---+---+ +---+ + + | | | | | | | | + + + + + + +---+---+ + + +---+---+ + | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+
OCaml
<lang ocaml>let seen = Hashtbl.create 7 let mark t = Hashtbl.add seen t true let marked t = Hashtbl.mem seen t
let walls = Hashtbl.create 7 let ord a b = if a <= b then (a,b) else (b,a) let join a b = Hashtbl.add walls (ord a b) true let joined a b = Hashtbl.mem walls (ord a b)
let () =
let nx = int_of_string Sys.argv.(1) in let ny = int_of_string Sys.argv.(2) in
let rec random_order = function
| [] -> []
| [a] -> [a]
| x -> let i = Random.int (List.length x) in
let rec del i = function
| [] -> failwith "del"
| h::t -> if i = 0 then t else h :: del (i-1) t in
(List.nth x i) :: random_order (del i x) in
let get_neighbours (x,y) = let lim n k = (0 <= k) && (k < n) in let bounds (x,y) = lim nx x && lim ny y in List.filter bounds [(x-1,y);(x+1,y);(x,y-1);(x,y+1)] in
let rec visit cell =
mark cell;
let check k =
if not (marked k) then (join cell k; visit k) in
List.iter check (random_order (get_neighbours cell)) in
let print_maze () =
begin
for i = 1 to nx do print_string "+---";done; print_endline "+";
let line n j k l s t u =
for i = 0 to n do print_string (if joined (i,j) (i+k,j+l) then s else t) done;
print_endline u in
for j = 0 to ny-2 do
print_string "| ";
line (nx-2) j 1 0 " " "| " "|";
line (nx-1) j 0 1 "+ " "+---" "+";
done;
print_string "| ";
line (nx-2) (ny-1) 1 0 " " "| " "|";
for i = 1 to nx do print_string "+---";done; print_endline "+";
end in
Random.self_init(); visit (Random.int nx, Random.int ny); print_maze ();</lang>Output from 'ocaml gen_maze.ml 10 10':
+---+---+---+---+---+---+---+---+---+---+ | | | | + +---+ +---+ + +---+ +---+ + | | | | | | + + +---+ +---+---+ +---+---+ + | | | | | | + + +---+ + +---+ +---+---+---+ | | | | | | | +---+---+ + + +---+---+ +---+ + | | | | | + +---+---+ +---+---+---+---+ +---+ | | | | | + +---+---+---+ + +---+ +---+ + | | | | | | +---+---+---+ +---+---+ +---+ + + | | | | | | + +---+ +---+ + + + +---+ + | | | | | | | +---+ + +---+ +---+---+---+ + + | | | | +---+---+---+---+---+---+---+---+---+---+
Perl
<lang perl>use List::Util 'max';
my ($w, $h) = @ARGV; $w ||= 26; $h ||= 127; my $avail = $w * $h;
- cell is padded by sentinel col and row, so I don't check array bounds
my @cell = (map([(('1') x $w), 0], 1 .. $h), [() x ($w + 1)]); my @ver = map([("| ") x $w], 1 .. $h); my @hor = map([("+--") x $w], 0 .. $h);
sub walk { my ($x, $y) = @_; $cell[$y][$x] = ; $avail-- or return; # no more bottles, er, cells
my @d = ([-1, 0], [0, 1], [1, 0], [0, -1]); while (@d) { my $i = splice @d, int(rand @d), 1; my ($x1, $y1) = ($x + $i->[0], $y + $i->[1]);
$cell[$y1][$x1] or next;
if ($x == $x1) { $hor[ max($y1, $y) ][$x] = '+ ' } if ($y == $y1) { $ver[$y][ max($x1, $x) ] = ' ' } walk($x1, $y1); } }
walk(int rand $w, int rand $h); # generate
for (0 .. $h) { # display
print @{$hor[$_]}, "+\n";
print @{$ver[$_]}, "|\n" if $_ < $h;
}</lang>
Run as maze.pl [width] [height] or use default dimensions.
- Sample 4 x 1 output:
+--+--+--+--+ | | +--+--+--+--+
Perl 6
Supply a width and height and optionally the x,y grid coords for the starting cell. If no starting cell is supplied, a random one will be selected automatically. 0,0 is the top left corner. <lang perl6>constant mapping = :OPEN(' '), :N< ╵ >, :E< ╶ >, :NE< └ >, :S< ╷ >, :NS< │ >, :ES< ┌ >, :NES< ├ >, :W< ╴ >, :NW< ┘ >, :EW< ─ >, :NEW< ┴ >, :SW< ┐ >, :NSW< ┤ >, :ESW< ┬ >, :NESW< ┼ >, :TODO< x >, :TRIED< · >;
enum Sym (mapping.map: *.key); my @ch = mapping.map: *.value;
enum Direction <DeadEnd Up Right Down Left>;
sub gen_maze ( $X,
$Y,
$start_x = (^$X).pick * 2 + 1,
$start_y = (^$Y).pick * 2 + 1 )
{
my @maze;
push @maze, $[ flat ES, -N, (ESW, EW) xx $X - 1, SW ];
push @maze, $[ flat (NS, TODO) xx $X, NS ];
for 1 ..^ $Y {
push @maze, $[ flat NES, EW, (NESW, EW) xx $X - 1, NSW ]; push @maze, $[ flat (NS, TODO) xx $X, NS ];
}
push @maze, $[ flat NE, (EW, NEW) xx $X - 1, -NS, NW ];
@maze[$start_y][$start_x] = OPEN;
my @stack;
my $current = [$start_x, $start_y];
loop {
if my $dir = pick_direction( $current ) {
@stack.push: $current;
$current = move( $dir, $current );
}
else {
last unless @stack;
$current = @stack.pop;
}
}
return @maze;
sub pick_direction([$x,$y]) {
my @neighbors = (Up if @maze[$y - 2][$x]), (Down if @maze[$y + 2][$x]), (Left if @maze[$y][$x - 2]), (Right if @maze[$y][$x + 2]); @neighbors.pick or DeadEnd;
}
sub move ($dir, @cur) {
my ($x,$y) = @cur; given $dir { when Up { @maze[--$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y--][$x+1] -= W; } when Down { @maze[++$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y++][$x+1] -= W; } when Left { @maze[$y][--$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x--] -= N; } when Right { @maze[$y][++$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x++] -= N; } } @maze[$y][$x] = 0; [$x,$y];
}
}
sub display (@maze) {
for @maze -> @y {
for @y.rotor(2) -> ($w, $c) { print @ch[abs $w]; if $c >= 0 { print @ch[$c] x 3 } else { print ' ', @ch[abs $c], ' ' } } say @ch[@y[*-1]];
}
}
display gen_maze( 29, 19 );</lang>
- Output:
┌ ╵ ────────────────────────────┬───────────────────────────────────────────┬───────────┬───────────────────────────┐ │ │ │ │ │ │ ╶───────────┬───────────┐ │ ┌───────────────────────╴ ┌───────┐ ├───╴ ╷ │ ┌───────────┬───┬───╴ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───────┐ ╵ ┌───┐ ├───┘ │ ┌───────────┬───────────┤ ╶───┤ │ ╶───┴───┤ │ ┌───┐ │ │ ╶───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ └───────┤ │ ╵ ┌───┘ │ ╷ ╶───┤ ┌───┐ │ ╷ │ ├───────╴ │ ╵ │ │ │ └───┐ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┬───────┐ │ ├───────┤ ╶───┤ └───┐ ╵ │ │ ╵ │ ╵ │ ┌───┐ └───┬───┘ │ │ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╶───┤ ╷ ╵ │ ╵ ╷ └───┐ ├───┐ ├───────┤ └───────┴───────┘ │ └───┐ └───╴ │ ╵ ├───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───╴ │ ├───────┴───┐ ├───╴ │ │ │ ╵ ╷ └───┐ ╶───┬───────┬───┘ ┌───┴───────╴ │ ┌───┘ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╷ │ │ ╶───┐ └───┤ ╷ │ │ └───────┴───┐ └───╴ │ ╷ ╵ ╷ ╵ ╶───────┬───┤ │ ┌───┴───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╷ ├───╴ ╵ │ │ │ ┌───────┐ └───────────┤ └───┬───┴───────────┐ ╵ │ │ ╵ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───┘ │ ┌───────┴───┘ │ ╵ ┌───┴───────╴ ╷ ├───┐ │ ╶───────┐ └───┐ │ └───┬───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───┘ │ ┌───┘ │ ┌───┬───────┼───╴ │ ╶───┬───────┤ ╵ │ └───┬───╴ ├───┐ │ └───┐ │ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───────┘ ├───────┤ │ ╵ ╷ │ ┌───┴───┐ │ ╶───┘ ┌───┴───╴ │ ┌───┘ │ │ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ ╷ │ ╷ │ └───┐ │ ╵ │ ╷ ╵ ├───────┐ │ ╶───────┤ └───┐ │ └───┤ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────────┤ │ │ └───╴ │ └───────┤ └───────┘ ╷ └───┴───┬───╴ ├───╴ │ └───┐ │ │ ╶───┴───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───╴ │ │ ├───╴ ┌───┴───────┬───┴───┐ ┌───────┴───────┐ ╵ ┌───┤ ╶───┤ ╷ │ ╵ └───┬───╴ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╶───┘ │ │ ╶───┤ ╶───┐ ╵ ╷ │ └───╴ ┌───╴ └───────┘ ├───╴ │ ├───┴───────┬───┘ ╷ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┬───┘ ├───────┴───┐ ├───────┤ └───────────┤ ┌───────────┐ │ ┌───┘ │ ╶───┐ ╵ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───╴ │ ╷ │ ╶───┐ ╵ │ ╷ └───────────┐ │ │ ┌───┐ └───┘ │ ╶───┴───┐ └───────┴───────┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────╴ │ └───┴───╴ └───────┴───┴───────────╴ │ └───┘ ╵ └───────────┴───╴ ╷ └───────────────┐ │ │ │ │ │ │ │ └───────────┴───────────────────────────────────────────┴───────────────────────────────────┴───────────────────┴ │ ┘
