# Maze solving

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

For a maze generated by this task, write a function that finds (and displays) the shortest path between two cells.

Note that because these mazes are generated by the Depth-first search algorithm, they contain no circular paths, and a simple depth-first tree search can be used.

## 11l

Translation of: Python
F dijkstra(graph, source)
V n = graph.len
V dist = [Float.infinity] * n
V previous = [-1] * n
dist[source] = 0
V Q = Array(0 .< n)
L !Q.empty
V u = min(Q, key' n -> @dist[n])
Q.remove(u)
I dist[u] == Float.infinity
L.break
L(v) 0 .< n
I graph[u][v] & (v C Q)
V alt = dist[u] + graph[u][v]
I alt < dist[v]
dist[v] = alt
previous[v] = u
R previous

F display_solution(predecessor)
V cell = predecessor.len - 1
L cell != 0
print(cell, end' ‘<’)
cell = predecessor[cell]
print(0)

V graph = [
[0,1,0,0,0,0],
[1,0,1,0,1,0],
[0,1,0,0,0,1],
[0,0,0,0,1,0],
[0,1,0,1,0,0],
[0,0,1,0,0,0]
]

display_solution(dijkstra(graph, 0))
Output:
5<2<1<0

## Action!

Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.

DEFINE TOP="0"
DEFINE RIGHT="1"
DEFINE BOTTOM="2"
DEFINE LEFT="3"
DEFINE WIDTH="160"
DEFINE HEIGHT="96"

DEFINE STACK_SIZE="5000"
BYTE ARRAY stack(STACK_SIZE)
INT stackSize

PROC InitStack()
stackSize=0
RETURN

BYTE FUNC IsEmpty()
IF stackSize=0 THEN
RETURN (1)
FI
RETURN (0)

BYTE FUNC IsFull()
IF stackSize>=STACK_SIZE THEN
RETURN (1)
FI
RETURN (0)

PROC Push(BYTE x,y)
IF IsFull() THEN Break() RETURN FI
stack(stackSize)=x stackSize==+1
stack(stackSize)=y stackSize==+1
RETURN

PROC Pop(BYTE POINTER x,y)
IF IsEmpty() THEN Break() RETURN FI
stackSize==-1 y^=stack(stackSize)
stackSize==-1 x^=stack(stackSize)
RETURN

PROC Push3(BYTE x,y,d)
IF IsFull() THEN Break() RETURN FI
stack(stackSize)=x stackSize==+1
stack(stackSize)=y stackSize==+1
stack(stackSize)=d stackSize==+1
RETURN

PROC Pop3(BYTE POINTER x,y,d)
IF IsEmpty() THEN Break() RETURN FI
stackSize==-1 d^=stack(stackSize)
stackSize==-1 y^=stack(stackSize)
stackSize==-1 x^=stack(stackSize)
RETURN

PROC FillScreen()
BYTE POINTER ptr ;pointer to the screen memory
INT screenSize=[3840]

ptr=PeekC(88)
SetBlock(ptr,screenSize,\$55)

Color=0
Plot(0,HEIGHT-1) DrawTo(WIDTH-1,HEIGHT-1) DrawTo(WIDTH-1,0)
RETURN

PROC GetNeighbors(BYTE x,y BYTE ARRAY n BYTE POINTER count)
DEFINE WALL="1"

count^=0
IF y>2 AND Locate(x,y-2)=WALL THEN
n(count^)=TOP count^==+1
FI
IF x<WIDTH-3 AND Locate(x+2,y)=WALL THEN
n(count^)=RIGHT count^==+1
FI
IF y<HEIGHT-3 AND Locate(x,y+2)=WALL THEN
n(count^)=BOTTOM count^==+1
FI
IF x>2 AND Locate(x-2,y)=WALL THEN
n(count^)=LEFT count^==+1
FI
RETURN

PROC DrawConnection(BYTE POINTER x,y BYTE dir)
Plot(x^,y^)
IF dir=TOP THEN
y^==-2
ELSEIF dir=RIGHT THEN
x^==+2
ELSEIF dir=BOTTOM THEN
y^==+2
ELSE
x^==-2
FI
DrawTo(x^,y^)
RETURN

PROC Maze(BYTE x,y)
BYTE ARRAY stack,neighbors
BYTE dir,nCount

FillScreen()

Color=2
InitStack()
Push(x,y)
WHILE IsEmpty()=0
DO
Pop(@x,@y)
GetNeighbors(x,y,neighbors,@nCount)
IF nCount>0 THEN
Push(x,y)
dir=neighbors(Rand(nCount))
DrawConnection(@x,@y,dir)
Push(x,y)
FI
OD
RETURN

BYTE FUNC IsConnection(BYTE x,y,dir)
DEFINE WAY="2"
IF dir=TOP AND y>2 AND Locate(x,y-1)=WAY THEN
RETURN (1)
ELSEIF dir=RIGHT AND x<WIDTH-3 AND Locate(x+1,y)=WAY THEN
RETURN (1)
ELSEIF dir=BOTTOM AND y<HEIGHT-3 AND Locate(x,y+1)=WAY THEN
RETURN (1)
ELSEIF dir=LEFT AND x>2 AND Locate(x-1,y)=WAY THEN
RETURN (1)
FI
RETURN (0)

PROC Solve(BYTE x1,y1,x2,y2)
BYTE dir,x,y,lastX,lastY,back

Color=3
Plot(x1,y1)
Plot(x2,y2)

InitStack()
Push3(x1,y1,TOP)
WHILE IsEmpty()=0
DO
Pop3(@x,@y,@dir)
IF back THEN
Color=2
Plot(lastX,lastY)
DrawTo(x,y)
FI
IF IsConnection(x,y,dir) THEN
Color=3
Push3(x,y,dir+1)
DrawConnection(@x,@y,dir)
IF x=x2 AND y=y2 THEN
RETURN
FI
Push3(x,y,TOP)
back=0
ELSEIF dir<=LEFT THEN
Push3(x,y,dir+1)
back=0
ELSE
lastX=x
lastY=y
back=1
FI
OD
RETURN

PROC Main()
BYTE CH=\$02FC,COLOR0=\$02C4,COLOR1=\$02C5,COLOR2=\$02C6
BYTE x,y,x2,y2

Graphics(7+16)
COLOR0=\$0A
COLOR1=\$04
COLOR2=\$A6

x=Rand((WIDTH RSH 1)-1) LSH 1+1
y=Rand((HEIGHT RSH 1)-1) LSH 1+1
Maze(x,y)

x=Rand((WIDTH RSH 1)-1) LSH 1+1
y=Rand((HEIGHT RSH 1)-1) LSH 1+1
x2=Rand((WIDTH RSH 1)-1) LSH 1+1
y2=Rand((HEIGHT RSH 1)-1) LSH 1+1
Solve(x,y,x2,y2)

DO UNTIL CH#\$FF OD
CH=\$FF
RETURN
Output:

The maze is read from the standard input. The size of the maze is hardwired into the program (see the constants X_Size and Y_Size).

procedure Maze_Solver is

X_Size: constant Natural := 45;
Y_Size: constant Natural := 17;

subtype X_Range is Natural range 1 .. X_Size;
subtype Y_Range is Natural range 1 .. Y_Size;

East:  constant X_Range := 2;
South: constant Y_Range := 1;

X_Start: constant X_Range  := 3; -- start at the upper left
Y_Start: constant Y_Range  := 1;
X_Finish: constant X_Range := X_Size-East; -- go to the lower right
Y_Finish: constant Y_Range := Y_Size;

type Maze_Type is array (Y_Range) of String(X_Range);

function Solved(X: X_Range; Y: Y_Range) return Boolean is
begin
return (X = X_Finish) and (Y = Y_Finish);
end Solved;

procedure Output_Maze(M: Maze_Type; Message: String := "") is
begin
if Message /= "" then
end if;
for I in M'Range loop
end loop;
end Output_Maze;

procedure Search(M: in out Maze_Type; X: X_Range; Y:Y_Range) is
begin
M(Y)(X) := '*';
if Solved(X, Y) then
Output_Maze(M, "Solution found!");
else
if Integer(Y)-South >= 1 and then M(Y-South)(X) = ' ' then
Search(M, X, Y-South);
end if;
if Integer(Y)+South <= Y_Size and then M(Y+South)(X) = ' ' then
Search(M, X, Y+South);
end if;
if Integer(X)-East >= 1 and then M(Y)(X-East) = ' ' then
Search(M, X-East, Y);
end if;
if Integer(Y)+East <= Y_Size and then M(Y)(X+East) = ' ' then
Search(M, X+East, Y);
end if;
end if;
M(Y)(X) := ' ';
end Search;

Maze: Maze_Type;
X: X_Range := X_Start;
Y: Y_Range := Y_Start;

begin
for I in 1 .. Y_Size loop
end loop;
Maze(Y_Start)(X_Start)   := ' '; -- Start from
Maze(Y_Finish)(X_Finish) := ' '; -- Go_To
Output_Maze(Maze, "The Maze:");

Search(Maze, X, Y) ; -- Will output *all* Solutions.
-- If there is no output, there is no solution.
end Maze_Solver;
Example output
:

(using a maze generated by the Ada implementation of the maze generation task as the input):

> ./maze_solver < maze.txt
The Maze:
+- -+---+---+---+---+---+---+---+---+---+---+
|                                       |   |
+   +   +---+---+---+---+---+---+---+   +   +
|   |           |       |               |   |
+   +---+---+   +---+   +   +---+---+---+   +
|   |           |       |   |   |           |
+---+   +---+---+   +---+   +   +   +---+   +
|       |           |       |   |   |       |
+   +---+   +---+---+   +---+   +   +   +---+
|       |   |           |           |       |
+---+---+   +   +---+---+---+---+   +---+   +
|           |       |           |       |   |
+   +   +---+---+   +---+   +   +---+---+   +
|   |           |           |               |
+   +---+   +---+---+---+---+---+---+---+   +
|       |                                   |
+---+---+---+---+---+---+---+---+---+---+- -+

Solution found!
+-*-+---+---+---+---+---+---+---+---+---+---+
| * * * * * * * * * * * * * * * * * * * |   |
+   +   +---+---+---+---+---+---+---+ * +   +
|   |           |       | * * * * * * * |   |
+   +---+---+   +---+   + * +---+---+---+   +
|   |           |       | * |   |           |
+---+   +---+---+   +---+ * +   +   +---+   +
|       |           | * * * |   |   |       |
+   +---+   +---+---+ * +---+   +   +   +---+
|       |   | * * * * * |           |       |
+---+---+   + * +---+---+---+---+   +---+   +
|           | * * * |     * * * |       |   |
+   +   +---+---+ * +---+ * + * +---+---+   +
|   |           | * * * * * | * * * * * * * |
+   +---+   +---+---+---+---+---+---+---+ * +
|       |                                 * |
+---+---+---+---+---+---+---+---+---+---+-*-+

## AutoHotkey

Generator and solver combined.