PHP
This solution use Php Gd for graphical randering. Source code : https://github.com/gallien69/phpMaze Demo online : http://gallien69.tk/ <lang PHP> <?php
// Convert Hex Color to RGB
function hexrgb(&$h) { return(array(hexdec($h[0].$h[1]),hexdec($h[2].$h[3]),hexdec($h[4].$h[5]))); }
// Allocate a color for an image from RGB
function rgbc(&$i, &$c) { return(imagecolorallocate($i, $c[0], $c[1], $c[2])); }
class Maze {
/* H : horizontal walls V : vertical walls x : number of rows y : numbers of cols r : resolve the maze b : walls thickness c : cell size f : background color m : walls color e : entrance color s : exit color i : gd image identifier
- /
private $H, $V, $x, $y, $r, $b, $c, $f, $m, $e, $s, $i;
// Initialize Maze class
function __construct($x, $y, $r, $b, $c, $f, $m, $e, $s) { $this->x = $x; $this->y = $y; $this->r = $r; $this->b = $b; $this->c = $c; $this->f = hexrgb($f); $this->m = hexrgb($m); $this->e = hexrgb($e); $this->s = hexrgb($s); }
// Checks if cell is a closed room
function isroom($x, $y) { return((empty($this->H[$x][$y]) && empty($this->V[$x][$y]) && empty($this->H[$x][$y+1]) && empty($this->V[$x+1][$y])) ? true : false); }
// Save the stack as solution path
function save(&$x, &$y, &$m) { if ($this->r == 1 && $x == $this->x - 1 && $y == $this->y - 1) { $this->r = $m; array_push($this->r, array($x, $y)); } }
// Dig the maze
function dig() { $x = 0; $y = 0; $cc = $this->x * $this->y; $v = 1; $m = array(); while ($v < $cc) { $c = ; if ($y > 0 && $this->isroom($x, $y - 1)) $c .= 'N'; if ($y < $this->y - 1 && $this->isroom($x, $y + 1)) $c .= 'S'; if ($x < $this->x - 1 && $this->isroom($x + 1, $y)) $c .= 'E'; if ($x > 0 && $this->isroom($x - 1, $y)) $c .= 'W'; if ($c) { $v++; array_push($m, array($x, $y)); $d = $c[rand(0, strlen($c) - 1)]; if ($d == 'N') $this->H[$x][$y--] = true; if ($d == 'S') $this->H[$x][$y++ + 1] = true; if ($d == 'E') $this->V[$x++ + 1][$y] = true; if ($d == 'W') $this->V[$x--][$y] = true; } else list($x, $y) = array_pop($m); $this->save($x, $y, $m); } $this->save($x, $y, $m); $this->V[0][0] = 1; $this->V[$this->x][$this->y - 1] = 1; }
// Draw the maze full grid
function grid(&$m) { for ($y = 0; $y <= $this->y; ++$y) { imagefilledrectangle($this->i, 0, $y * ($this->c + $this->b), $this->b + $this->x * ($this->c + $this->b) - 1, $this->b + $y * ($this->c + $this->b) - 1, $m); } for ($x = 0; $x <= $this->x; ++$x) { imagefilledrectangle($this->i, $x * ($this->c + $this->b), 0, $this->b + $x * ($this->c + $this->b) - 1, $this->b + $this->y * ($this->c + $this->b) - 1, $m); } }
// Breaks the horizontal walls
function line($x, $y, &$f) { imagefilledrectangle($this->i, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b), $x * ($this->c + $this->b) + $this->b + $this->c - 1, $y * ($this->c + $this->b) + $this->b, $f); }
// Breaks the vertical walls
function col($x, $y, &$f) { imagefilledrectangle($this->i, $x * ($this->c + $this->b), $y * ($this->c + $this->b) + $this->b, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b) + $this->b + $this->c - 1, $f); }
// Breaks the walls
function dot(&$f) { for ($x = 0; $x <= $this->x; ++$x) { for ($y = 0; $y <= $this->y; ++$y) { if (isset($this->H[$x][$y])) $this->line($x, $y, $f); if (isset($this->V[$x][$y])) $this->col($x, $y, $f); } } }
// Fill color cell
function cellfill(&$x, &$y, &$c) { imagefilledrectangle($this->i, $x * ($this->c + $this->b) + $this->b, $y * ($this->c + $this->b) + $this->b, $x * ($this->c + $this->b) + $this->b + $this->c - 1, $y * ($this->c + $this->b) + $this->b + $this->c - 1, $c); }
// Draw solution
function path() { $l = count($this->r); for ($i = 0; $i < $l; ++$i) { list($x, $y) = $this->r[$i]; $r = ($this->e[0] * ($l - $i) + $this->s[0] * $i) / $l; $g = ($this->e[1] * ($l - $i) + $this->s[1] * $i) / $l; $b = ($this->e[2] * ($l - $i) + $this->s[2] * $i) / $l; if (!isset($c[$r][$g][$b])) $c[$r][$g][$b] = imagecolorallocate($this->i, $r, $g, $b); $this->cellfill($x, $y, $c[$r][$g][$b]); if (isset($ox, $oy)) { if ($ox - $x == -1) $this->col($x, $y, $c[$r][$g][$b]); if ($oy - $y == -1) $this->line($x, $y, $c[$r][$g][$b]); if ($ox - $x == 1) $this->col($ox, $oy, $c[$r][$g][$b]); if ($oy - $y == 1) $this->line($ox, $oy, $c[$r][$g][$b]); } if ($i == 0) $this->col(0, 0, $c[$r][$g][$b]); if ($i == $l - 1) $this->col($x + 1, $y, $c[$r][$g][$b]); $ox = $x; $oy = $y; } }
// Call digger and make rendering
function __destruct() { $this->dig(); $this->i = imagecreatetruecolor( $this->b + $this->x * ($this->c + $this->b), $this->b + $this->y * ($this->c + $this->b)); $f = rgbc($this->i, $this->f); $m = rgbc($this->i, $this->m); unset($this->f, $this->m); imagefill($this->i, 0, 0, $f); $this->grid($m); $this->dot($f); unset($f, $m, $this->H, $this->V); if ($this->r) $this->path(); unset($this->r, $this->e, $this->s); header('content-disposition:inline;filename="maze.png"'); header('cache-control:no-store,no-cache,must-revalidate'); header('content-type:image/png'); imagepng($this->i, NULL, 9, PNG_ALL_FILTERS); imagedestroy($this->i); } } </lang>
PicoLisp
This solution uses 'grid' from "lib/simul.l" to generate the two-dimensional structure. <lang PicoLisp>(load "@lib/simul.l")
(de maze (DX DY)
(let Maze (grid DX DY)
(let Fld (get Maze (rand 1 DX) (rand 1 DY))
(recur (Fld)
(for Dir (shuffle '((west . east) (east . west) (south . north) (north . south)))
(with ((car Dir) Fld)
(unless (or (: west) (: east) (: south) (: north))
(put Fld (car Dir) This)
(put This (cdr Dir) Fld)
(recurse This) ) ) ) ) )
(for (X . Col) Maze
(for (Y . This) Col
(set This
(cons
(cons
(: west)
(or
(: east)
(and (= Y 1) (= X DX)) ) )
(cons
(: south)
(or
(: north)
(and (= X 1) (= Y DY)) ) ) ) ) ) )
Maze ) )
(de display (Maze)
(disp Maze 0 '((This) " ")) )</lang>
- Output:
: (display (maze 11 8))
+ +---+---+---+---+---+---+---+---+---+---+
8 | | | |
+ + + + + + +---+ +---+---+ +
7 | | | | | | | | |
+---+ +---+---+ + + +---+ + + +
6 | | | | | | | |
+ +---+ +---+ +---+---+---+ + +---+
5 | | | | | |
+---+ +---+ +---+---+---+ +---+---+ +
4 | | | | | | |
+ +---+ +---+ +---+ + + +---+ +
3 | | | | | | | |
+ +---+---+ + + + + +---+ + +
2 | | | | | | | | |
+ + + +---+ + +---+ + +---+ +
1 | | | |
+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j kPL/I
<lang pli>*process source attributes xref or(!);
mgg: Proc Options(main);
/* REXX ***************************************************************
* 04.09.2013 Walter Pachl translated from REXX version 3
**********************************************************************/
Dcl (MIN,MOD,RANDOM,REPEAT,SUBSTR) Builtin;
Dcl SYSIN STREAM INPUT;
Dcl print Print;
Dcl imax Bin Fixed(31) init(10);
Dcl jmax Bin Fixed(31) init(15);
Dcl seed Bin Fixed(31) init(4711);
Get File(sysin) Data(imax,jmax,seed);
Dcl ii Bin Fixed(31);
Dcl jj Bin Fixed(31);
Dcl id Bin Fixed(31);
Dcl jd Bin Fixed(31);
id=2*imax+1; /* vertical dimension of a.i.j */
jd=2*jmax+1; /* horizontal dimension of a.i.j */
Dcl c Char(2000) Var;
c=repeat('123456789'!!'abcdefghijklmnopqrstuvwxyz'!!
'ABCDEFGHIJKLMNOPQRSTUVWXYZ',20);
Dcl x Bin Float(53);
x=random(seed);
Dcl ps Bin Fixed(31) Init(1); /* first position */
Dcl na Bin Fixed(31) Init(1); /* number of points used */
Dcl si Bin Fixed(31); /* loop to compute paths */
Begin;
Dcl a(id,jd) Bin Fixed(15);
Dcl p(imax,jmax) Char(1);
Dcl 1 pl(imax*jmax),
2 ic Bin Fixed(15),
2 jc Bin Fixed(15);
Dcl 1 np(imax*jmax),
2 ic Bin Fixed(15),
2 jc Bin Fixed(15);
Dcl 1 pos(imax*jmax),
2 ic Bin Fixed(15),
2 jc Bin Fixed(15);
Dcl npl Bin Fixed(31) Init(0);
a=1; /* mark all borders present */
p='.'; /* Initialize all grid points */
ii=rnd(imax); /* find a start position */
jj=rnd(jmax);
Do si=1 To 1000; /* Do Forever - see Leave */
Call path(ii,jj); /* compute a path starting at ii/jj */
If na=imax*jmax Then /* all points used */
Leave; /* we are done */
Call select_next(ii,jj); /* get a new start from a path*/
End;
Call show;
Return;
path: Procedure(ii,jj);
/**********************************************************************
* compute a path starting from point (ii,jj)
**********************************************************************/
Dcl ii Bin Fixed(31);
Dcl jj Bin Fixed(31);
Dcl nb Bin Fixed(31);
Dcl ch Bin Fixed(31);
Dcl pp Bin Fixed(31);
p(ii,jj)='1';
pos.ic(ps)=ii;
pos.jc(ps)=jj;
Do pp=1 to 50; /* compute a path of maximum length 50*/
nb=neighbors(ii,jj); /* number of free neighbors */
Select;
When(nb=1) /* just one */
Call advance((1),ii,jj); /* go for it */
When(nb>0) Do; /* more Than 1 */
ch=rnd(nb); /* choose one possibility */
Call advance(ch,ii,jj); /* and go for that */
End;
Otherwise /* none available */
Leave;
End;
End;
End;
neighbors: Procedure(i,j) Returns(Bin Fixed(31)); /********************************************************************** * count the number of free neighbors of point (i,j) **********************************************************************/ Dcl i Bin Fixed(31); Dcl j Bin Fixed(31); Dcl in Bin Fixed(31); Dcl jn Bin Fixed(31); Dcl nb Bin Fixed(31) Init(0); in=i-1; If in>0 Then Call check(in,j,nb); in=i+1; If in<=imax Then Call check(in,j,nb); jn=j-1; If jn>0 Then Call check(i,jn,nb); jn=j+1; If jn<=jmax Then Call check(i,jn,nb); Return(nb); End;
check: Procedure(i,j,n);
/**********************************************************************
* check if point (i,j) is free and note it as possible successor
**********************************************************************/
Dcl i Bin Fixed(31);
Dcl j Bin Fixed(31);
Dcl n Bin Fixed(31);
If p(i,j)='.' Then Do; /* point is free */
n+=1; /* number of free neighbors */
np.ic(n)=i; /* note it as possible choice */
np.jc(n)=j;
End;
End;
advance: Procedure(ch,ii,jj); /********************************************************************** * move to the next point of the current path **********************************************************************/ Dcl ch Bin Fixed(31); Dcl ii Bin Fixed(31); Dcl jj Bin Fixed(31); Dcl ai Bin Fixed(31); Dcl aj Bin Fixed(31); Dcl pii Bin Fixed(31) Init((ii)); Dcl pjj Bin Fixed(31) Init((jj)); Dcl z Bin Fixed(31); ii=np.ic(ch); jj=np.jc(ch); ps+=1; /* position number */ pos.ic(ps)=ii; /* note its coordinates */ pos.jc(ps)=jj; p(ii,jj)=substr(c,ps,1); /* mark the point as used */ ai=pii+ii; /* vertical border position */ aj=pjj+jj; /* horizontal border position */ a(ai,aj)=0; /* tear the border down */ na+=1; /* number of used positions */ z=npl+1; /* add the point to the list */ pl.ic(z)=ii; /* of follow-up start pos. */ pl.jc(z)=jj; npl=z; End;
show: Procedure;
/*********************************************************************
* Show the resulting maze
*********************************************************************/
Dcl i Bin Fixed(31);
Dcl j Bin Fixed(31);
Dcl ol Char(300) Var;
Put File(print) Edit('mgg',imax,jmax,seed)(Skip,a,3(f(4)));
Put File(print) Skip Data(na);
Do i=1 To id;
ol=;
Do j=1 To jd;
If mod(i,2)=1 Then Do; /* odd lines */
If a(i,j)=1 Then Do; /* border to be drawn */
If mod(j,2)=0 Then
ol=ol!!'---'; /* draw the border */
Else
ol=ol!!'+';
End;
Else Do; /* border was torn down */
If mod(j,2)=0 Then
ol=ol!!' '; /* blanks instead of border */
Else
ol=ol!!'+';
End;
End;
Else Do; /* even line */
If a(i,j)=1 Then Do;
If mod(j,2)=0 Then /* even column */
ol=ol!!' '; /* moving space */
Else /* odd column */
ol=ol!!'!'; /* draw the border */
End;
Else /* border was torn down */
ol=ol!!' '; /* blank instead of border */
End;
End;
Select;
When(i=6) substr(ol,11,1)='A';
When(i=8) substr(ol, 3,1)='B';
Otherwise;
End;
Put File(print) Edit(ol,i)(Skip,a,f(3));
End;
End;
select_next: Procedure(is,js);
/**********************************************************************
* look for a point to start the nnext path
**********************************************************************/
Dcl is Bin Fixed(31);
Dcl js Bin Fixed(31);
Dcl n Bin Fixed(31);
Dcl nb Bin Fixed(31);
Dcl s Bin Fixed(31);
Do Until(nb>0); /* loop until one is found */
n=npl; /* number of points recorded */
s=rnd(n); /* pick a random index */
is=pl.ic(s); /* its coordinates */
js=pl.jc(s);
nb=neighbors(is,js); /* count free neighbors */
If nb=0 Then Do; /* if there is none */
pl.ic(s)=pl.ic(n); /* remove this point */
pl.jc(s)=pl.jc(n);
npl-=1;
End;
End;
End;
rnd: Proc(n) Returns(Bin Fixed(31)); /********************************************************************* * return a pseudo-random integer between 1 and n *********************************************************************/ dcl (r,n) Bin Fixed(31); r=min(random()*n+1,n); Return(r); End;
End; End;</lang>
Output:
�mgg 5 15 43 NA= 75; +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 ! ! ! ! ! 2 + + + +---+---+---+ +---+---+ +---+ + + + + 3 ! ! ! ! ! ! ! ! 4 + +---+---+ +---+---+---+---+ +---+ +---+---+---+---+ 5 ! A ! ! ! ! ! ! 6 +---+---+ +---+---+ + +---+---+ +---+ + +---+---+ 7 ! B ! ! ! ! ! ! 8 + + +---+ + + +---+---+---+---+---+---+ + + + 9 ! ! ! ! ! ! 10 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 11
Prolog
Works with SWI-Prolog and XPCE. <lang Prolog>:- dynamic cell/2.
maze(Lig,Col) :- retractall(cell(_,_)),
new(D, window('Maze')),
% creation of the grid forall(between(0,Lig, I), (XL is 50, YL is I * 30 + 50, XR is Col * 30 + 50, new(L, line(XL, YL, XR, YL)), send(D, display, L))),
forall(between(0,Col, I), (XT is 50 + I * 30, YT is 50, YB is Lig * 30 + 50, new(L, line(XT, YT, XT, YB)), send(D, display, L))),
SX is Col * 30 + 100, SY is Lig * 30 + 100, send(D, size, new(_, size(SX, SY))),
% choosing a first cell L0 is random(Lig), C0 is random(Col), assert(cell(L0, C0)), \+search(D, Lig, Col, L0, C0), send(D, open).
search(D, Lig, Col, L, C) :- Dir is random(4), nextcell(Dir, Lig, Col, L, C, L1, C1), assert(cell(L1,C1)), assert(cur(L1,C1)), erase_line(D, L, C, L1, C1), search(D, Lig, Col, L1, C1).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% erase_line(D, L, C, L, C1) :- ( C < C1 -> C2 = C1; C2 = C), XT is C2 * 30 + 50, YT is L * 30 + 51, YR is (L+1) * 30 + 50, new(Line, line(XT, YT, XT, YR)), send(Line, colour, white), send(D, display, Line).
erase_line(D, L, C, L1, C) :- XT is 51 + C * 30, XR is 50 + (C + 1) * 30, ( L < L1 -> L2 is L1; L2 is L), YT is L2 * 30 + 50, new(Line, line(XT, YT, XR, YT)), send(Line, colour, white), send(D, display, Line).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nextcell(Dir, Lig, Col, L, C, L1, C1) :- next(Dir, Lig, Col, L, C, L1, C1); ( Dir1 is (Dir+3) mod 4, next(Dir1, Lig, Col, L, C, L1, C1)); ( Dir2 is (Dir+1) mod 4, next(Dir2, Lig, Col, L, C, L1, C1)); ( Dir3 is (Dir+2) mod 4, next(Dir3, Lig, Col, L, C, L1, C1)).
% 0 => northward next(0, _Lig, _Col, L, C, L1, C) :- L > 0, L1 is L - 1, \+cell(L1, C).
% 1 => rightward next(1, _Lig, Col, L, C, L, C1) :- C < Col - 1, C1 is C + 1, \+cell(L, C1).
% 2 => southward next(2, Lig, _Col, L, C, L1, C) :- L < Lig - 1, L1 is L + 1, \+cell(L1, C).
% 3 => leftward next(2, _Lig, _Col, L, C, L, C1) :- C > 0, C1 is C - 1, \+cell(L, C1).
</lang>
- Output:
PureBasic
<lang PureBasic>Enumeration
;indexes for types of offsets from maze coordinates (x,y) #visited ;used to index visited(x,y) in a given direction from current maze cell #maze ;used to index maze() in a given direction from current maze cell #wall ;used to index walls in maze() in a given direction from current maze cell #numOffsets = #wall ;direction indexes #dir_ID = 0 ;identity value, produces no changes #firstDir #dir_N = #firstDir #dir_E #dir_S #dir_W #numDirs = #dir_W
EndEnumeration
DataSection
;maze(x,y) offsets for visited, maze, & walls for each direction Data.i 1, 1, 0, 0, 0, 0 ;ID Data.i 1, 0, 0, -1, 0, 0 ;N Data.i 2, 1, 1, 0, 1, 0 ;E Data.i 1, 2, 0, 1, 0, 1 ;S Data.i 0, 1, -1, 0, 0, 0 ;W Data.i %00, %01, %10, %01, %10 ;wall values for ID, N, E, S, W
EndDataSection
- cellDWidth = 4
Structure mazeOutput
vWall.s hWall.s
EndStructure
- setup reference values indexed by type and direction from current map cell
Global Dim offset.POINT(#numOffsets, #numDirs) Define i, j For i = 0 To #numDirs
For j = 0 To #numOffsets Read.i offset(j, i)\x: Read.i offset(j, i)\y Next
Next
Global Dim wallvalue(#numDirs) For i = 0 To #numDirs: Read.i wallvalue(i): Next
Procedure makeDisplayMazeRow(Array mazeRow.mazeOutput(1), Array maze(2), y)
;modify mazeRow() to produce output of 2 strings showing the vertical walls above and horizontal walls across a given maze row Protected x, vWall.s, hWall.s Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2) vWall = "": hWall = "" For x = 0 To mazeWidth If maze(x, y) & wallvalue(#dir_N): vWall + "+ ": Else: vWall + "+---": EndIf If maze(x, y) & wallvalue(#dir_W): hWall + " ": Else: hWall + "| ": EndIf Next mazeRow(0)\vWall = Left(vWall, mazeWidth * #cellDWidth + 1) If y <> mazeHeight: mazeRow(0)\hWall = Left(hWall, mazeWidth * #cellDWidth + 1): Else: mazeRow(0)\hWall = "": EndIf
EndProcedure
Procedure displayMaze(Array maze(2))
Protected x, y, vWall.s, hWall.s, mazeHeight = ArraySize(maze(), 2) Protected Dim mazeRow.mazeOutput(0) For y = 0 To mazeHeight makeDisplayMazeRow(mazeRow(), maze(), y) PrintN(mazeRow(0)\vWall): PrintN(mazeRow(0)\hWall) Next
EndProcedure
Procedure generateMaze(Array maze(2), mazeWidth, mazeHeight)
Dim maze(mazeWidth, mazeHeight) ;Each cell specifies walls present above and to the left of it,
;array includes an extra row and column for the right and bottom walls
Dim visited(mazeWidth + 1, mazeHeight + 1) ;Each cell represents a cell of the maze, an extra line of cells are included
;as padding around the representative cells for easy border detection
Protected i
;mark outside border as already visited (off limits)
For i = 0 To mazeWidth
visited(i + offset(#visited, #dir_N)\x, 0 + offset(#visited, #dir_N)\y) = #True
visited(i + offset(#visited, #dir_S)\x, mazeHeight - 1 + offset(#visited, #dir_S)\y) = #True
Next
For i = 0 To mazeHeight
visited(0 + offset(#visited, #dir_W)\x, i + offset(#visited, #dir_W)\y) = #True
visited(mazeWidth - 1 + offset(#visited, #dir_E)\x, i + offset(#visited, #dir_E)\y) = #True
Next
;generate maze
Protected x = Random(mazeWidth - 1), y = Random (mazeHeight - 1), cellCount, nextCell
visited(x + offset(#visited, #dir_ID)\x, y + offset(#visited, #dir_ID)\y) = #True
PrintN("Maze of size " + Str(mazeWidth) + " x " + Str(mazeHeight) + ", generation started at " + Str(x) + " x " + Str(y))
NewList stack.POINT()
Dim unvisited(#numDirs - #firstDir)
Repeat
cellCount = 0
For i = #firstDir To #numDirs
If Not visited(x + offset(#visited, i)\x, y + offset(#visited, i)\y)
unvisited(cellCount) = i: cellCount + 1
EndIf
Next
If cellCount
nextCell = unvisited(Random(cellCount - 1))
visited(x + offset(#visited, nextCell)\x, y + offset(#visited, nextCell)\y) = #True
maze(x + offset(#wall, nextCell)\x, y + offset(#wall, nextCell)\y) | wallvalue(nextCell)
If cellCount > 1
AddElement(stack())
stack()\x = x: stack()\y = y
EndIf
x + offset(#maze, nextCell)\x: y + offset(#maze, nextCell)\y
ElseIf ListSize(stack()) > 0
x = stack()\x: y = stack()\y
DeleteElement(stack())
Else
Break ;end maze generation
EndIf
ForEver
; ;mark random entry and exit point
; x = Random(mazeWidth - 1): y = Random(mazeHeight - 1)
; maze(x, 0) | wallvalue(#dir_N): maze(mazeWidth, y) | wallvalue(#dir_E)
ProcedureReturn
EndProcedure
If OpenConsole()
Dim maze(0, 0) Define mazeWidth = Random(5) + 7: mazeHeight = Random(5) + 3 generateMaze(maze(), mazeWidth, mazeHeight) displayMaze(maze()) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf</lang> The maze is represented by an array of cells where each cell indicates the walls present above (#dir_N) and to its left (#dir_W). Maze generation is done with a additional array marking the visited cells. Neither an entry nor an exit are created, these were not part of the task. A simple means of doing so is included but has been commented out.