Width := 10, Height	:= 10												; set grid size
SleepTime := 0

gosub, Startup

Gui, +AlwaysOnTop
Gui, font, s12, consolas
Gui, add, edit, vEditGrid x10, % maze
Gui, add, button, xs gStartup Default, Generate maze
Gui, add, button, x+10 gSolve, Solve
Gui, show,, maze
GuiControl,, EditGrid, % maze											; show maze
return

;-----------------------------------------------------------------------
^Esc::
GuiEscape:
GuiClose:
ExitApp
return

;-----------------------------------------------------------------------
Startup:
oMaze := []																; initialize
Solved := false
loop, % Height
{
row := A_Index
loop, % Width														; create oMaze[row,column] borders
col := A_Index, oMaze[row,col] :=  "LRTB"						; i.e. oMaze[2,5] := LRTB (add all borders)
}
Random, row, 1, % Height												; random row
Random, col, 1, % Width													; random col
grid := maze2text(oMaze)												; object to text
GuiControl,, EditGrid, % Grid											; show Grid
row := col := 1															; reset to 1,1
oMaze := Generate_maze(row, col, oMaze)									; generate maze starting from random row/column
oMaze[1,1] .= "X"														; start from 1,1
maze := maze2text(oMaze)												; object to text
GuiControl,, EditGrid, % maze											; show maze
GuiControl,, EditRoute													; clear route
GuiControl, Enable, Solve
return

;-----------------------------------------------------------------------
Solve:
GuiControl, Disable, Generate maze
GuiControl, Disable, Solve
loop % oRoute.MaxIndex()
oRoute.pop()

oSolution	:= Solve(1, 1, oMaze)										; solve starting from 1,1
oMaze 		:= oSolution.1
oRoute 		:= oSolution.2
Update(oMaze, oRoute)
Solved := true
GuiControl, Enable, Generate maze
return

;-----------------------------------------------------------------------
Update(oMaze, oRoute){
global SleepTime
GuiControl,, EditGrid, % maze2text(oMaze)
Sleep, % SleepTime
}

;-----------------------------------------------------------------------
maze2text(oMaze){
width := oMaze.1.MaxIndex()
BLK := "█"
for row, objRow in oMaze
{
for col, val in objRow											; add ceiling
{
ceiling := InStr(oMaze[row, col] , "x") && InStr(oMaze[row-1, col] , "x") ? "+ " BLK " " : "+   "
grid .= (InStr(val, "T") ? "+---" : ceiling) (col = Width ? "+`n" : "")
}
for col, val in objRow											; add left wall
{
wall := SubStr(val, 0) = "X" ? BLK : " "
grid .= (InStr(val, "L") ? "| " : "  ") wall " " (col = Width ? "|`n" : "") ; add left wall if needed then outer right border
}
}
Loop % Width
Grid .= "+---"													; add bottom floor
Grid .= "+"															; add right bottom corner
return RegExReplace(grid , BLK "   (?=" BLK ")" ,  BLK BLK BLK BLK)	; fill gaps
}

;-----------------------------------------------------------------------
Generate_maze(row, col, oMaze) {
neighbors := row+1 "," col "`n" row-1 "," col  "`n" row "," col+1  "`n" row "," col-1
Sort, neighbors, random												; randomize neighbors list
Loop, parse, neighbors, `n											; for each neighbor
{
rowX := StrSplit(A_LoopField, ",").1							; this neighbor row
colX := StrSplit(A_LoopField, ",").2							; this neighbor column
if !instr(oMaze[rowX,colX], "LRTB") || !oMaze[rowX, colX]		; if visited (has a missing border) or out of bounds
continue													; skip

; remove borders
if (row > rowX)													; Cell is below this neighbor
oMaze[row,col] := StrReplace(oMaze[row,col], "T") , oMaze[rowX,colX] := StrReplace(oMaze[rowX,colX], "B")
else if (row < rowX)											; Cell is above this neighbor
oMaze[row,col] := StrReplace(oMaze[row,col], "B") , oMaze[rowX,colX] := StrReplace(oMaze[rowX,colX], "T")
else if (col > colX)											; Cell is right of this neighbor
oMaze[row,col] := StrReplace(oMaze[row,col], "L") , oMaze[rowX,colX] := StrReplace(oMaze[rowX,colX], "R")
else if (col < colX)											; Cell is left of this neighbor
oMaze[row,col] := StrReplace(oMaze[row,col], "R") , oMaze[rowX,colX] := StrReplace(oMaze[rowX,colX], "L")

Generate_maze(rowX, colX, oMaze)								; recurse for this neighbor
}
return, oMaze
}

;-----------------------------------------------------------------------
Solve(row, col, oMaze){
static oRoute := []
oNeighbor := [], targetrow := oMaze.MaxIndex(), targetCol := oMaze.1.MaxIndex()

;~ Update(oMaze, oRoute)
oRoute.push(row ":" col)											; push current cell address to oRoute
oMaze[row, col] .= "X"												; mark it visited "X"

if (row = targetrow) && (Col = targetCol)							; if solved
return true														; return ture

; create list of Neighbors
oNeighbor[row, col] := []
if !InStr(oMaze[row, col], "R")										; if no Right border
oNeighbor[row, col].push(row "," col+1)							; add neighbor
if !InStr(oMaze[row, col], "B")										; if no Bottom border
oNeighbor[row, col].push(row+1 "," col)							; add neighbor
if !InStr(oMaze[row, col], "T")										; if no Top border
oNeighbor[row, col].push(row-1 "," col)							; add neighbor
if !InStr(oMaze[row, col], "L")										; if no Left border
oNeighbor[row, col].push(row "," col-1)							; add neighbor

; recurese for each oNeighbor
for each, neighbor in oNeighbor[row, col]							; for each neighbor
{
Update(oMaze, oRoute)
startrow := StrSplit(neighbor, ",").1							; this neighbor
startCol := StrSplit(neighbor, ",").2							; becomes starting point

if !InStr(oMaze[startrow, startCol], "X")						; if it was not visited
if Solve(startrow, startCol, oMaze)							; recurse for current neighbor
return [oMaze, oRoute]									; return solution if solved
}
oRoute.pop()														; no solution found, back track
oMaze[row, Col] := StrReplace(oMaze[row, Col], "X")					; no solution found, back track
;~ Update(oMaze, oRoute)
}

;-----------------------------------------------------------------------
#IfWinActive, maze
Right::
Left::
Up::
Down::
if Solved
return

if (A_ThisHotkey="Right") && (!InStr(oMaze[row,col], "R"))
oMaze[row, col] := StrReplace(oMaze[row, col], "X")		, col++
if (A_ThisHotkey="Left") && (!InStr(oMaze[row,col], "L"))
oMaze[row, col] := StrReplace(oMaze[row, col], "X")		, col--
if (A_ThisHotkey="Up") && (!InStr(oMaze[row,col], "T"))
oMaze[row, col] := StrReplace(oMaze[row, col], "X")		, row--
if (A_ThisHotkey="Down") && (!InStr(oMaze[row,col], "B"))
oMaze[row, col] := StrReplace(oMaze[row, col], "X")		, row++

oMaze[row, col] .= "X"
GuiControl,, EditGrid, % maze2text(oMaze)

if (col = Width) && (row = Height)
{
Solved := true
oMaze[height, width] := StrReplace(oMaze[height, width], "X")
SleepTime := 0
gosub, solve
return
}
return
#IfWinActive

Outputs:

+---+---+---+---+---+---+---+---+---+---+
| ¦¦¦¦¦ |     ¦¦¦¦¦ |     ¦¦¦¦¦¦¦¦¦¦¦¦¦ |
+---+ ¦ +---+ ¦ + ¦ +---+ ¦ +---+---+ ¦ +
|   | ¦ | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ |
+   + ¦ + ¦ +---+---+---+---+ ¦ + ¦ + ¦ +
| ¦¦¦¦¦ | ¦ | ¦¦¦¦¦¦¦¦¦¦¦¦¦ | ¦ | ¦¦¦¦¦ |
+ ¦ +---+ ¦ + ¦ +---+---+ ¦ + ¦ +---+---+
| ¦ |     ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ |   |
+ ¦ +---+---+---+ ¦ +---+---+---+ ¦ +   +
| ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ |             ¦¦¦¦¦ |
+---+ ¦ + ¦ +---+---+   +---+---+---+ ¦ +
| ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ |   | ¦¦¦¦¦ |   | ¦ |
+ ¦ +---+---+---+ ¦ +---+ ¦ + ¦ +   + ¦ +
| ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ | ¦¦¦¦¦ |
+---+ ¦ + ¦ +---+---+ ¦ +---+ ¦ + ¦ +---+
| ¦¦¦¦¦ | ¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ |   |
+ ¦ +---+ ¦ + ¦ +---+---+ ¦ +---+ ¦ +   +
| ¦ |     ¦¦¦¦¦     | ¦¦¦¦¦ |   | ¦¦¦¦¦ |
+ ¦ +---+---+---+---+ ¦ +---+   +---+ ¦ +
| ¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦ |             ¦ |
+---+---+---+---+---+---+---+---+---+---+

## BBC BASIC

Maze generation code also included.

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
OFF
PROCgeneratemaze(Maze&(), MazeWidth%, MazeHeight%, MazeCell%)
PROCsolvemaze(Path{()}, Maze&(), 0, MazeHeight%-1, MazeWidth%-1, 0, MazeCell%)
END

DEF PROCsolvemaze(RETURN s{()}, m&(), x%, y%, dstx%, dsty%, s%)
LOCAL h%, i%, n%, p%, q%, w%
w% = DIM(m&(),1)
h% = DIM(m&(),2)
DIM s{(w%*h%) x%,y%}
GCOL 3,14
m&(x%,y%) OR= &80
REPEAT
FOR i% = 0 TO 3
CASE i% 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%) < &80 THEN
IF p% > x% IF m&(p%,q%) AND 1 EXIT FOR
IF q% > y% IF m&(p%,q%) AND 2 EXIT FOR
IF x% > p% IF m&(x%,y%) AND 1 EXIT FOR
IF y% > q% IF m&(x%,y%) AND 2 EXIT FOR
ENDIF
NEXT
IF i% < 4 THEN
m&(p%,q%) OR= &80
s{(n%)}.x% = x%
s{(n%)}.y% = y%
n% += 1
ELSE
IF n% > 0 THEN
n% -= 1
p% = s{(n%)}.x%
q% = s{(n%)}.y%
ENDIF
ENDIF
LINE (x%+0.5)*s%,(y%+0.5)*s%,(p%+0.5)*s%,(q%+0.5)*s%
x% = p%
y% = q%
UNTIL x%=dstx% AND y%=dsty%
s{(n%)}.x% = x%
s{(n%)}.y% = y%
ENDPROC

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

## C

See Maze generation for combined gen/solve code.