- Sample output:
Maze of size 11 x 8, generation started at 9 x 3 +---+---+---+---+---+---+---+---+---+---+---+ | | | | | + + +---+ + +---+ + +---+ + + | | | | | | | | + +---+ +---+---+ +---+ + +---+---+ | | | | | | + + +---+---+ +---+---+---+---+---+ + | | | | | | + +---+ +---+ + +---+ + +---+---+ | | | | | | +---+---+---+ + + +---+---+ +---+ + | | | | | | + +---+---+ +---+ +---+---+ + +---+ | | | | | | | + + + +---+---+---+ + +---+---+ + | | | | +---+---+---+---+---+---+---+---+---+---+---+
Python
<lang python>from random import shuffle, randrange
def make_maze(w = 16, h = 8):
vis = [[0] * w + [1] for _ in range(h)] + [[1] * (w + 1)] ver = [["| "] * w + ['|'] for _ in range(h)] + [[]] hor = [["+--"] * w + ['+'] for _ in range(h + 1)]
def walk(x, y):
vis[y][x] = 1
d = [(x - 1, y), (x, y + 1), (x + 1, y), (x, y - 1)]
shuffle(d)
for (xx, yy) in d:
if vis[yy][xx]: continue
if xx == x: hor[max(y, yy)][x] = "+ "
if yy == y: ver[y][max(x, xx)] = " "
walk(xx, yy)
walk(randrange(w), randrange(h))
s = ""
for (a, b) in zip(hor, ver):
s += .join(a + ['\n'] + b + ['\n'])
return s
if __name__ == '__main__':
print(make_maze())</lang>
- Output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | | | | | | + + + + + + + + +--+--+--+--+--+ +--+ + | | | | | | | | | | +--+ +--+--+ + +--+--+--+ + +--+ +--+--+ + | | | | | | | | | | + +--+ +--+ + + + + + +--+ + + +--+--+ | | | | | | | | | | + +--+ +--+--+ + +--+ +--+--+ +--+--+ + + | | | | | | | | +--+ + + +--+--+--+ +--+--+--+--+--+--+--+ + | | | | | | | | + +--+--+ +--+--+ +--+--+ +--+ +--+ + + + | | | | | | | | + +--+ +--+--+--+ + +--+--+--+--+ +--+ + + | | | | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
Racket
Maze generator <lang racket>
- lang racket
- the structure representing a maze of size NxM
(struct maze (N M tbl))
- managing cell properties
(define (connections tbl c) (dict-ref tbl c '()))
(define (connect! tbl c n)
(dict-set! tbl c (cons n (connections tbl c))) (dict-set! tbl n (cons c (connections tbl n))))
(define (connected? tbl a b) (member a (connections tbl b)))
- Returns a maze of a given size
- build-maze
- : Index Index -> Maze
(define (build-maze N M)
(define tbl (make-hash))
(define (visited? tbl c) (dict-has-key? tbl c))
(define (neigbours c)
(filter
(match-lambda [(list i j) (and (<= 0 i (- N 1)) (<= 0 j (- M 1)))])
(for/list ([d '((0 1) (0 -1) (-1 0) (1 0))]) (map + c d))))
; generate the maze
(let move-to-cell ([c (list (random N) (random M))])
(for ([n (shuffle (neigbours c))] #:unless (visited? tbl n))
(connect! tbl c n)
(move-to-cell n)))
; return the result
(maze N M tbl))
</lang>
Printing out the maze
<lang racket>
- Shows a maze
(define (show-maze m)
(match-define (maze N M tbl) m)
(for ([i N]) (display "+---"))
(displayln "+")
(for ([j M])
(display "|")
(for ([i (- N 1)])
(if (connected? tbl (list i j) (list (+ 1 i) j))
(display " ")
(display " |")))
(display " |")
(newline)
(for ([i N])
(if (connected? tbl (list i j) (list i (+ j 1)))
(display "+ ")
(display "+---")))
(displayln "+"))
(newline))
</lang>
Example:
-> (define m (build-maze 10 7)) -> (show-maze m) +---+---+---+---+---+---+---+---+---+---+ | | | | | + +---+---+ + + +---+ +---+ + | | | | | | | + + +---+ + +---+ +---+---+ + | | | | | | | + +---+ +---+---+ +---+---+ + + | | | | | | + + +---+---+---+ + + +---+ + | | | | | | | +---+ + +---+ +---+ + + +---+ | | | | | | | + +---+ + +---+ +---+---+---+ + | | | +---+---+---+---+---+---+---+---+---+---+
Rascal
<lang rascal>import IO; import util::Math; import List;
public void make_maze(int w, int h){ vis = _ <- [1..w | _ <- [1..h]]; ver = "| _ <- [1..w + ["|"] | _ <- [1..h]] + [[]]; hor = _ <- [1..w + ["+"] | _ <- [1..h + 1]];
void walk(int x, int y){ vis[y][x] = 1;
d = [<x - 1, y>, <x, y + 1>, <x + 1, y>, <x, y - 1>]; while (d != []){ <<xx, yy>, d> = takeOneFrom(d); if (xx < 0 || yy < 0 || xx >= w || yy >= w) continue; if (vis[yy][xx] == 1) continue; if (xx == x) hor[max([y, yy])][x] = "+ "; if (yy == y) ver[y][max([x, xx])] = " "; walk(xx, yy); }
}
walk(arbInt(w), arbInt(h)); for (<a, b> <- zip(hor, ver)){ println(("" | it + "<z>" | z <- a)); println(("" | it + "<z>" | z <- b)); } }</lang>
rascal>make_maze(10,10) +--+--+--+--+--+--+--+--+--+--+ | | | | + +--+ +--+ +--+--+--+ + + | | | | | | | + + +--+ +--+--+--+ + + + | | | | | | | + +--+--+ + + +--+--+--+ + | | | | | + +--+--+--+ + + +--+--+--+ | | | | | | + +--+ +--+--+ + + +--+ + | | | | | | + + +--+ +--+--+ +--+--+ + | | | | | | | | +--+ + +--+ +--+ + + + + | | | | | | + + +--+ +--+--+--+--+ + + | | | | | | | | + +--+ +--+ + + + + + + | | | | | +--+--+--+--+--+--+--+--+--+--+ ok
REXX
prettified maze version
In order to preserve the aspect ratio (for most display terminals), several changestr invocations and
some other instructions were added to increase the horizontal dimension (cell size).
<lang rexx>/*REXX program generates and displays a rectangular solvable maze (of any size).*/
height=0; @.=0 /*default for all cells visited. */
parse arg rows cols seed . /*allow user to specify the maze size. */
if rows= | rows=="," then rows=19 /*No rows given? Then use the default.*/
if cols= | cols=="," then cols=19 /* " cols " ? " " " " */
if seed\== then call random ,,seed /*use a random seed for repeatability.*/
call buildRow '┌'copies("~┬",cols-1)'~┐' /*construct the top edge of the maze. */
/* [↓] construct the maze's grid. */
do r=1 for rows; _=; __=; hp= "|"; hj='├'
do c=1 for cols; _= _||hp'1'; __=__||hj"~"; hj='┼'; hp="│"
end /*c*/
call buildRow _'│' /*construct the right edge of the cells*/
if r\==rows then call buildRow __'┤' /* " " " " " " maze.*/
end /*r*/
call buildRow '└'copies("~┴", cols-1)'~┘' /*construct the bottom edge of the maze*/ r!=random(1,rows)*2; c!=random(1,cols)*2; @.r!.c!=0 /*choose the first cell in maze*/
/* [↓] traipse through the maze. */ do forever; n=hood(r!,c!) if n==0 then if \fCell() then leave call ?; @._r._c=0 /*get the (next) maze direction to go. */ ro=r!; co=c!; r!=_r; c!=_c /*save original maze cell coordinates. */ ?.zr=?.zr%2; ?.zc=?.zc%2 /*get the maze row and cell directions.*/ rw=ro+?.zr; cw=co+?.zc /*calculate the next row and column. */ @.rw.cw=. /*mark the maze cell as being visited. */ end /*forever*/
do r=1 for height; _= /*display the maze. */
do c=1 for cols*2 + 1; _=_ || @.r.c; end /*c*/
if \(r//2) then _=translate(_, '\', .) /*trans to backslash*/
@.r=_ /*save the row in @.*/
end /*r*/
do #=1 for height; _=@.# /*display the maze to the terminal. */
call makeNice /*make some cell corners look prettier.*/
_=changestr(1 , _, 111) /*──────these four ────────────────────*/
_=changestr(0 , _, 000) /*───────── statements are ────────────*/
_=changestr(. , _, " ") /*────────────── used for preserving ──*/
_=changestr('~' , _, "───") /*────────────────── the aspect ratio. */
say translate(_ , '─│', "═|\10") /*make it presentable for the screen. */
end /*#*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a maze cell. */ hood: parse arg rh,ch; return @(rh+2,ch) + @(rh-2,ch) + @(rh,ch-2) + @(rh,ch+2) /*──────────────────────────────────────────────────────────────────────────────────────*/ ?: do forever; ?.=0; ?=random(1,4); if ?==1 then ?.zc=-2 /*north*/
if ?==2 then ?.zr= 2 /* east*/
if ?==3 then ?.zc= 2 /*south*/
if ?==4 then ?.zr=-2 /* west*/
_r=r!+?.zr; _c=c!+?.zc; if @._r._c==1 then return
end /*forever*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ buildRow: parse arg z; height=height+1; width=length(z)
do c=1 for width; @.height.c=substr(z,c,1); end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ fCell: do r=1 for rows; rr=r+r
do c=1 for cols; cc=c+c
if hood(rr, cc)==1 then do; r!=rr; c!=cc; @.r!.c!=0; return 1; end
end /*c*/
end /*r*/ /* [↑] r! and c! are used by invoker.*/
return 0
/*──────────────────────────────────────────────────────────────────────────────────────*/ makeNice: width=length(_); old=#-1; new=#+1; old_=@.old; new_=@.new
if left(_,2) =='├.' then _=translate(_, "|", '├')
if right(_,2)=='.┤' then _=translate(_, "|", '┤')
/* [↓] handle the top row of the grid.*/
do k=1 for width while #==1; z=substr(_,k,1) /*maze top row.*/
if z\=='┬' then iterate
if substr(new_,k,1)=='\' then _=overlay("═",_,k)
end /*k*/
do k=1 for width while #==height; z=substr(_,k,1) /*maze bot row.*/
if z\=='┴' then iterate
if substr(old_, k, 1)=='\' then _=overlay("═", _, k)
end /*k*/
/* [↓] handle the mid rows of the grid*/
do k=3 to width-2 by 2 while #//2; z=substr(_,k,1) /*maze mid rows*/
if z\=='┼' then iterate
le=substr(_,k-1,1)
ri=substr(_,k+1,1)
up=substr(old_,k,1)
dw=substr(new_,k,1)
select
when le== . & ri== . & up=='│' & dw=="│" then _=overlay('|',_,k)
when le=='~' & ri=="~" & up=='\' & dw=="\" then _=overlay('═',_,k)
when le=='~' & ri=="~" & up=='\' & dw=="│" then _=overlay('┬',_,k)
when le=='~' & ri=="~" & up=='│' & dw=="\" then _=overlay('┴',_,k)
when le=='~' & ri== . & up=='\' & dw=="\" then _=overlay('═',_,k)
when le== . & ri=="~" & up=='\' & dw=="\" then _=overlay('═',_,k)
when le== . & ri== . & up=='│' & dw=="\" then _=overlay('|',_,k)
when le== . & ri== . & up=='\' & dw=="│" then _=overlay('|',_,k)
when le== . & ri=="~" & up=='\' & dw=="│" then _=overlay('┌',_,k)
when le== . & ri=="~" & up=='│' & dw=="\" then _=overlay('└',_,k)
when le=='~' & ri== . & up=='\' & dw=="│" then _=overlay('┐',_,k)
when le=='~' & ri== . & up=='│' & dw=="\" then _=overlay('┘',_,k)
when le=='~' & ri== . & up=='│' & dw=="│" then _=overlay('┤',_,k)
when le== . & ri=="~" & up=='│' & dw=="│" then _=overlay('├',_,k)
otherwise nop
end /*select*/
end /*k*/
return</lang>
Some older REXXes don't have a changestr BIF, so one is included here ──► CHANGESTR.REX.