## C#

Translation of: Go
using System;
using System.Text;

public class Maze
{
private char[,] cells;
private char[,] hWalls; // Horizontal walls
private char[,] vWalls; // Vertical walls
private Random rand = new Random();

public Maze(int rows, int cols)
{
cells = new char[rows, cols];
hWalls = new char[rows + 1, cols]; // Include walls for the bottom
vWalls = new char[rows, cols + 1]; // Include walls for the right side

// Initialize walls
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
hWalls[i, j] = '-';
vWalls[i, j] = '|';
}
}

// Set the outer walls for the bottom and right
for (int i = 0; i < cols; i++)
{
hWalls[rows, i] = '-';
}
for (int i = 0; i < rows; i++)
{
vWalls[i, cols] = '|';
}
}

public override string ToString()
{
var builder = new StringBuilder();

for (int i = 0; i < cells.GetLength(0); i++)
{
// Top walls
for (int j = 0; j < cells.GetLength(1); j++)
{
builder.Append("+");
builder.Append(hWalls[i, j] == '-' ? "---" : "   ");
}
builder.AppendLine("+");

// Side walls and cells
for (int j = 0; j < cells.GetLength(1); j++)
{
builder.Append(vWalls[i, j] == '|' ? "| " : "  ");
char cell = cells[i, j] == '\0' ? ' ' : cells[i, j];
builder.Append(cell + " ");
}
builder.AppendLine("|");
}

// Bottom walls
for (int j = 0; j < cells.GetLength(1); j++)
{
builder.Append("+---");
}
builder.AppendLine("+");

return builder.ToString();
}

public void Generate()
{
Generate(rand.Next(cells.GetLength(0)), rand.Next(cells.GetLength(1)));
}

private void Generate(int r, int c)
{
cells[r, c] = ' ';
int[] dirs = { 0, 1, 2, 3 };
Shuffle(dirs);

foreach (int dir in dirs)
{
switch (dir)
{
case 0: // Up
if (r > 0 && cells[r - 1, c] == '\0')
{
hWalls[r, c] = ' ';
Generate(r - 1, c);
}
break;
case 1: // Down
if (r < cells.GetLength(0) - 1 && cells[r + 1, c] == '\0')
{
hWalls[r + 1, c] = ' ';
Generate(r + 1, c);
}
break;
case 2: // Right
if (c < cells.GetLength(1) - 1 && cells[r, c + 1] == '\0')
{
vWalls[r, c + 1] = ' ';
Generate(r, c + 1);
}
break;
case 3: // Left
if (c > 0 && cells[r, c - 1] == '\0')
{
vWalls[r, c] = ' ';
Generate(r, c - 1);
}
break;
}
}
}

private void Shuffle(int[] array)
{
for (int i = array.Length - 1; i > 0; i--)
{
int j = rand.Next(i + 1);
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}
}

public void Solve(int startRow, int startCol, int endRow, int endCol)
{
if (Solve(startRow, startCol, endRow, endCol, -1))
{
cells[startRow, startCol] = 'S';
cells[endRow, endCol] = 'F';
}
}

private bool Solve(int r, int c, int endRow, int endCol, int dir)
{
if (r == endRow && c == endCol) return true;

// Up
if (dir != 1 && r > 0 && hWalls[r, c] == ' ' && Solve(r - 1, c, endRow, endCol, 0))
{
cells[r, c] = '^';
return true;
}
// Down
if (dir != 0 && r < cells.GetLength(0) - 1 && hWalls[r + 1, c] == ' ' && Solve(r + 1, c, endRow, endCol, 1))
{
cells[r, c] = 'v';
return true;
}
// Right
if (dir != 3 && c < cells.GetLength(1) - 1 && vWalls[r, c + 1] == ' ' && Solve(r, c + 1, endRow, endCol, 2))
{
cells[r, c] = '>';
return true;
}
// Left
if (dir != 2 && c > 0 && vWalls[r, c] == ' ' && Solve(r, c - 1, endRow, endCol, 3))
{
cells[r, c] = '<';
return true;
}

return false;
}
}

class Program
{
static void Main(string[] args)
{
var maze = new Maze(4, 7);
maze.Generate();
Random rand = new Random();
maze.Solve(rand.Next(4), rand.Next(7), rand.Next(4), rand.Next(7));
Console.WriteLine(maze);
}
}
Output:
+---+---+---+---+---+---+---+
|           |       | v   S |
+   +---+   +---+   +   +---+
|       |   |       | >   v |
+---+---+   +   +---+---+   +
|           |   |       | F |
+   +---+---+   +   +   +   +
|                   |       |
+---+---+---+---+---+---+---+

## C++

Generator and solver combined. The generator is the same found in Maze generation

#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.biBitCount	   = sizeof( DWORD ) * 8;

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 )
{
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 ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

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, 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(); }

BYTE* getMaze() const { return _world; }

void create( int side )
{
_s = side;
generate();
}

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;
}
}
}

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;
};
//--------------------------------------------------------------------------------------------------
class mazeSolver
{
public:
mazeSolver()
{
_bmp.create( BMP_SIZE, BMP_SIZE );
_pts = 0;
}

~mazeSolver() { killPoints(); }

void solveIt( BYTE* maze, int size, int sX, int sY, int eX, int eY )
{
_lastDir = NONE;
_world = maze; _s = size; _sx = sX; _sy = sY; _ex = eX; _ey = eY;

for( int y = 0; y < _s; y++ )
for( int x = 0; x < _s; x++ )
_world[x + _s * y] &= 0x0f;

_world[_sx + _s * _sy] |= NOR << 4;

killPoints();
_pts = new BYTE[_s * _s];
ZeroMemory( _pts, _s * _s );

findTheWay();

_sx = sX; _sy = sY;
display();
}

private:
int invert( int d )
{
switch( d )
{
case NOR: return SOU;
case SOU: return NOR;
case WES: return EAS;
case EAS: return WES;
}
return NONE;
}

void updatePosition( int d )
{
switch( d )
{
case NOR: _sy--; break;
case EAS: _sx++; break;
case SOU: _sy++; break;
case WES: _sx--;
}
}

void findTheWay()
{
while( true )
{
int d = getDirection();
if( d < NOR ) return;
_lastDir = invert( d );
_world[_sx + _s * _sy] |= d;
_pts[_sx + _s * _sy] = d;
updatePosition( d );
if( _sx == _ex && _sy == _ey ) return;
_world[_sx + _s * _sy] |= _lastDir << 4;
}
}

int getDirection()
{
int d = 1 << rand() % 4;
while( true )
{
for( int x = 0; x < 4; x++ )
{
if( testDirection( d ) ) return d;
d <<= 1;
if( d > 8 ) d = 1;
}

d = ( _world[_sx + _s * _sy] & 0xf0 ) >> 4;
if( !d ) return -1;
_pts[_sx + _s * _sy] = 0;
updatePosition( d );
_lastDir = invert( d );
d = 1 << rand() % 4;
}
}

bool testDirection( int d )
{
if( d == _lastDir || !( _world[_sx + _s * _sy] & d ) ) return false;
switch( d )
{
case NOR:
return _sy - 1 > -1 && !( _world[_sx + _s * ( _sy - 1 )] & 0xf0 );
case EAS:
return _sx + 1 < _s && !( _world[_sx + 1 + _s * _sy] & 0xf0 );
case SOU:
return _sy + 1 < _s && !( _world[_sx + _s * ( _sy + 1 )] & 0xf0 );
case WES:
return _sx - 1 > -1 && !( _world[_sx - 1 + _s * _sy] & 0xf0 );
}
return false;
}

void display()
{
_bmp.setPenColor( RGB( 0, 255, 0 ) );
_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 );
}
}
}

drawEndPoints( dc );
_bmp.setPenColor( RGB( 255, 0, 0 ) );

for( int y = 0; y < _s; y++ )
{
int yy = y * _s;
for( int x = 0; x < _s; x++ )
{
BYTE d = _pts[x + yy];
if( !d ) continue;

int nx = x * CELL_SIZE + 4,
ny = y * CELL_SIZE + 4;

MoveToEx( dc, nx, ny, NULL );
switch( d )
{
case NOR: LineTo( dc, nx, ny - CELL_SIZE - 1 ); break;
case EAS: LineTo( dc, nx + CELL_SIZE + 1, ny ); break;
case SOU: LineTo( dc, nx, ny + CELL_SIZE + 1 ); break;
case WES: LineTo( dc, nx - CELL_SIZE - 1, ny ); break;
}
}
}

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

void drawEndPoints( HDC dc )
{
RECT rc;
int x = 1 + _sx * CELL_SIZE, y = 1 + _sy * CELL_SIZE;
SetRect( &rc, x, y, x + CELL_SIZE - 1, y + CELL_SIZE - 1 );
FillRect( dc, &rc, ( HBRUSH )GetStockObject( WHITE_BRUSH ) );
x = 1 + _ex * CELL_SIZE, y = 1 + _ey * CELL_SIZE;
SetRect( &rc, x, y, x + CELL_SIZE - 1, y + CELL_SIZE - 1 );
FillRect( dc, &rc, ( HBRUSH )GetStockObject( WHITE_BRUSH ) );
}

void killPoints() { if( _pts ) delete [] _pts; }

BYTE*    _world, *_pts;
int      _s, _sx, _sy, _ex, _ey, _lastDir;
myBitmap _bmp;
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );
srand( GetTickCount() );

mazeGenerator mg;
mazeSolver ms;
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 );
int sx, sy, ex, ey;
while( true )
{
sx = rand() % s; sy = rand() % s;
ex = rand() % s; ey = rand() % s;
if( ex != sx || ey != sy ) break;
}
ms.solveIt( mg.getMaze(), s, sx, sy, ex, ey );
cout << endl;
}
system( "pause" );
system( "cls" );
}
return 0;
}
//--------------------------------------------------------------------------------------------------

## Clojure

(ns small-projects.find-shortest-way
(:require [clojure.string :as str]))

;Misk functions
(defn cell-empty? [maze coords]
(= :empty (get-in maze coords)))

(defn wall? [maze coords]
(= :wall (get-in maze coords)))

(defn track? [maze coords]
(= :track (get-in maze coords)))

(defn get-neighbours [maze [y x cell]]
[[y (dec x)] [(inc y) x] [y (inc x)] [(dec y) x]])

(defn get-difference [coll1 filter-coll]
(filter #(not (contains? filter-coll %)) coll1))

(defn get-empties [maze cell]
(->> (get-neighbours maze cell)
(filter (partial cell-empty? maze))))

(defn possible-ways [maze cell filter-coll]
(-> (get-empties maze cell)
(get-difference filter-coll)))

(defn replace-cells [maze coords v]
(if (empty? coords)
maze
(recur (assoc-in maze (first coords) v) (rest coords) v)))

;Print and parse functions
(def cell-code->str
["  " "  " "  " "  " "· " "╵ " "╴ " "┘ "
"  " "  " "  " "  " "╶─" "└─" "──" "┴─"
"  " "  " "  " "  " "╷ " "│ " "┐ " "┤ "
"  " "  " "  " "  " "┌─" "├─" "┬─" "┼─"
"  " "  " "  " "  " "■ " "╹ " "╸ " "┛ "
"  " "  " "  " "  " "╺━" "┗━" "━━" "┻━"
"  " "  " "  " "  " "╻ " "┃ " "┓ " "┫ "
"  " "  " "  " "  " "┏━" "┣━" "┳━" "╋━"
"  "])

(defn get-cell-code [maze coords]
(let [mode (if (track? maze coords) 1 0)
check (if (zero? mode) wall? track?)]
(transduce
(comp
(map (partial check maze))
(keep-indexed (fn [idx test] (when test idx)))
(map (partial bit-shift-left 1)))
(completing bit-or)
(bit-shift-left mode 5)
(sort (conj (get-neighbours maze coords) coords)))))

(defn code->str [cell-code]
(nth cell-code->str cell-code))

(defn maze->str-symbols [maze]
(for [y (range (count maze))]
(for [x (range (count (nth maze y)))]
(code->str (get-cell-code maze [y x])))))

(defn maze->str [maze]
(->> (maze->str-symbols maze)
(map str/join)
(str/join "\n")))

(defn parse-pretty-maze [maze-str]
(->> (str/split-lines maze-str)
(map (partial take-nth 2))
(map (partial map #(if (= \space %) :empty :wall)))
(map vec)
(vec)))

;Core
(defn find-new-border [maze border old-border]
(apply conj (map (fn [cell]
(zipmap (possible-ways maze cell (conj border old-border))
(repeat cell)))
(keys border))))

(defn backtrack [visited route]
(let [cur-cell (get visited (first route))]
(if (= cur-cell :start)
route
(recur visited (conj route cur-cell)))))

(defn breadth-first-search [maze start-cell end-cell]
(loop [visited {start-cell :start}
border {start-cell :start}
old-border {start-cell :start}]
(if (contains? old-border end-cell)
(backtrack visited (list end-cell))
(recur
(conj visited border)
(find-new-border maze border old-border)
border))))

(def maze (parse-pretty-maze maze-str))

(def solved-maze
(replace-cells maze (breadth-first-search maze [1 1] [19 19]) :track))

(println (maze->str solved-maze))
Input:
┌───────────┬───────┬───────┬───────────┐
│           │       │       │           │
│   ╶───────┘   ╷   ╵   ╷   ╵   ┌───╴   │
│               │       │       │       │
│   ╶───────┬───┴───┬───┴───┬───┘   ╷   │
│           │       │       │       │   │
├───────╴   │   ╷   ╵   ╷   │   ┌───┘   │
│           │   │       │   │   │       │
│   ┌───┬───┘   ├───────┤   │   ├───────┤
│   │   │       │       │   │   │       │
│   ╵   ╵   ╶───┴───┐   │   │   ╵   ╷   │
│                   │   │   │       │   │
├───────────────┐   ╵   │   │   ╶───┤   │
│               │       │   │       │   │
│   ╶───┐   ┌───┴───╴   │   │   ┌───┘   │
│       │   │           │   │   │       │
├───╴   │   │   ╶───┬───┤   └───┤   ╶───┤
│       │   │       │   │       │       │
│   ╶───┤   └───╴   ╵   └───┐   └───╴   │
│       │                   │           │
└───────┴───────────────────┴───────────┘
Output:
┌───────────┬───────┬───────┬───────────┐
│ ╻         │       │       │           │
│ ┃ ╶───────┘   ╷   ╵   ╷   ╵   ┌───╴   │
│ ┃             │       │       │       │
│ ┃ ╶───────┬───┴───┬───┴───┬───┘   ╷   │
│ ┗━━━━━━━┓ │ ┏━━━┓ │ ┏━━━┓ │       │   │
├───────╴ ┃ │ ┃ ╷ ┃ ╵ ┃ ╷ ┃ │   ┌───┘   │
│ ┏━━━━━━━┛ │ ┃ │ ┗━━━┛ │ ┃ │   │       │
│ ┃ ┌───┬───┘ ┃ ├───────┤ ┃ │   ├───────┤
│ ┃ │   │ ┏━━━┛ │       │ ┃ │   │       │
│ ┃ ╵   ╵ ┃ ╶───┴───┐   │ ┃ │   ╵   ╷   │
│ ┗━━━━━━━┛         │   │ ┃ │       │   │
├───────────────┐   ╵   │ ┃ │   ╶───┤   │
│               │       │ ┃ │       │   │
│   ╶───┐   ┌───┴───╴   │ ┃ │   ┌───┘   │
│       │   │           │ ┃ │   │       │
├───╴   │   │   ╶───┬───┤ ┃ └───┤   ╶───┤
│       │   │       │   │ ┗━━━┓ │       │
│   ╶───┤   └───╴   ╵   └───┐ ┃ └───╴   │
│       │                   │ ┗━━━━━━━╸ │
└───────┴───────────────────┴───────────┘

## D

 This example is incorrect. Please fix the code and remove this message.Details: Is output double spaced, with only two dots above the E rather than 4, see comment Pete Lomax (talk) 06:09, 19 March 2017 (UTC)

This entry reads a maze generated by http://rosettacode.org/wiki/Maze_generation#D and chooses two random start-end points.

import std.stdio, std.random, std.string, std.array, std.algorithm,
std.file, std.conv;

enum int cx = 4, cy = 2; // Cell size x and y.
enum int cx2 = cx / 2, cy2 = cy / 2;
enum pathSymbol = '.';
struct V2 { int x, y; }

bool solveMaze(char[][] maze, in V2 s, in V2 end) pure nothrow @safe @nogc {
if (s == end)
return true;

foreach (immutable d; [V2(0, -cy), V2(+cx, 0), V2(0, +cy), V2(-cx, 0)])
if (maze[s.y + (d.y / 2)][s.x + (d.x / 2)] == ' ' &&
maze[s.y + d.y][s.x + d.x] == ' ') {
//Would this help?
//          maze[s.y + (d.y / 2)][s.x + (d.x / 2)] = pathSymbol;
maze[s.y + d.y][s.x + d.x] = pathSymbol;
if (solveMaze(maze, V2(s.x + d.x, s.y + d.y), end))
return true;
maze[s.y + d.y][s.x + d.x] = ' ';
}

return false;
}

void main() {
auto maze = "maze.txt".File.byLine.map!(r => r.chomp.dup).array;
immutable h = (maze.length.signed - 1) / cy;
assert (h > 0);
immutable w = (maze[0].length.signed - 1) / cx;

immutable start = V2(cx2 + cx * uniform(0, w), cy2 + cy * uniform(0, h));
immutable end = V2(cx2 + cx * uniform(0, w), cy2 + cy * uniform(0, h));

maze[start.y][start.x] = pathSymbol;
if (!solveMaze(maze, start, end))
return "No solution path found.".writeln;
maze[start.y][start.x] = 'S';
maze[end.y][end.x] = 'E';
writefln("%-(%s\n%)", maze);
}
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|   |               |           | . . . . . . . . .     |
+   +   +---+---+   +   +---+   + . +---+---+---+ . +   +
|               |           |   | . . . |       | . |   |
+---+---+---+---+---+---+---+   +---+ . +---+   + . +---+
|                   |       |       | . . . . . | E     |
+   +---+---+---+   +   +   +---+   +---+---+ . +---+---+
|       | . . . |   |   |               |   | . . . |   |
+---+   + . + . +   +   +---+---+---+   +   +---+ . +   +
|       | . | . |       | . . . |           | . . . |   |
+   +---+ . + . +---+---+ . + . +---+---+---+ . +---+   +
| . . . . . | . | . . . . . | . . . . . . . | . . . . . |
+ . +---+---+ . + . +---+---+---+---+---+ . +---+---+ . +
| . . . |   | . . . |   |               | .         | . |
+---+ . +   +---+---+   +   +---+   +   + . +---+---+ . +
|   | . . . . . . . |       |       |   | . | . . . . . |
+   +---+---+---+ . +   +---+   +---+   + . + . +---+---+
|   | . . . . . . . |   |       |   |   | . . . |       |
+   + . +---+---+---+---+   +---+   +   +---+---+   +   +
|     . . . . . . S         |                       |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

## Delphi

Code requires source code of Maze generation

procedure SolveMaze(var AMaze: TMaze; const S, E: TPoint);
var
Route    : TRoute;
Position : TPoint;
V        : TPoint; // delta vector
begin
ClearVisited(AMaze);
Position := S;
Route    := TStack<TPoint>.Create;
with Position do
try
AMaze[x, y].Visited := True;
repeat
if (y > 0)         and not AMaze[x, y-1].Visited and AMaze[x, y].PassTop    then V := Point(0, -1) else
if (x < mwidth-1)  and not AMaze[x+1, y].Visited and AMaze[x+1, y].PassLeft then V := Point(1,  0) else
if (y < mheight-1) and not AMaze[x, y+1].Visited and AMaze[x, y+1].PassTop  then V := Point(0,  1) else
if (x > 0)         and not AMaze[x-1, y].Visited and AMaze[x, y].PassLeft   then V := Point(-1, 0) else
begin
if Route.Count = 0 then Exit;  // we are back at start so no way found
Position := Route.Pop;         // step back
Continue;
end;

Route.Push(Position);            // save current position to route
Offset(V);                       // move forward
AMaze[x, y].Visited := True;
until Position = E;                // solved