output when using the input of: 23 19 55
┌───┬───────────────────┬───────────┬───────────────────────────────────────┐ │ │ │ │ │ │ │ │ │ ┌───────┘ ┌──── │ │ │ ────┐ │ ┌──── ┌──── │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ────────┤ ────┘ │ └───┐ ├───┘ └───────┤ ────┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───┴──────── ├───────┐ └───┐ │ │ ┌───┬──── └───┐ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───┐ ┌───────┬───┘ │ └───────┤ │ │ │ │ ────┐ └───┤ │ │ │ │ │ │ │ │ │ │ │ │ ├───┴───┐ │ │ ┌───┘ ┌───┴───────┐ │ │ └───────┼──── ├──── │ │ │ │ │ │ │ │ │ │ │ │ ────┘ ├───────┘ ┌───┴──────── │ ────┼───────┬───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────────┘ ┌───────┘ │ ┌───────┼───────┘ │ │ ────┴───┤ └───┤ │ │ │ │ │ │ │ │ │ │ ────┬───────┤ ────────┤ └──── │ │ │ │ └──────── │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├──────── ├───────────┘ │ └───┴───┐ ────┬───┴───┘ │ │ │ │ │ │ │ │ │ │ │ ├───────┤ │ │ │ │ ────┬───────┴───────┐ ├──── │ │ ────┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┤ │ └───┐ └───┬───────┐ │ └───────┼───┴───┐ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───┬───┘ │ │ │ └───────┴───┐ │ │ │ │ ┌──── │ ────┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───┘ │ └───────┬──── │ │ │ │ │ │ ────┴───┐ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ────┤ ┌───┴───────────┘ │ ├───────┘ │ └───┤ ┌──── │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├──── │ │ ┌───────────────┴───┘ │ ┌───┴───┐ └───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ┌───┴───────┤ ┌───────┬───────┬───┘ │ │ ├──── │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───────┐ │ │ │ │ │ │ ────┤ │ │ ────┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├───┘ │ └───┼──── │ └───┴───────┐ ├───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───────┤ │ ┌───┴───┐ │ │ └───────┐ │ └───┘ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ ├──────── │ ┌───┴───┐ │ ┌───┴───┬──── │ └───┬───┬───┘ ┌───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ────┬───┴───┤ │ │ └───┤ │ │ │ └───┐ │ │ ┌───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └───────┘ │ │ │ └──── │ │ │ ├──── │ ────┤ │ │ │ │ │ │ │ │ │ │ │ │ │ └───────────────┴───────┴───────────┴───┴───────┴───────┴───────┴───────┴───┘
simpler version of above
The above REXX version had a quite of bit of code to "dress up" the maze presentation,
so a slimmed down version was included here.
<lang rexx>/*REXX program generates and displays a rectangular solvable maze (of any size). */
height=0; @.=0 /*default for all cells visited. */
parse arg rows cols seed . /*allow user to specify the maze size. */
if rows= | rows=="," then rows=19 /*No rows given? Then use the default.*/
if cols= | cols=="," then cols=19 /* " cols " ? " " " " */
if seed\== then call random ,,seed /*use a random seed for repeatability.*/
call buildRow '┌'copies("─┬", cols-1)'─┐' /*construct the top edge of the maze.*/
/* [↓] construct the maze's grid. */
do r=1 for rows; _=; __=; hp= "|"; hj='├'
do c=1 for cols; _= _||hp'1'; __=__||hj"─"; hj='┼'; hp="│"
end /*c*/
call buildRow _'│' /*construct the right edge of the cells*/
if r\==rows then call buildRow __'┤' /* " " " " " " maze.*/
end /*r*/
call buildRow '└'copies("─┴", cols-1)'─┘' /*construct the bottom edge of the maze*/ r!=random(1,rows)*2; c!=random(1,cols)*2; @.r!.c!=0 /*choose the first cell.*/
/* [↓] traipse through the maze. */ do forever; n=hood(r!, c!) /*number of free maze cells. */ if n==0 then if \fCell() then leave /*if no free maze cells left, then done*/ call ?; @._r._c=0 /*get the (next) maze direction to go. */ ro=r!; co=c!; r!=_r; c!=_c /*save the original cell coordinates. */ ?.zr=?.zr%2; ?.zc=?.zc%2 /*get the maze row and cell directions.*/ rw=ro+?.zr; cw=co+?.zc /*calculate the next maze row and col. */ @.rw.cw=. /*mark the maze cell as being visited. */ end /*forever*/
do r=1 for height; _= /*display the maze. */
do c=1 for cols*2 + 1; _=_ || @.r.c; end /*c*/
if \(r//2) then _=translate(_, '\', .) /*trans to backslash*/
_=changestr(1 , _, 111) /*──────these four ────────────────────*/
_=changestr(0 , _, 000) /*───────── statements are ────────────*/
_=changestr(. , _, " ") /*────────────── used for preserving ──*/
_=changestr('─', _, "───") /*────────────────── the aspect ratio. */
say translate(_, '│', "|\10") /*make it presentable for the screen. */
end /*r*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg _r,_c; return @._r._c /*a fast way to reference a maze cell. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ ?: do forever; ?.=0; ?=random(1,4); if ?==1 then ?.zc=-2 /*north*/
if ?==2 then ?.zr= 2 /* east*/
if ?==3 then ?.zc= 2 /*south*/
if ?==4 then ?.zr=-2 /* west*/
_r=r!+?.zr; _c=c!+?.zc; if @._r._c==1 then return
end /*forever*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ buildRow: parse arg z; height=height+1; width=length(z)
do c=1 for width; @.height.c=substr(z,c,1); end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ fCell: do r=1 for rows; rr=r+r
do c=1 for cols; cc=c+c
if hood(rr,cc)==1 then do; r!=rr; c!=cc; @.r!.c!=0; return 1; end
end /*c*/
end /*r*/ /* [↑] r! and c! are used by invoker.*/
return 0
/*──────────────────────────────────────────────────────────────────────────────────────*/ hood: parse arg rh,ch; return @(rh+2,ch) + @(rh-2,ch) + @(rh,ch-2) + @(rh,ch+2)</lang> output when using the input: 10 10
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐ │ │ │ │ │ ├ ┼ ┼───┼───┼ ┼ ┼───┼───┼ ┼ ┤ │ │ │ │ │ │ │ ├ ┼ ┼ ┼ ┼───┼───┼ ┼ ┼───┼ ┤ │ │ │ │ │ │ │ │ │ ├ ┼ ┼ ┼ ┼───┼ ┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ │ │ ├ ┼ ┼ ┼───┼───┼───┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ ├ ┼───┼───┼───┼───┼ ┼ ┼ ┼ ┼ ┤ │ │ │ │ │ │ │ │ ├───┼ ┼───┼ ┼ ┼───┼ ┼───┼ ┼ ┤ │ │ │ │ │ │ ├ ┼───┼ ┼───┼───┼ ┼───┼───┼───┼ ┤ │ │ │ │ │ ├ ┼ ┼───┼───┼───┼───┼ ┼───┼───┼ ┤ │ │ │ │ │ │ ├ ┼───┼ ┼───┼───┼ ┼ ┼ ┼ ┼───┤ │ │ │ │ │ └───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
version 3
<lang rexx>/* REXX ***************************************************************
- 04.09.2013 Walter Pachl
- /
Parse Arg imax jmax seed If imax= Then imax=10 If jmax= Then jmax=15 If seed= Then seed=4711 c='123456789'||,
'abcdefghijklmnopqrstuvwxyz'||,
translate('abcdefghijklmnopqrstuvwxyz')
c=copies(c,10) call random 1,10,seed id=2*imax+1 /* vertical dimension of a.i.j */ jd=2*jmax+1 /* horizontal dimension of a.i.j */ a.=1 /* mark all borders present */ p.='.' /* Initialize all grid points */ pl.=0 /* path list */ ii=random(1,imax) /* find a start position */ jj=random(1,jmax) p=1 /* first position */ na=1 /* number of points used */ Do si=1 To 1000 /* Do Forever - see Leave */
/* Say 'loop' si na show progress */ Call path ii,jj /* compute a path starting at ii/jj */ If na=imax*jmax Then /* all points used */ Leave /* we are done */ Parse Value select_next() With ii jj /* get a new start from a path*/ End
/*************** Do i=1 To imax
ol= Do j=1 To jmax ol=ol||p.i.j End Say ol End
Say ' '
- /
Call show /*********************** Do pi=1 To imax*jmax
Say right(pi,3) pos.pi End
- /
Exit
path: Procedure Expose p. np. p pl. c a. na imax jmax id jd pos. /**********************************************************************
- compute a path starting from point (ii,jj)
- /
Parse Arg ii,jj
p.ii.jj='1'
pos.p=ii jj
Do pp=1 to 50 /* compute a path of maximum length 50*/
neighbors=neighbors(ii,jj) /* number of free neighbors */
Select
When neighbors=1 Then /* just one */
Call advance 1,ii,jj /* go for it */
When neighbors>0 Then Do /* more Than 1 */
ch=random(1,neighbors) /* choose one possibility */
Call advance ch,ii,jj /* and go for that */
End
Otherwise /* none available */
Leave
End
End
Return
neighbors: Procedure Expose p. np. imax jmax neighbors pl. /**********************************************************************
- count the number of free neighbors of point (i,j)
- /
Parse Arg i,j neighbors=0 in=i-1; If in>0 Then Call check in,j in=i+1; If in<=imax Then Call check in,j jn=j-1; If jn>0 Then Call check i,jn jn=j+1; If jn<=jmax Then Call check i,jn Return neighbors
check: Procedure Expose p. imax jmax np. neighbors pl. /**********************************************************************
- check if point (i,j) is free and note it as possible successor
- /
Parse Arg i,j If p.i.j='.' Then Do /* point is free */ neighbors=neighbors+1 /* number of free neighbors */ np.neighbors=i j /* note it as possible choice */ End Return