ClearVisited(AMaze);
while Route.Count > 0 do           // Route to Maze
with Route.Pop do
AMaze[x, y].Visited := True;

finally
Route.Free;
end;
end;

procedure Main;
var
Maze: TMaze;
S, E: TPoint;
begin
Randomize;
PrepareMaze(Maze);
S := Point(Random(mwidth), Random(mheight));
E := Point(Random(mwidth), Random(mheight));
SolveMaze(Maze, S, E);
Write(MazeToString(Maze, S, E));
end;

begin
Main;
end.
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|   |               |                         S   *   *                             |           |
+   +   +   +---+   +   +---+---+---+   +   +---+---+   +---+---+---+---+---+---+   +---+   +   +
|   |   |       |   |   |           |   |   |       | * |                       |       |   |   |
+   +   +---+   +   +---+   +---+   +---+   +   +---+   +   +---+   +---+---+   +---+   +   +   +
|   |       |   |           |   |           | *   *   * |   |               |       |       |   |
+   +   +---+   +---+---+---+   +---+---+---+   +---+---+   +---+---+---+---+---+   +---+---+   +
|       |       | *   *   *   *   *         | * |   |       |       |               |   |       |
+   +---+   +---+   +---+---+---+   +---+---+   +   +   +---+   +   +   +---+---+   +   +   +---+
|   |   |       | *   *   * |   | *   *   * | *   * |       |   |       |           |   |   |   |
+   +   +---+   +---+---+   +   +---+---+   +---+   +---+   +   +---+---+---+   +---+   +   +   +
|           |       |   | * |           | *   *   * |       |       |       |           |       |
+---+---+   +---+   +   +   +   +---+   +---+---+---+   +---+---+   +   +   +---+   +---+---+   +
|       |   |       |   | * |   |               |       |           |   |       |   |           |
+   +   +   +   +---+   +   +---+   +---+---+   +   +---+   +---+   +   +---+   +---+   +---+---+
|   |       |   | E   * | *   * |   |   |       |   |       |       |   |   |           |       |
+   +---+---+   +---+   +---+   +   +   +   +---+   +---+   +---+---+   +   +---+---+---+---+   +
|   |       |       | *     | *     |       |       |       |       |           |               |
+   +---+   +---+   +   +---+   +---+---+---+   +---+   +---+   +   +---+---+   +---+   +---+---+
|           |   |   | *   * | * |               |       |       |           |       |           |
+---+---+   +   +   +   +   +   +   +---+---+---+   +---+   +---+---+   +   +---+   +---+---+   +
|           |   |   |   | *   * |       |   |               |           |       |               |
+   +---+---+   +   +---+---+---+---+   +   +   +---+---+---+   +---+---+---+   +---+---+---+   +
|       |       |       |               |   |       |       |           |       |               |
+---+   +---+   +---+   +   +---+---+---+   +---+   +---+   +---+---+   +---+---+   +---+---+---+
|   |   |           |   |           |       |   |       |       |   |   |       |   |           |
+   +   +   +---+   +   +---+---+   +   +   +   +---+   +   +   +   +   +   +   +   +   +---+   +
|           |       |               |   |                   |       |       |           |       |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

## EasyLang

size = 15
n = 2 * size + 1
f = 100 / (n - 0.5)
len m[] n * n
#
background 000
proc show_maze . .
clear
for i = 1 to len m[]
if m[i] = 0
x = (i - 1) mod n
y = (i - 1) div n
color 999
move x * f - f / 2 y * f - f / 2
rect f * 1.5 f * 1.5
.
.
sleep 0.01
.
offs[] = [ 1 n -1 (-n) ]
proc m_maze pos . .
m[pos] = 0
show_maze
d[] = [ 1 2 3 4 ]
for i = 4 downto 1
d = random i
dir = offs[d[d]]
d[d] = d[i]
if m[pos + dir] = 1 and m[pos + 2 * dir] = 1
m[pos + dir] = 0
m_maze pos + 2 * dir
.
.
.
endpos = n * n - 1
proc make_maze . .
for i = 1 to len m[]
m[i] = 1
.
for i = 1 to n
m[i] = 2
m[n * i] = 2
m[n * i - n + 1] = 2
m[n * n - n + i] = 2
.
h = 2 * random 15 - n + n * 2 * random 15
m_maze h
m[endpos] = 0
.
make_maze
show_maze
#
proc mark pos col . .
x = (pos - 1) mod n
y = (pos - 1) div n
color col
move x * f + f / 4 y * f + f / 4
circle f / 3.5
.
global found .
proc solve dir0 pos . .
if found = 1
return
.
mark pos 900
sleep 0.05
if pos = endpos
found = 1
return
.
of = random 4 - 1
for h = 1 to 4
dir = (h + of) mod1 4
posn = pos + offs[dir]
if dir <> dir0 and m[posn] = 0
solve (dir + 1) mod 4 + 1 posn
if found = 0
mark posn 888
sleep 0.08
.
.
.
.
sleep 1
solve 0 n + 2

## EGL

program MazeGenAndSolve

// 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[][];

// Solution variables
solution Dictionary;
done boolean;
startingRow, startingCol, endingRow, endingCol int;

function main()
initMaze();
generateMaze();
drawMaze(false); // Draw maze without solution

solveMaze();
drawMaze(true); // Draw maze with solution
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(solve boolean in)

line string;

// Iterate over wall arrays (skipping dead border cells as required).
// Construct a row 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 ::= cellTest(col, row, solve);
else
line ::= cellTest(col, row, solve);
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

private function cellTest(col int in, row int in, solve boolean in) returns(string)

wall string;

// Determine cell wall structure. If in solve mode, show start, end and
// solution markers.
if(!solve)
if(west[col][row])
wall = "|   ";
else
wall = "    ";
end
else
if(west[col][row])

case
when(col == startingCol and row == startingRow)
wall = "| S ";
when(col == endingCol and row == endingRow)
wall = "| E ";
when(solution.containsKey("x=" + col + "y=" + row))
wall = "| * ";
otherwise
wall = "|   ";
end

else
case
when(col == startingCol and row == startingRow)
wall = "  S ";
when(col == endingCol and row == endingRow)
wall = "  E ";
when(solution.containsKey("x=" + col + "y=" + row))
wall = "  * ";
otherwise
wall = "    ";
end
end
end

return(wall);
end

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

if(col == 1 || row == 1 || col == mazeSize || row == mazeSize)
return;
end

if(done || visited[col][row])
return;
end

visited[col][row] = true;

solution["x=" + col + "y=" + row] = true;

// Reached the end point
if(col == endingCol && row == endingRow)
done = true;
end

if(!south[col][row]) // Go South
solve(col, row + 1);
end
if(!west[col + 1][row]) // Go East
solve(col + 1, row);
end
if(!south[col][row - 1]) // Go North
solve(col, row - 1);
end
if(!west[col][row]) // Go West
solve(col - 1, row);
end

if(done)
return;
end

solution.removeElement("x=" + col + "y=" + row);

end

private function solveMaze()
for(col int from 1 to mazeSize)
for(row int from 1 to mazeSize)
visited[col][row] = false;
end
end

solution = new Dictionary(false, OrderingKind.byInsertion);
done = false;

// Pick random start position on first visible row
startingCol = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
startingRow = 2;

// Pick random end position on last visible row
endingCol = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
endingRow = mazeSize - 1;

solve(startingCol, startingRow);
end

end
Output example (for 10x10 maze):
+---+---+---+---+---+---+---+---+---+---+
|       |               |       |       |
+   +---+   +---+---+   +   +   +---+   +
|       |   |       |       |   |   |   |
+---+   +   +---+   +---+---+   +   +   +
|       |       |       |   |       |   |
+   +---+---+   +   +   +   +---+---+   +
|   |       |   |   |               |   |
+   +   +   +   +   +---+---+---+   +   +
|       |       |   |       |       |   |
+   +---+---+---+   +   +---+   +---+   +
|       |           |   |       |       |
+---+   +---+   +---+   +   +---+   +   +
|   |   |       |           |       |   |
+   +   +   +---+   +---+---+---+---+   +
|   |   |   |   |                   |   |
+   +   +   +   +---+---+---+---+   +   +
|   |   |   |           |       |   |   |
+   +   +   +   +---+---+   +   +   +   +
|           |               |           |
+---+---+---+---+---+---+---+---+---+---+

+---+---+---+---+---+---+---+---+---+---+
|       | *   *   S     |       |       |
+   +---+   +---+---+   +   +   +---+   +
|       | * |       |       |   |   |   |
+---+   +   +---+   +---+---+   +   +   +
|       | *   * | *   * |   |       |   |
+   +---+---+   +   +   +   +---+---+   +
|   | *   * | * | * | *   *   *   * |   |
+   +   +   +   +   +---+---+---+   +   +
| *   * | *   * | * |       | *   * |   |
+   +---+---+---+   +   +---+   +---+   +
| *   * |     *   * |   | *   * |       |
+---+   +---+   +---+   +   +---+   +   +
|   | * | *   * | *   *   * |       |   |
+   +   +   +---+   +---+---+---+---+   +
|   | * | * |   | *   *   *   *   * |   |
+   +   +   +   +---+---+---+---+   +   +
|   | * | * |           | *   * | * |   |
+   +   +   +   +---+---+   +   +   +   +
|     *   * |             E | *   *     |
+---+---+---+---+---+---+---+---+---+---+

## Emacs Lisp

Library: cl-lib
(require 'cl-lib)

(cl-defstruct maze rows cols data)

(defmacro maze-pt (w r c)
`(+ (* (mod ,r (maze-rows ,w)) (maze-cols ,w))
(mod ,c (maze-cols ,w))))

(defmacro maze-ref (w r c)
`(aref (maze-data ,w) (maze-pt ,w ,r ,c)))

(defun new-maze (rows cols)
(setq rows (1+ rows)
cols (1+ cols))
(let ((m (make-maze :rows rows :cols cols :data (make-vector (* rows cols) nil))))

(dotimes (r rows)
(dotimes (c cols)
(setf (maze-ref m r c) (copy-sequence '(wall ceiling)))))

(dotimes (r rows)
(maze-set m r (1- cols) 'visited))

(dotimes (c cols)
(maze-set m (1- rows) c 'visited))

(maze-unset m 0 0 'ceiling) ;; Maze Entrance
(maze-unset m (1- rows) (- cols 2) 'ceiling) ;; Maze Exit

m))

(defun maze-is-set (maze r c v)
(member v (maze-ref maze r c)))

(defun maze-set (maze r c v)
(let ((cell (maze-ref maze r c)))
(when (not (member v cell))
(setf (maze-ref maze r c) (cons v cell)))))

(defun maze-unset (maze r c v)
(setf (maze-ref maze r c) (delete v (maze-ref maze r c))))

(defun print-maze (maze &optional marks)
(dotimes (r (1- (maze-rows maze)))

(dotimes (c (1- (maze-cols maze)))
(princ (if (maze-is-set maze r c 'ceiling) "+---" "+   ")))
(princ "+")
(terpri)