advance: Procedure Expose p pos. np. p. c ii jj a. na pl. pos. /**********************************************************************
- move to the next point of the current path
- /
Parse Arg ch,pii,pjj Parse Var np.ch ii jj p=p+1 /* position number */ pos.p=ii jj /* note its coordinates */ p.ii.jj=substr(c,p,1) /* mark the point as used */ ai=pii+ii /* vertical border position */ aj=pjj+jj /* horizontal border position */ a.ai.aj=0 /* tear the border down */ na=na+1 /* number of used positions */ z=pl.0+1 /* add the point to the list */ pl.z=ii jj /* of follow-up start pos. */ pl.0=z Return
show: Procedure Expose id jd a. na /*********************************************************************
- Show the resulting maze
- /
say 'mgg 6 18 4711'
say 'show na='na
Do i=1 To id
ol=
Do j=1 To jd
If i//2=1 Then Do /* odd lines */
If a.i.j=1 Then Do /* border to be drawn */
If j//2=0 Then
ol=ol||'---' /* draw the border */
Else
ol=ol'+'
End
Else Do /* border was torn down */
If j//2=0 Then
ol=ol||' ' /* blanks instead of border */
Else
ol=ol||'+'
End
End
Else Do /* even line */
If a.i.j=1 Then Do
If j//2=0 Then /* even column */
ol=ol||' ' /* moving space */
Else /* odd column */
ol=ol||'|' /* draw the border */
End
Else /* border was torn down */
ol=ol||' ' /* blank instead of border */
End
End
Select
When i=6 Then ol=overlay('A',ol,11)
When i=8 Then ol=overlay('B',ol, 3)
Otherwise Nop
End
Say ol format(i,2)
End
Return
select_next: Procedure Expose p. pl. imax jmax /*********************************************************************
- look for a point to start the nnext path
- /
Do Until neighbors>0 /* loop until one is found */
n=pl.0 /* number of points recorded */
s=random(1,n) /* pick a random index */
Parse Var pl.s is js /* its coordinates */
neighbors=neighbors(is,js) /* count free neighbors */
If neighbors=0 Then Do /* if there is none */
pl.s=pl.n /* remove this point */
pl.0=pl.0-1
End
End
Return is js /* return the new start point*/</lang>
Output:
rexx mgg 6 18 4711 show na=108 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 | | | | | | | | 2 + +---+ + + + + +---+ + +---+---+ + +---+ + +---+ 3 | | | | | | | | | | | | 4 +---+---+ + +---+---+---+ + + + + +---+---+ + +---+ + 5 | | A | | | | | | | 6 + + +---+---+---+---+ +---+ +---+---+ + +---+ + +---+---+ 7 | B | | | | | | | | | | | 8 + + +---+ + + +---+ + + + +---+ +---+ + + + + 9 | | | | | | | | | | | | | | 10 + + + +---+---+---+ + + + +---+---+---+ + + +---+ + 11 | | | | | | | 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 13
Ruby
<lang ruby>class Maze
DIRECTIONS = [ [1, 0], [-1, 0], [0, 1], [0, -1] ]
def initialize(width, height)
@width = width
@height = height
@start_x = rand(width)
@start_y = 0
@end_x = rand(width)
@end_y = height - 1
# Which walls do exist? Default to "true". Both arrays are
# one element bigger than they need to be. For example, the
# @vertical_walls[x][y] is true if there is a wall between
# (x,y) and (x+1,y). The additional entry makes printing easier.
@vertical_walls = Array.new(width) { Array.new(height, true) }
@horizontal_walls = Array.new(width) { Array.new(height, true) }
# Path for the solved maze.
@path = Array.new(width) { Array.new(height) }
# "Hack" to print the exit.
@horizontal_walls[@end_x][@end_y] = false
# Generate the maze.
generate
end
# Print a nice ASCII maze.
def print
# Special handling: print the top line.
puts @width.times.inject("+") {|str, x| str << (x == @start_x ? " +" : "---+")}
# For each cell, print the right and bottom wall, if it exists.
@height.times do |y|
line = @width.times.inject("|") do |str, x|
str << (@path[x][y] ? " * " : " ") << (@vertical_walls[x][y] ? "|" : " ")
end
puts line
puts @width.times.inject("+") {|str, x| str << (@horizontal_walls[x][y] ? "---+" : " +")}
end
end
private
# Reset the VISITED state of all cells.
def reset_visiting_state
@visited = Array.new(@width) { Array.new(@height) }
end
# Is the given coordinate valid and the cell not yet visited?
def move_valid?(x, y)
(0...@width).cover?(x) && (0...@height).cover?(y) && !@visited[x][y]
end
# Generate the maze.
def generate
reset_visiting_state
generate_visit_cell(@start_x, @start_y)
end
# Depth-first maze generation.
def generate_visit_cell(x, y)
# Mark cell as visited.
@visited[x][y] = true
# Randomly get coordinates of surrounding cells (may be outside
# of the maze range, will be sorted out later).
coordinates = DIRECTIONS.shuffle.map { |dx, dy| [x + dx, y + dy] }
for new_x, new_y in coordinates
next unless move_valid?(new_x, new_y)
# Recurse if it was possible to connect the current and
# the cell (this recursion is the "depth-first" part).
connect_cells(x, y, new_x, new_y)
generate_visit_cell(new_x, new_y)
end
end
# Try to connect two cells. Returns whether it was valid to do so.
def connect_cells(x1, y1, x2, y2)
if x1 == x2
# Cells must be above each other, remove a horizontal wall.
@horizontal_walls[x1][ [y1, y2].min ] = false
else
# Cells must be next to each other, remove a vertical wall.
@vertical_walls[ [x1, x2].min ][y1] = false
end
end
end
- Demonstration:
maze = Maze.new 20, 10 maze.print</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+ | | | | | | | | + +---+ +---+ + + +---+---+---+ + + +---+ + +---+ +---+ + | | | | | | | | | | | | | | + + + +---+---+ + + +---+ +---+ +---+ +---+---+ + + +---+ | | | | | | | | | | | | + + +---+---+ +---+---+ + +---+---+ + +---+ + + +---+---+ + | | | | | | | | | | + +---+---+ +---+---+ + +---+---+ +---+---+ +---+ +---+---+---+ + | | | | | | | | | | +---+---+ +---+ + + +---+ + + +---+---+---+---+ +---+ + + + | | | | | | | | | | + + +---+ +---+---+---+---+---+ +---+---+ + +---+---+ +---+---+---+ | | | | | | | | | | | + +---+ +---+---+---+---+---+ + +---+ + +---+ + + +---+---+ + | | | | | | | | | | + + +---+---+ + + +---+---+---+---+ +---+ +---+---+ + +---+---+ | | | | | | | | | | + + +---+ +---+ +---+ + +---+---+---+ +---+ +---+---+---+---+ + | | | | | +---+---+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+---+
Scala
<lang scala>import scala.util.Random
object MazeTypes {
case class Direction(val dx: Int, val dy: Int)
case class Loc(val x: Int, val y: Int) {
def +(that: Direction): Loc = Loc(x + that.dx, y + that.dy)
}
case class Door(val from: Loc, to: Loc)
val North = Direction(0,-1) val South = Direction(0,1) val West = Direction(-1,0) val East = Direction(1,0) val directions = Set(North, South, West, East)
}
object MazeBuilder {
import MazeTypes._
def shuffle[T](set: Set[T]): List[T] = Random.shuffle(set.toList)
def buildImpl(current: Loc, grid: Grid): Grid = {
var newgrid = grid.markVisited(current)
val nbors = shuffle(grid.neighbors(current))
nbors.foreach { n =>
if (!newgrid.isVisited(n)) {
newgrid = buildImpl(n, newgrid.markVisited(current).addDoor(Door(current, n)))
}
}
newgrid
}
def build(width: Int, height: Int): Grid = {
val exit = Loc(width-1, height-1)
buildImpl(exit, new Grid(width, height, Set(), Set()))
}
}
class Grid(val width: Int, val height: Int, val doors: Set[Door], val visited: Set[Loc]) {
def addDoor(door: Door): Grid =
new Grid(width, height, doors + door, visited)
def markVisited(loc: Loc): Grid =
new Grid(width, height, doors, visited + loc)
def isVisited(loc: Loc): Boolean =
visited.contains(loc)
def neighbors(current: Loc): Set[Loc] =
directions.map(current + _).filter(inBounds(_)) -- visited
def printGrid(): List[String] = {
(0 to height).toList.flatMap(y => printRow(y))
}
private def inBounds(loc: Loc): Boolean =
loc.x >= 0 && loc.x < width && loc.y >= 0 && loc.y < height
private def printRow(y: Int): List[String] = {
val row = (0 until width).toList.map(x => printCell(Loc(x, y)))
val rightSide = if (y == height-1) " " else "|"
val newRow = row :+ List("+", rightSide)
List.transpose(newRow).map(_.mkString)
}
private val entrance = Loc(0,0)
private def printCell(loc: Loc): List[String] = {
if (loc.y == height)
List("+--")
else List(
if (openNorth(loc)) "+ " else "+--",
if (openWest(loc) || loc == entrance) " " else "| "
)
}
def openNorth(loc: Loc): Boolean = openInDirection(loc, North)
def openWest(loc: Loc): Boolean = openInDirection(loc, West)
private def openInDirection(loc: Loc, dir: Direction): Boolean =
doors.contains(Door(loc, loc + dir)) || doors.contains(Door(loc + dir, loc))
}</lang>
- Output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| | |
+--+--+ + +--+--+ + + +--+--+--+ +--+ +