(dotimes (c (1- (maze-cols maze)))
(princ (if (maze-is-set maze r c 'wall) "|" " "))
(princ (if (member (cons r c) marks) " * " "   ")))
(princ "|")
(terpri))

(dotimes (c (1- (maze-cols maze)))
(princ (if (maze-is-set maze (1- (maze-rows maze)) c 'ceiling) "+---" "+   ")))
(princ "+")
(terpri))

(defun shuffle (lst)
(sort lst (lambda (a b) (= 1 (random 2)))))

(defun to-visit (maze row col)
(let (unvisited)
(dolist (p '((0 . +1) (0 . -1) (+1 . 0) (-1 . 0)))
(let ((r (+ row (car p)))
(c (+ col (cdr p))))
(unless (maze-is-set maze r c 'visited)
(push (cons r c) unvisited))))
unvisited))

(defun make-passage (maze r1 c1 r2 c2)
(if (= r1 r2)
(if (< c1 c2)
(maze-unset maze r2 c2 'wall) ; right
(maze-unset maze r1 c1 'wall))  ; left
(if (< r1 r2)
(maze-unset maze r2 c2 'ceiling)   ; up
(maze-unset maze r1 c1 'ceiling))))  ; down

(defun dig-maze (maze row col)
(let (backup
(run 0))
(maze-set maze row col 'visited)
(push (cons row col) backup)
(while backup
(setq run (1+ run))
(when (> run (/ (+ row col) 3))
(setq run 0)
(setq backup (shuffle backup)))
(setq row (caar backup)
col (cdar backup))
(let ((p (shuffle (to-visit maze row col))))
(if p
(let ((r (caar p))
(c (cdar p)))
(make-passage maze row col r c)
(maze-set maze r c 'visited)
(push (cons r c) backup))
(pop backup)
(setq backup (shuffle backup))
(setq run 0))))))

(defun generate (rows cols)
(let* ((m (new-maze rows cols)))
(dig-maze m (random rows) (random cols))
(print-maze m)))

(defun parse-ceilings (line)
(let (rtn
(i 1))
(while (< i (length line))
(push (eq ?- (elt line i)) rtn)
(setq i (+ i 4)))
(nreverse rtn)))

(defun parse-walls (line)
(let (rtn
(i 0))
(while (< i (length line))
(push (eq ?| (elt line i)) rtn)
(setq i (+ i 4)))
(nreverse rtn)))

(defun parse-maze (file-name)
(let ((rtn)
(lines (with-temp-buffer
(insert-file-contents-literally file-name)
(split-string (buffer-string) "\n" t))))
(while lines
(push (parse-ceilings (pop lines)) rtn)
(push (parse-walls (pop lines)) rtn))
(nreverse rtn)))

(let* ((raw (parse-maze file-name))
(rows (1- (/ (length raw) 2)))
(cols (length (car raw)))
(maze (new-maze rows cols)))
(dotimes (r rows)
(let ((ceilings (pop raw)))
(dotimes (c cols)
(unless (pop ceilings)
(maze-unset maze r c 'ceiling))))
(let ((walls (pop raw)))
(dotimes (c cols)
(unless (pop walls)
(maze-unset maze r c 'wall)))))
maze))

(defun find-exits (maze row col)
(let (exits)
(dolist (p '((0 . +1) (0 . -1) (-1 . 0) (+1 . 0)))
(let ((r (+ row (car p)))
(c (+ col (cdr p))))
(unless
(cond
((equal p '(0 . +1)) (maze-is-set maze r   c   'wall))
((equal p '(0 . -1)) (maze-is-set maze row col 'wall))
((equal p '(+1 . 0)) (maze-is-set maze r   c   'ceiling))
((equal p '(-1 . 0)) (maze-is-set maze row col 'ceiling)))
(push (cons r c) exits))))
exits))

(defun drop-visited (maze points)
(let (not-visited)
(while points
(unless (maze-is-set maze (caar points) (cdar points) 'visited)
(push (car points) not-visited))
(pop points))
not-visited))

(defun solve-maze (maze)
(let (solution
(exit (cons (- (maze-rows maze) 2) (- (maze-cols maze) 2)))
(pt (cons 0 0)))
(while (not (equal pt exit))
(maze-set maze (car pt) (cdr pt) 'visited)
(let ((exits (drop-visited maze (find-exits maze (car pt) (cdr pt)))))
(if (null exits)
(setq pt (pop solution))
(push pt solution)
(setq pt (pop exits)))))
(push pt solution)))

(defun solve (file-name)
(let* ((maze (read-maze file-name))
(solution (solve-maze maze)))
(print-maze maze solution)))

(solve "maze.txt")
Output:
+   +---+---+---+---+---+---+---+---+---+
| *   *   * |   |                   |   |
+---+---+   +   +---+---+   +---+---+   +
|   |     * |   |       |   |       |   |
+   +   +   +   +---+   +   +   +---+   +
|       | *   *   *   * |           |   |
+---+---+---+---+---+   +---+---+   +   +
|   |       |   |   | *   * |   |   |   |
+   +---+   +   +   +---+   +   +   +   +
|   |   |   |   |         *   * |       |
+   +   +   +   +---+   +   +   +---+   +
|   |   |   |           |   | *   *   * |
+   +   +   +---+---+---+   +---+---+   +
|   |   |               |   |   |     * |
+   +   +---+---+   +   +   +   +   +   +
|       |   |       |       |       | * |
+   +   +   +---+---+---+---+---+   +   +
|   |       |       |               | * |
+   +---+---+   +   +   +---+---+---+   +
|               |       |             * |
+---+---+---+---+---+---+---+---+---+   +

## Erlang

Using the maze from Maze_generation. When the path splits each possibility gets its own process that checks if it is the correct one or a dead end. It is intentional that the receive statement in loop_stop/5 only selects successful result.

-module( maze_solving ).

cells( {Start_x, Start_y}, {Stop_x, Stop_y}, Maze ) ->
Start_pid = maze:cell_pid( Start_x, Start_y, Maze ),
Stop_pid =  maze:cell_pid( Stop_x,  Stop_y, Maze ),
{ok, Cells} = loop( Start_pid, Stop_pid, maze:cell_accessible_neighbours(Start_pid), [Start_pid] ),
Cells.

Max_x = 16,
Max_y = 8,
Maze = maze:generation( Max_x, Max_y ),
Start_x = random:uniform( Max_x ),
Start_y = random:uniform( Max_y ),
Stop_x = random:uniform( Max_x ),
Stop_y = random:uniform( Max_y ),
Cells = cells( {Start_x, Start_y}, {Stop_x, Stop_y}, Maze ),
[maze:cell_content_set(X, ".") || X <- Cells],
maze:cell_content_set( maze:cell_pid(Start_x, Start_y, Maze), "S" ),
maze:cell_content_set( maze:cell_pid(Stop_x, Stop_y, Maze), "G" ),
maze:display( Maze ),
maze:stop( Maze ).

loop( _Start, _Stop, [], _Acc) -> {error, dead_end};
loop( _Start, Stop, [Stop], Acc ) -> {ok, lists:reverse( [Stop | Acc] )};
loop( Start, Stop, [Next], [Previous | _T]=Acc ) -> loop( Start, Stop, lists:delete(Previous, maze:cell_accessible_neighbours(Next)), [Next | Acc] );
loop( Start, Stop, Nexts, Acc ) -> loop_stop( lists:member(Stop, Nexts), Start, Stop, Nexts, Acc ).

loop_stop( true, _Start, Stop, _Nexts, Acc ) -> {ok, lists:reverse( [Stop | Acc] )};
loop_stop( false, Start, Stop, Nexts, Acc ) ->
My_pid = erlang:self(),
[erlang:spawn( fun() -> My_pid ! loop( Start, Stop, [X], Acc ) end ) || X <- Nexts],
{ok, Cells} -> {ok, Cells}
end.
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|     .   .   .   . | .   .   .   . | .   .   .   . |           |
+---+   +---+---+   +   +---+---+   +   +---+---+   +   +---+   +
| .   . |       | .   . |       | .   . |       | .   . |       |
+   +---+   +   +---+---+   +---+---+---+   +   +---+   +---+   +
| . |       |           |                   |       | . |   |   |
+   +---+   +---+---+   +   +   +---+---+   +---+---+   +   +---+
| .   . |   |       |   |   |   |           | .   . | . |       |
+   +   +   +   +   +---+   +   +---+---+---+   +   +   +---+   +
|   | . |       |           |             S   . | .   .     |   |
+---+   +---+---+   +---+---+---+   +---+---+---+   +---+---+   +
| .   . | .   . |       | .   . |   |           |   |           |
+   +   +   +   +---+   +   +   +   +   +---+   +   +   +---+---+
| . |   | . | . |       | . | . |   | G   . |   |   |           |
+   +---+   +   +---+---+   +   +---+---+   +   +---+---+---+   +
| .   .   . | .   .   .   . | .   .   .   . |                   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

## FreeBASIC

Const MazeWidth = 11
Const MazeHeight = 9
Const MazeCell = 50

Dim Shared dstx As Integer = MazeWidth - 1
Dim Shared dsty As Integer = 0

Screenres MazeWidth * MazeCell, MazeHeight * MazeCell, 32
Windowtitle "Maze solving"

Sub Cell(Maze() As Integer, Byval x As Integer, Byval y As Integer, Byval w As Integer, Byval h As Integer, Byval s As Integer)
Dim As Integer i, p, q, r
Maze(x, y) Or= &H40
r = Rnd * 4
For i = r To r + 3
Select Case i Mod 4
Case 0: p = x - 1 : q = y
Case 1: p = x + 1 : q = y
Case 2: p = x : q = y - 1
Case 3: p = x : q = y + 1
End Select
If p >= 0 And p < w And q >= 0 And q < h And Maze(p, q) < &H40 Then
If p > x Then Maze(p, q) Or= 1 : Line (p * s, y * s + 4) - (p * s, (y + 1) * s - 4), Rgb(0, 0, 0)
If q > y Then Maze(p, q) Or= 2 : Line (x * s + 4, q * s) - ((x + 1) * s - 4, q * s), Rgb(0, 0, 0)
If x > p Then Maze(x, y) Or= 1 : Line (x * s, y * s + 4) - (x * s, (y + 1) * s - 4), Rgb(0, 0, 0)
If y > q Then Maze(x, y) Or= 2 : Line (x * s + 4, y * s) - ((x + 1) * s - 4, y * s), Rgb(0, 0, 0)
Cell Maze(), p, q, w, h, s
End If
Next
End Sub