| | | | | | | | | |
+ + +--+--+ + + + +--+--+--+ +--+ + +
| | | | | | | |
+ +--+--+--+--+ +--+--+--+ + +--+ + + +
| | | | | | | | | |
+ + + +--+--+--+ +--+ + +--+ + + + +
| | | | | | | | | | |
+ +--+ + +--+--+--+ + + + + +--+--+ +
| | | | | | | | | |
+ + + +--+ +--+--+ + +--+--+--+ +--+ +
| | | | | | |
+ + + +--+--+--+--+ +--+--+--+ +--+--+ +
| | | | | | | |
+--+ +--+--+ +--+--+ + + + +--+--+ +--+
| | | | | | | | |
+ +--+--+ +--+--+ + + +--+ + + +--+ +
| | | | | | | | |
+ +--+ +--+--+ + +--+--+ +--+ +--+ + +
| | | | | | | | |
+--+ +--+ + +--+ +--+ +--+--+--+ + + +
| | | | | | | | | |
+ +--+ +--+--+ +--+ + + +--+ +--+ + +
| | | | | | | |
+ + +--+--+ + +--+--+--+--+--+--+ +--+ +
| | | | | | | |
+ + + +--+--+--+ +--+--+--+--+--+--+ + +
| | |
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
Sidef
<lang ruby>var(w:5, h:5) = ARGV.map{.to_i}... var avail = (w * h)
- cell is padded by sentinel col and row, so I don't check array bounds
var cell = (1..h -> map {([true] * w) + [false]} + [[false] * w+1]) var ver = (1..h -> map {["| "] * w }) var hor = (0..h -> map {["+--"] * w })
func walk(x, y) {
cell[y][x] = false; avail-- > 0 || return; # no more bottles, er, cells
var d = [[-1, 0], [0, 1], [1, 0], [0, -1]]
while (!d.is_empty) {
var i = d.pop_rand
var (x1, y1) = (x + i[0], y + i[1])
cell[y1][x1] || next
if (x == x1) { hor[[y1, y].max][x] = '+ ' }
if (y == y1) { ver[y][[x1, x].max] = ' ' }
walk(x1, y1)
}
}
walk(w.rand.int, h.rand.int) # generate
for i in (0 .. h) {
say (hor[i].join() + '+')
if (i < h) {
say (ver[i].join() + '|')
}
}</lang>
- Output:
+--+--+--+--+--+ | | | +--+ +--+ + + | | | + +--+--+--+--+ | | | +--+ + +--+ + | | | | + +--+--+ +--+ | | +--+--+--+--+--+
Swift
<lang Swift>import Foundation
class Direction {
var vect:(Int, Int, Int)
var bit:Int {
let (bit, dx, dy) = vect
return bit
}
var dx:Int {
let (bit, dx, dy) = vect
return dx
}
var dy:Int {
let (bit, dx, dy) = vect
return dy
}
var opposite:Direction {
switch (vect) {
case (1, 0, -1):
return Direction(bit: 2, dx: 0, dy: 1)
case (2, 0, 1):
return Direction(bit: 1, dx: 0, dy: -1)
case (4, 1, 0):
return Direction(bit: 8, dx: -1, dy: 0)
case (8, -1, 0):
return Direction(bit: 4, dx: 1, dy: 0)
default:
return Direction(bit: 0, dx: 0, dy: 0)
}
}
init(bit:Int, dx:Int, dy:Int) {
self.vect = (bit, dx, dy)
}
}
let N = Direction(bit: 1, dx: 0, dy: -1) let S = Direction(bit: 2, dx: 0, dy: 1) let E = Direction(bit: 4, dx: 1, dy: 0) let W = Direction(bit: 8, dx: -1, dy: 0)
class MazeGenerator {
let x:Int! let y:Int! var maze:Int! init(_ x:Int, _ y:Int) { self.x = x self.y = y var col = [Int](count: y, repeatedValue: 0) self.maze = Int(count: x, repeatedValue: col) generateMaze(0, 0) } func display() { for i in 0..<y { // Draw top edge for j in 0..<x { print((maze[j][i] & 1) == 0 ? "+---" : "+ ") } println("+") // Draw left edge for j in 0..<x { print((maze[j][i] & 8) == 0 ? "| " : " ") } println("|") } // Draw bottom edge for j in 0..<x { print("+---") } println("+") } func generateMaze(cx:Int, _ cy:Int) { var dirs = [N, S, E, W] as NSMutableArray for i in 0..<dirs.count { let x1 = Int(arc4random()) % dirs.count let x2 = Int(arc4random()) % dirs.count dirs.exchangeObjectAtIndex(x1, withObjectAtIndex: x2) } for dir in dirs { var dir = dir as Direction let nx = cx + dir.dx let ny = cy + dir.dy if (between(nx, self.x) && between(ny, self.y) && (maze[nx][ny] == 0)) { maze[cx][cy] |= dir.bit maze[nx][ny] |= dir.opposite.bit generateMaze(nx, ny) } } } func between(v:Int, _ upper:Int) -> Bool { return (v >= 0) && (v < upper) }
}
let x = 10 let y = 10 let maze = MazeGenerator(x, y) maze.display()</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+ | | | | + + + +---+---+---+---+ +---+ + | | | | | | + +---+ +---+---+ +---+---+---+ + | | | | | +---+---+---+ + +---+ +---+ + + | | | | | | +---+ + +---+---+ + +---+ + + | | | | | | | | + +---+---+ + + + + + + + | | | | | | | | | + + +---+---+ + +---+ + + + | | | | | | | | | + + + + +---+---+ + +---+ + | | | | | | | + + + +---+---+ +---+---+ +---+ | | | | | | | | + +---+ + + + + + + + + | | | | | +---+---+---+---+---+---+---+---+---+---+
Tcl
<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:
+ +---+---+---+---+---+---+---+---+---+---+ | | | | +---+---+ +---+---+ + +---+ +---+ + | | | | | | + + +---+ +---+---+ +---+ + + + | | | | | | | | + +---+ +---+---+---+ + + + + + | | | | | | | | + + + + +---+---+ + +---+---+ + | | | | | | | | +---+---+---+---+ + +---+ + + +---+ | | | | | | | | + +---+---+ + + + + + +---+ + | | | | | | | | +---+ + +---+---+---+---+ + +---+ + | | +---+---+---+---+---+---+---+---+---+---+---+
TXR
Simple, Depth-First
Legend: cu = current location; vi = boolean hash of visited locations; pa = hash giving a list neighboring cells to which there is a path from a given cell.
<lang txr>@(bind (width height) (15 15)) @(do
(defvar *r* (make-random-state nil)) (defvar vi) (defvar pa)
(defun scramble (list)
(let ((out ()))
(each ((item list))
(let ((r (random *r* (+ 1 (length out)))))
(set [out r..r] (list item))))
out))
(defun neigh (loc)
(let ((x (from loc))
(y (to loc)))
(list (- x 1)..y (+ x 1)..y
x..(- y 1) x..(+ y 1))))
(defun make-maze-rec (cu)
(set [vi cu] t)
(each ((ne (scramble (neigh cu))))
(cond ((not [vi ne])
(push ne [pa cu])
(push cu [pa ne])
(make-maze-rec ne)))))
(defun make-maze (w h)
(let ((vi (hash :equal-based))
(pa (hash :equal-based)))
(each ((x (range -1 w)))
(set [vi x..-1] t)
(set [vi x..h] t))
(each ((y (range* 0 h)))
(set [vi -1..y] t)
(set [vi w..y] t))
(make-maze-rec 0..0)
pa))
(defun print-tops (pa w j)
(each ((i (range* 0 w)))
(if (memqual i..(- j 1) [pa i..j])
(put-string "+ ")
(put-string "+----")))
(put-line "+"))
(defun print-sides (pa w j)
(let ((str ""))
(each ((i (range* 0 w)))
(if (memqual (- i 1)..j [pa i..j])
(set str `@str `)
(set str `@str| `)))
(put-line `@str|\n@str|`)))
(defun print-maze (pa w h)
(each ((j (range* 0 h)))
(print-tops pa w j)
(print-sides pa w j))
(print-tops pa w h)))
@;; @(bind m @(make-maze width height)) @(do (print-maze m width height))</lang>
- Output:
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ | | | | | | | | | | + + + + + +----+----+ + +----+----+----+ + +----+ | | | | | | | | | | | | | | | | | | | | + +----+----+----+----+ +----+----+ +----+ + + +----+ + | | | | | | | | | | | | | | | | +----+----+----+ + + + +----+----+ +----+ + + +----+ | | | | | | | | | | | | | | | | | | | | | | | | + +----+ + + +----+ + +----+ + + + +----+ + | | | | | | | | | | | | | | | | | | | | +----+ + + +----+----+----+----+ +----+ + +----+----+ + | | | | | | | | | | | | | | | | + +----+ +----+----+----+ + +----+ +----+----+----+ + + | | | | | | | | | | | | | | +----+ + +----+----+----+----+----+----+----+----+----+ + + + | | | | | | | | | | | | + +----+ + +----+----+ +----+----+----+ + + +----+ + | | | | | | | | | | | | | | | | | | | | + +----+ + + + +----+----+ + +----+----+ + +----+ | | | | | | | | | | | | | | | | | | | | + + +----+ +----+ + +----+----+----+----+----+ + + + | | | | | | | | | | | | | | | | + +----+----+----+ +----+----+ + +----+----+ + +----+ + | | | | | | | | | | | | | | | | | | +----+----+ + + +----+ +----+ + + +----+----+ +----+ | | | | | | | | | | | | | | | | + + +----+----+----+ + +----+----+----+----+----+ + + + | | | | | | | | | | | | | | + +----+ +----+----+----+----+----+----+ +----+ +----+----+ + | | | | | | | | +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Quality Breadth-First
The following is a complete, self-contained command line utility. We also drop use of the TXR pattern extraction language and work purely in TXR Lisp.
The algorithm is quite different from the previous. This version is not recursive. This algorithm divides the maze cells into visited cells, frontier cells and unvisited cells. As in the DFS version, border cells outside of the maze area are pre-initialized as visited, for convenience. The frontier set initially contains the upper left hand corner.
The algorithm's main loop iterates while there are frontier cells. As the generation progresses, unvisited cells adjacent to frontier cells added to the frontier set. Frontier cells that are only surrounded by other frontier cells or visited cells are removed from the frontier set and become visited cells. Eventually, all unvisited cells become frontier cells and then visited cells, at which point the frontier set becomes empty and the algorithm terminates.
At every step, the algorithm picks the first cell in the frontier list. In the code, the frontier cells are kept in a hash called fr and also in a queue q. The algorithm tries to extend the frontier around the frontier cell which is at the head of the queue q by randomly choosing an adjacent unvisited cell. (If there is no such cell, the node is not a frontier node any more and is popped from the queue and fr set). If an unvisited node is picked, then a two-way path is broken from the given frontier cell to that cell, and that cell is added to the frontier set. Important: the new frontier cell is added to the head of the queue, rather than the tail.
The algorithm is modified by a "straightness" parameter, which is used to initialize a counter. Every time a new frontier node is added to the front of the queue, the counter decrements. When it reaches zero, the frontier queue is scrambled, and the counter is reset. As long as the count is nonzero, the maze growth proceeds from the previously traversed node, because the new node is placed at the head of the queue. This behavior mimics the DFS algorithm, resulting in long corridors without a lot of branching.
At the user interface level, the straightness parameter is represented as a percentage. This percentage is converted to a number of cells based on the width and height of the maze. For instance if the straightness parameter is 15, and the maze size is 20x20, it means that 15% out of 400 cells, or 60 cells will be traversed before the queue is scrambled. Then another 60 will be traversed and the queue will be scrambled, and so forth.
<lang txrlisp>(defvar vi) ;; visited hash (defvar pa) ;; path connectivity hash (defvar sc) ;; count, derived from straightness fator
(defun scramble (list)
(let ((out ()))
(each ((item list))
(let ((r (rand (+ 1 (length out)))))
(set [out r..r] (list item))))
out))
(defun rnd-pick (list)
(if list [list (rand (length list))]))
(defun neigh (loc)
(let ((x (from loc))
(y (to loc)))
(list (- x 1)..y (+ x 1)..y
x..(- y 1) x..(+ y 1))))
(defun make-maze-impl (cu)
(let ((fr (hash :equal-based))
(q (list cu))
(c sc))
(set [fr cu] t)
(while q
(let* ((cu (first q))
(ne (rnd-pick (remove-if (orf vi fr) (neigh cu)))))
(cond (ne (set [fr ne] t)
(push ne [pa cu])
(push cu [pa ne])
(push ne q)
(cond ((<= (dec c) 0)
(set q (scramble q))
(set c sc))))
(t (set [vi cu] t)
(del [fr cu])
(pop q)))))))
(defun make-maze (w h sf)
(let ((vi (hash :equal-based))
(pa (hash :equal-based))
(sc (max 1 (trunc (* sf w h) 100))))
(each ((x (range -1 w)))
(set [vi x..-1] t)
(set [vi x..h] t))
(each ((y (range* 0 h)))
(set [vi -1..y] t)
(set [vi w..y] t))
(make-maze-impl 0..0)
pa))
(defun print-tops (pa w j)
(each ((i (range* 0 w)))
(if (memqual i..(- j 1) [pa i..j])
(put-string "+ ")
(put-string "+----")))
(put-line "+"))
(defun print-sides (pa w j)
(let ((str ""))
(each ((i (range* 0 w)))
(if (memqual (- i 1)..j [pa i..j])
(set str `@str `)
(set str `@str| `)))
(put-line `@str|\n@str|`)))
(defun print-maze (pa w h)
(each ((j (range* 0 h))) (print-tops pa w j) (print-sides pa w j)) (print-tops pa w h))
(defun usage ()
(let ((invocation (ldiff *full-args* *args*))) (put-line "usage: ") (put-line `@invocation <width> <height> [<straightness>]`) (put-line "straightness-factor is a percentage, defaulting to 15") (exit 1)))
(let ((args [mapcar int-str *args*])
(*random-state* (make-random-state nil)))
(if (memq nil args)
(usage))
(tree-case args
((w h s ju . nk) (usage))
((w h : (s 15)) (set w (max 1 w))
(set h (max 1 h))
(print-maze (make-maze w h s) w h))
(else (usage))))</lang>
- Output:
Three mazes are generated, at the lowest, intermediate and highest "straightness factors".
It is immediately obvious that the style of each maze is quite different.
# 10x10 maze with zero percent "straightness factor" $ txr maze-generation3.txr 10 10 0 +----+----+----+----+----+----+----+----+----+----+ | | | | | | | | + + +----+----+ + + +----+----+----+ | | | | | | | | | | | | + + +----+ +----+----+----+----+ + + | | | | | | | | | | | | + +----+ +----+ +----+ +----+----+----+ | | | | | | +----+ + + + + + +----+----+----+ | | | | | | | | | | | | | | +----+ + +----+----+ +----+----+----+ + | | | | | | | | | | + +----+ +----+----+ + + +----+ + | | | | | | | | | | | | | | + +----+ + + + + + + + + | | | | | | | | | | | | | | | | | | | | +----+ + +----+ + + +----+----+ + | | | | | | | | | | | | | | + + + + +----+----+----+----+----+ + | | | | | | | | | | | | +----+----+----+----+----+----+----+----+----+----+ # with 10% straightnes factor $ txr maze-generation3.txr 10 10 10 +----+----+----+----+----+----+----+----+----+----+ | | | | | | | | | | | | + + +----+ + + + + +----+ + | | | | | | | | | | + +----+----+ +----+----+----+----+----+----+ | | | | | | | | | | +----+ + +----+ + +----+----+ + + | | | | | | | | | | | | | | + +----+----+ +----+ + + + +----+ | | | | | | | | | | | | | | + + +----+----+----+----+----+----+ + + | | | | | | | | + + +----+ + + + +----+----+----+ | | | | | | | | | | | | | | | | | | + +----+ +----+ +----+ + + + + | | | | | | | | | | | | + + +----+----+ +----+ + +----+----+ | | | | | | | | | | | | | | +----+----+ +----+ + +----+----+ + + | | | | | | | | +----+----+----+----+----+----+----+----+----+----+ # with 100 percent straight factor $ txr maze-generation3.txr 10 10 100 +----+----+----+----+----+----+----+----+----+----+ | | | | | | | | +----+ +----+ +----+----+ + + + + | | | | | | | | | | | | | | | | + +----+ +----+----+----+ + + + + | | | | | | | | | | | | | | | | + +----+ + + + +----+ +----+ + | | | | | | | | | | | | | | + + +----+ + + + +----+----+ + | | | | | | | | | | | | | | | | + + +----+ + +----+ + +----+----+ | | | | | | | | | | | | + +----+----+----+----+ +----+----+----+ + | | | | | | | | | | + +----+----+ + +----+----+ + + + | | | | | | | | | | | | | | + + + +----+ + + +----+----+ + | | | | | | | | | | | | + +----+----+ +----+----+----+----+----+ + | | | | | | +----+----+----+----+----+----+----+----+----+----+
XPL0
<lang XPL0>code Ran=1, CrLf=9, Text=12; \intrinsic routines def Cols=20, Rows=6; \dimensions of maze (cells) int Cell(Cols+1, Rows+1, 3); \cells (plus right and bottom borders) def LeftWall, Ceiling, Connected; \attributes of each cell (= 0, 1 and 2)
proc ConnectFrom(X, Y); \Connect cells starting from cell X,Y int X, Y; int Dir, Dir0; [Cell(X, Y, Connected):= true; \mark current cell as connected Dir:= Ran(4); \randomly choose a direction Dir0:= Dir; \save this initial direction repeat case Dir of \try to connect to cell at Dir
0: if X+1<Cols & not Cell(X+1, Y, Connected) then \go right
[Cell(X+1, Y, LeftWall):= false; ConnectFrom(X+1, Y)];
1: if Y+1<Rows & not Cell(X, Y+1, Connected) then \go down
[Cell(X, Y+1, Ceiling):= false; ConnectFrom(X, Y+1)];
2: if X-1>=0 & not Cell(X-1, Y, Connected) then \go left
[Cell(X, Y, LeftWall):= false; ConnectFrom(X-1, Y)];
3: if Y-1>=0 & not Cell(X, Y-1, Connected) then \go up
[Cell(X, Y, Ceiling):= false; ConnectFrom(X, Y-1)]
other []; \(never occurs)
Dir:= Dir+1 & $03; \next direction
until Dir = Dir0; ];
int X, Y; [for Y:= 0 to Rows do
for X:= 0 to Cols do
[Cell(X, Y, LeftWall):= true; \start with all walls and
Cell(X, Y, Ceiling):= true; \ ceilings in place
Cell(X, Y, Connected):= false; \ and all cells disconnected
];
Cell(0, 0, LeftWall):= false; \make left and right doorways Cell(Cols, Rows-1, LeftWall):= false; ConnectFrom(Ran(Cols), Ran(Rows)); \randomly pick a starting cell for Y:= 0 to Rows do \display the maze
[CrLf(0);
for X:= 0 to Cols do
Text(0, if X#Cols & Cell(X, Y, Ceiling) then "+--" else "+ ");
CrLf(0);
for X:= 0 to Cols do
Text(0, if Y#Rows & Cell(X, Y, LeftWall) then "| " else " ");
];
]</lang>
Output:
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| | | |
+ +--+ +--+ +--+--+--+ + +--+ + +--+--+--+--+--+--+ +
| | | | | | | | | | | |
+ + + + +--+ + +--+--+ + +--+--+ +--+--+ +--+ +--+
| | | | | | | | | | |
+ +--+--+ + +--+ + +--+--+--+--+--+--+ + +--+ +--+ +
| | | | | | | | | |
+--+ + +--+--+ + + + +--+--+ + +--+--+--+--+--+--+ +
| | | | | | | | | | | | |
+ + + + +--+--+ + + + + +--+--+ + + + + +--+--+
| | | | | |
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
zkl
Generate a maze without marked entry or exit points.
<lang zkl> fcn make_maze(w = 16, h = 8){
// make arrays with lists of lists (all mutable) vis:=(w.pump(List().write,0)+1)*h + w.pump(List().write,1); ver:=(w.pump(List().write,T(Void,"| ")) + "|")*h + T; hor:=(w.pump(List().write,T(Void,"+---")) + "+")*(h + 1);
fcn(x,y,vis,ver,hor){
vis[y][x] = 1;
d:=L(T(x - 1, y), T(x, y + 1), T(x + 1, y), T(x, y - 1)).shuffle();
foreach xx,yy in (d){
if(vis[yy][xx]) continue; if(xx==x) hor[y.max(yy)][x]="+ "; if(yy==y) ver[y][x.max(xx)]=" "; self.fcn(xx,yy,vis,ver,hor);
}
}((0).random(w),(0).random(h),vis,ver,hor);
foreach a,b in (hor.zip(ver)) { println(a.concat(),"\n",b.concat()) }
return(ver,hor);
} make_maze();</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | | +---+---+ + + +---+ + + + + +---+---+---+ + + | | | | | | | | | | | + +---+ + + +---+---+ +---+---+ + +---+ + + + | | | | | | | | | | | | + + +---+ + + + + +---+ +---+ + +---+ + + | | | | | | | | | | | + + +---+ +---+---+---+---+ +---+ +---+ + +---+ + | | | | | | | | | | + +---+ +---+ + + + +---+ +---+ +---+---+ +---+ | | | | | | | | | | + +---+---+---+---+ + + + + + +---+---+---+---+ + | | | | | | | | | | + + + + + + + + +---+---+---+ +---+---+ + + | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
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