Sub GenerateMaze(Maze() As Integer, Byval w As Integer, Byval h As Integer, Byval s As Integer)
Dim As Integer x, y
Redim Maze(w, h)
For y = 0 To h - 1
Line (0, y * s) - (w * s, y * s), Rgb(255, 255, 255)
Next
For x = 0 To w - 1
Line (x * s, 0) - (x * s, h * s), Rgb(255, 255, 255)
Next
Cell Maze(), Rnd * w, Rnd * h, w, h, s
End Sub

Sub SolveMaze(Path() As Integer, Maze() As Integer, Byval x As Integer, Byval y As Integer, Byval dstx As Integer, Byval dsty As Integer, Byval s As Integer)
Dim As Integer h, i, n, p, q, w
w = Ubound(Maze, 1)
h = Ubound(Maze, 2)
Redim Path(w * h, 1)
Maze(x, y) Or= &H80
Do
For i = 0 To 3
Select Case i
Case 0: p = x - 1 : q = y
Case 1: p = x + 1 : q = y
Case 2: p = x : q = y - 1
Case 3: p = x : q = y + 1
End Select
If p >= 0 And p < w And q >= 0 And q < h And Maze(p, q) < &H80 Then
If p > x And Maze(p, q) And 1 Then Exit For
If q > y And Maze(p, q) And 2 Then Exit For
If x > p And Maze(x, y) And 1 Then Exit For
If y > q And Maze(x, y) And 2 Then Exit For
End If
Next
If i < 4 Then
Maze(p, q) Or= &H80
Path(n, 0) = x
Path(n, 1) = y
Line ((x + 0.5) * s, (y + 0.5) * s) - ((p + 0.5) * s, (q + 0.5) * s), Rgb(255, 0, 0), , &b0001111111111100
n += 1
Else
If n > 0 Then
n -= 1
p = Path(n, 0)
q = Path(n, 1)
Line ((x + 0.5) * s, (y + 0.5) * s) - ((p + 0.5) * s, (q + 0.5) * s), Rgb(0, 0, 0)
End If
End If
x = p
y = q
Sleep 200
Loop Until x = dstx And y = dsty Or Inkey <> ""
Path(n, 0) = x
Path(n, 1) = y
End Sub

Dim Maze() As Integer
Dim Path() As Integer

Randomize Timer
GenerateMaze(Maze(), MazeWidth, MazeHeight, MazeCell)
SolveMaze(Path(), Maze(), 0, MazeHeight - 1, MazeWidth - 1, 0, MazeCell)
Windowtitle "Maze solving  ** RESOLVED **"

Sleep

## Frege

Works with: Frege version 3.20.113

On standard input, takes a maze made up of "+", "|", and "---" (i. e. each cell is two lines high and four characters wide), such as produced by the Haskell or Java generators.

module MazeSolver where

import frege.IO
import Data.Maybe

-- given two points, returns the average of them
average :: (Int, Int) -> (Int, Int) -> (Int, Int)
average (x, y) (x', y') = ((x + x') `div` 2, (y + y') `div` 2)

-- given a maze and a tuple of position and wall position, returns
-- true if the wall position is not blocked (first position is unused)
notBlocked :: [String] -> ((Int, Int), (Int, Int)) -> Bool
notBlocked maze (_, (x, y)) = (' ' == String.charAt (maze !! y) x)

-- given a list, a position, and an element, returns a new list
-- with the new element substituted at the position
substitute :: [a] -> Int -> a -> [a]
substitute orig pos el =
let (before, after) = splitAt pos orig
in before ++ [el] ++ tail after

-- like above, but for strings, since Frege strings are not
-- lists of characters
substituteString :: String -> Int -> String -> String
substituteString orig pos el =
let before = substr orig 0 pos
after = strtail orig (pos + 1)
in before ++ el ++ after

-- given a maze and a position, draw a '*' at that position in the maze
draw :: [String] -> (Int, Int) -> [String]
draw maze (x,y) = substitute maze y \$ substituteString row x "*"
where row = maze !! y

-- given a maze, a previous position, and a list of tuples of potential
-- new positions and their wall positions, returns the solved maze, or
-- None if it cannot be solved
tryMoves :: [String] -> (Int, Int) -> [((Int, Int), (Int, Int))] -> Maybe [String]
tryMoves _ _ [] = Nothing
tryMoves maze prevPos ((newPos,wallPos):more) =
case solve' maze newPos prevPos
of Nothing -> tryMoves maze prevPos more
Just maze' -> Just \$ foldl draw maze' [newPos, wallPos]

-- given a maze, a new position, and a previous position, returns
-- the solved maze, or None if it cannot be solved
-- (assumes goal is upper-left corner of maze)
solve' :: [String] -> (Int, Int) -> (Int, Int) -> Maybe [String]
solve' maze (2, 1) _ = Just maze
solve' maze (x, y) prevPos =
let newPositions = [(x, y - 2), (x + 4, y), (x, y + 2), (x - 4, y)]
notPrev pos' = pos' /= prevPos
newPositions' = filter notPrev newPositions
wallPositions = map (average (x,y)) newPositions'
zipped = zip newPositions' wallPositions
legalMoves = filter (notBlocked maze) zipped
in tryMoves maze (x,y) legalMoves

-- given a maze, returns a solved maze, or None if it cannot be solved
-- (starts at lower right corner and goes to upper left corner)
solve :: [String] -> Maybe [String]
solve maze = solve' (draw maze start) start (-1, -1)
where startx = (length \$ head maze) - 3
starty = (length maze) - 2
start = (startx, starty)

-- takes unsolved maze on standard input, prints solved maze on standard output
main _ = do
isin  <- stdin
isrin <- InputStreamReader.new isin
brin  <- BufferedReader.fromISR isrin
lns <- BufferedReader.getlines brin
printStr \$ unlines \$ fromMaybe ["can't solve"] \$ solve lns
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| * |         * * * * * |       |       |                   |       |       |
+ * +---+---+ * +---+ * +---+   +   +   +   +---+---+---+   +   +   +   +   +
| * | * * * * * |   | * |       |   |       | * * * * * |       |       |   |
+ * + * +---+---+   + * +   +---+   +---+---+ * +---+ * +   +---+---+---+   +
| * * * |       |   | * |   |       | * * * * * | * * * |   | * * * * * |   |
+---+---+   +   +   + * +   +   +---+ * +---+---+ * +---+---+ * +---+ * +   +
|           |       | * |       |   | * |   | * * * | * * * * * | * * * |   |
+   +   +---+---+---+ * +   +---+   + * +   + * +---+ * +---+---+ * +---+   +
|   |   | * * * * * * * |           | * |     * * * * * |       | * * * * * |
+   +   + * +---+---+---+---+---+---+ * +---+---+---+---+   +   +---+---+ * +
|   |   | * * * | * * * * * | * * * | * * * | * * * |       |           | * |
+   +---+---+ * + * +---+ * + * + * +---+ * + * + * +---+   +---+   +   + * +
|   |       | * | * | * * * | * | * * * | * * * | * * * |   |   |   |   | * |
+   +   +   + * + * + * +---+ * +---+ * +---+---+---+ * +   +   +   +---+ * +
|       |     * * * | * * * * * |     * * * * * * * * * |       |         * |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
runtime 0.249 wallclock seconds.

## Go

Generates maze, picks start and finish cells randomly, solves, prints.

package main

import (
"bytes"
"fmt"
"math/rand"
"time"
)

type maze struct {
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{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 r, hw := range m.h2 {
for _, h := range hw {
if h == '-' || r == 0 {
b = append(b, hWall...)
} else {
b = append(b, hOpen...)
if h != '-' && h != 0 {
b[len(b)-2] = h
}
}
}
b = append(b, rightCorner...)
for c, vw := range m.v2[r] {
if vw == '|' || c == 0 {
b = append(b, vWall...)
} else {
b = append(b, vOpen...)
if vw != '|' && vw != 0 {
b[len(b)-4] = vw
}
}
if m.c2[r][c] != 0 {
b[len(b)-2] = m.c2[r][c]
}
}
b = append(b, rightWall...)
}
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())
const height = 4
const width = 7
m := newMaze(height, width)
m.gen()
m.solve(
rand.Intn(height), rand.Intn(width),
rand.Intn(height), rand.Intn(width))
fmt.Print(m)
}

func (m *maze) solve(ra, ca, rz, cz int) {
var rSolve func(ra, ca, dir int) bool
rSolve = func(r, c, dir int) bool {
if r == rz && c == cz {
m.c2[r][c] = 'F'
return true
}
if dir != dn && m.h2[r][c] == 0 {
if rSolve(r-1, c, up) {
m.c2[r][c] = '^'
m.h2[r][c] = '^'
return true
}
}
if dir != up && r+1 < len(m.h2) && m.h2[r+1][c] == 0 {
if rSolve(r+1, c, dn) {
m.c2[r][c] = 'v'
m.h2[r+1][c] = 'v'
return true
}
}
if dir != lf && c+1 < len(m.v2[0]) && m.v2[r][c+1] == 0 {
if rSolve(r, c+1, rt) {
m.c2[r][c] = '>'
m.v2[r][c+1] = '>'
return true
}
}
if dir != rt && m.v2[r][c] == 0 {
if rSolve(r, c-1, lf) {
m.c2[r][c] = '<'
m.v2[r][c] = '<'
return true
}
}
return false
}
rSolve(ra, ca, -1)
m.c2[ra][ca] = 'S'
}
Example output
:
+---+---+---+---+---+---+---+
|           | v < < < < < < |
+   +---+   + v +   +---+ ^ +
|       | F < < |   |     ^ |
+---+---+---+---+   +---+ ^ +
|               |       | ^ |
+   +---+---+   +---+   + ^ +
|   |                   | S |
+---+---+---+---+---+---+---+

Works with: GHC version 7.4.1

On standard input, takes a maze made up of "+", "|", and "---" (i. e. each cell is two lines high and four characters wide), such as produced by the Haskell or Java generators.

import Data.Maybe (fromMaybe)

-- given two points, returns the average of them
average :: (Int, Int) -> (Int, Int) -> (Int, Int)
average (x, y) (x_, y_) = ((x + x_) `div` 2, (y + y_) `div` 2)

-- given a maze and a tuple of position and wall position, returns
-- true if the wall position is not blocked (first position is unused)
notBlocked :: [String] -> ((Int, Int), (Int, Int)) -> Bool
notBlocked maze (_, (x, y)) = ' ' == (maze !! y) !! x

-- given a list, a position, and an element, returns a new list
-- with the new element substituted at the position
-- (it seems such a function should exist in the standard library;
-- I must be missing it)
substitute :: [a] -> Int -> a -> [a]
substitute orig pos el =
let (before, after) = splitAt pos orig
in before ++ [el] ++ tail after

-- given a maze and a position, draw a '*' at that position in the maze
draw :: [String] -> (Int, Int) -> [String]
draw maze (x, y) =
let row = maze !! y
in substitute maze y \$ substitute row x '*'

-- given a maze, a previous position, and a list of tuples of potential
-- new positions and their wall positions, returns the solved maze, or
-- None if it cannot be solved
tryMoves :: [String]
-> (Int, Int)
-> [((Int, Int), (Int, Int))]
-> Maybe [String]
tryMoves _ _ [] = Nothing
tryMoves maze prevPos ((newPos, wallPos):more) =
case solve_ maze newPos prevPos of
Nothing -> tryMoves maze prevPos more
Just maze_ -> Just \$ foldl draw maze_ [newPos, wallPos]

-- given a maze, a new position, and a previous position, returns
-- the solved maze, or None if it cannot be solved
-- (assumes goal is upper-left corner of maze)
solve_ :: [String] -> (Int, Int) -> (Int, Int) -> Maybe [String]
solve_ maze (2, 1) _ = Just maze
solve_ maze pos@(x, y) prevPos =
let newPositions = [(x, y - 2), (x + 4, y), (x, y + 2), (x - 4, y)]
notPrev pos_ = pos_ /= prevPos
newPositions_ = filter notPrev newPositions
wallPositions = map (average pos) newPositions_
zipped = zip newPositions_ wallPositions
legalMoves = filter (notBlocked maze) zipped
in tryMoves maze pos legalMoves

-- given a maze, returns a solved maze, or None if it cannot be solved
-- (starts at lower right corner and goes to upper left corner)
solve :: [String] -> Maybe [String]
solve maze = solve_ (draw maze start) start (-1, -1)
where
startx = length (head maze) - 3
starty = length maze - 2
start = (startx, starty)

-- takes unsolved maze on standard input, prints solved maze on standard output
main =
let main_ = unlines . fromMaybe ["can_t solve"] . solve . lines
in interact main_
Output:
+---+---+---+---+---+---+---+---+---+---+---+
| * |           |               |           |
+ * +   +---+   +   +---+   +---+   +---+   +
| * |       |   |       |   |           |   |
+ * +---+   +   +---+   +---+   +---+---+   +
| *         |       |       |   |   |       |
+ * +---+---+---+   +---+   +   +   +   +   +
| * * * * * * * |       |           |   |   |
+---+---+---+ * +---+   +---+---+---+   +   +
|           | * * * |   |           |   |   |
+   +---+   +---+ * +   +   +---+   +   +---+
|       |   | * * * |       |   |   |       |
+---+---+   + * +---+---+---+   +   +---+   +
|           | * * * * * |       |       |   |
+   +---+---+---+---+ * +---+   +---+---+   +
|                     * * * * * * * * * * * |
+---+---+---+---+---+---+---+---+---+---+---+

## Icon and Unicon

The following code works with the solution from Maze Generation.

Replace the main with this:

procedure main(A)
/mh := \A[1] | 12
/mw := \A[2] | 16
mz := DisplayMaze(GenerateMaze(mh,mw))
WriteImage(mz.filename)              # save file
WAttrib(mz.window,"canvas=normal")   # show it
until Event() == &lpress # wait for left mouse press
Solver(mz.maze)
DisplayMazeSolution(mz)
WriteImage(mz.filename ?:= (="maze-", "maze-solved-" || tab(0)))
until Event() == &lpress # wait
close(mz.window)
end

And include this after the Generator and Display procedures.

procedure Solver(r,c)
static maze,h,w,rd

if type(r) == "list" then { # ------------------- Top Level (r == maze)
h := *(maze := r)                              # height
w := *maze[1]                                  # width
every r := 1 to h & c := 1 to w do             # remove breadcrumbs
maze[r,c] := iand(maze[r,c],NORTH+EAST+SOUTH+WEST+START+FINISH)
every ((r := 1 | h) & (c := 1 to w)) |         # search perimiter
((r := 1 to h) & (c := 1 | w)) do
if iand(maze[r,c],START) > 0 then break  # until start found
Solver(r,c)                                    # recurse through maze
return 1(.maze,maze := &null)                  # return maze and reset
}
else                        # ------------------- Recurse way through maze
if iand(x := maze[r,c],SEEN) = 0  then {       # in bounds and not seen?
(iand(x,FINISH) > 0, maze[r,c] +:= PATH, return ) # at finish? - done!
maze[r,c] +:= SEEN                          # drop bread crumb
(iand(x,NORTH) > 0, Solver(r-1,c), maze[r,c] +:= PATH, return)
(iand(x,EAST)  > 0, Solver(r,c+1), maze[r,c] +:= PATH, return)
(iand(x,SOUTH) > 0, Solver(r+1,c), maze[r,c] +:= PATH, return)
(iand(x,WEST)  > 0, Solver(r,c-1), maze[r,c] +:= PATH, return)
}
end

procedure DisplayMazeSolution(mz)                  #: draw marked PATH
&window := mz.window
maze := mz.maze
WAttrib("dx="||(dxy:=BORDER+CELL/2),"dy="||dxy)
every (r := 1 to *maze) & (c := 1 to *maze[1]) do {
if fg ~=== "blue" then Fg(fg := "blue")
if iand(maze[r,c],START) > 0 then Fg(fg := "red")
if iand(maze[r,c],PATH) > 0 then
FillCircle(x := CELL*(c-1),y := CELL*(r-1),rad := CELL/5)
}
return mz
end

The following Unicon-only solution is a variant of the above. It shares the same maze generation code and maze display code with the above but spawns threads to parallelize the searching. The algorithm runs each path to a dead end, a target, or a length greater than the current shortest path to a target and works if there are multiple target cells, multiple paths to those targets, or cyclic paths. The shortest solution path is then marked and displayed.

global showMice

import Utils	# To get 'Args' singleton class

procedure main(A)
Args(A)
if \Args().get("help","yes") then helpMesg()
showMice := Args().get("showmice","yes") # Show movements of all mice
mh := Args().get("rows") | 32            # Maze height (rows)
mw := Args().get("cols") | 48            # Maze width (columns)

mz := DisplayMaze(GenerateMaze(mh,mw))   # Build and show maze

QMouse(mz.maze,findStart(mz.maze),&null,0)   # Start first quantum mouse
waitForCompletion() # block until all quantum mice have finished

# Mark the best path into the maze and display it.
if showPath(mz.maze) then DisplayMazeSolution(mz) else write("No path found!")
end

procedure helpMesg()
write(&errout,"Usage: qSolve [--showmice] [--cols=C] [--rows=R]")
write(&errout,"\twhere:")
write(&errout,"\t\t--showmice # displays all mice paths as they search")
write(&errout,"\t\t--cols=C   # sets maze width to C (default 16) columns")
write(&errout,"\t\t--rows=R   # sets maze height to R (default 12) rows")
stop()
end

# A "Quantum-mouse" for traversing mazes. Each mouse lives for just one cell, but
#   can spawn other mice to search from adjoining cells.

global qMice, bestMouse, bestMouseLock, region, qMiceEmpty
record Position(r,c)

# Must match values used in maze generation!
\$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

class QMouse(maze, loc, parent, len, val)

method getLoc(); return loc; end
method getParent(); return \parent; end
method getLen(); return len; end
method atEnd();   return EMPTY ~= iand(val, FINISH); end
method goNorth(); if EMPTY ~= iand(val,NORTH) then return visit(loc.r-1, loc.c); end
method goSouth(); if EMPTY ~= iand(val,SOUTH) then return visit(loc.r+1, loc.c); end
method goEast();  if EMPTY ~= iand(val,EAST)  then return visit(loc.r, loc.c+1); end
method goWest();  if EMPTY ~= iand(val,WEST)  then return visit(loc.r, loc.c-1); end

method visit(r,c)
critical region[r,c]: if EMPTY = iand(maze[r,c],SEEN) then {
if /bestMouse | (len <= bestMouse.getLen()) then { # Keep going?
mark(maze, r,c)
unlock(region[r,c])
return Position(r,c)
}
}
end

initially (m, l, p, n)
initial {   # Construct critical region mutexes and completion condvar
qMice := mutex(set())
qMiceEmpty := condvar()
bestMouseLock := mutex()
region := list(*m)            # Minimize critical region size
every r := 1 to *m do region[r] := list(*m[1])
every !!region := mutex()
}
maze := m
loc := l
parent := p
len := n+1
val := maze[loc.r,loc.c] | fail   # Fail if outside maze
insert(qMice, self)
if atEnd() then {
critical bestMouseLock:
if /bestMouse | (len < bestMouse.getLen()) then bestMouse := self
}
else {         # Spawn more mice to look for finish
QMouse(maze, goNorth(), self, len)
QMouse(maze, goSouth(), self, len)
QMouse(maze, goEast(), self, len)
QMouse(maze, goWest(), self, len)
}

delete(qMice, self)
if *qMice=0 then signal(qMiceEmpty)
}
end

procedure mark(maze, r,c)
ior(maze[r,c],SEEN)
if \showMice then markCell(r,c,"grey",5)
return Position(r,c)
end

procedure clearMaze(maze)  # Clear out dregs from maze creation
every r := 1 to *maze & c := 1 to *maze[1] do  # remove breadcrumbs
maze[r,c] := iand(maze[r,c],NORTH+EAST+SOUTH+WEST+START+FINISH)
end

procedure findStart(maze)  # Anywhere in maze
clearMaze(maze)                                # Remove breadcrumbs
every r := 1 to *maze & c := 1 to *maze[1] do  # Locate START cell
if EMPTY ~= iand(maze[r,c],START) then return mark(maze, r,c)
end

procedure showPath(maze)
if path := \bestMouse then {   # Mark it in maze
repeat {
loc := path.getLoc()
maze[loc.r,loc.c] +:= PATH
path := \path.getParent() | break
}
return
}
end

procedure waitForCompletion()
critical qMiceEmpty: while *qMice > 0 do wait(qMiceEmpty)
end

## J

Due to reports that the program failed, the generation and solver are shown together. The display verb was extended to include a dyadic definition. The complete program was tested with j 8.0.2 on linux using no profile, the command \$ ijconsole -jprofile

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
)

NB. source Dijkstra_equal_weights graph
NB.
NB.        +   +---+---+
NB.        | 0   1   2 |  (sample cell numbers)
NB.        +---+   +   +
NB.        | 3   4 | 5
NB.        +---+---+---+
NB.
NB. graph =: 1;0 2 4;1 5;4;1 3;2
NB. The graph is a vector of boxed vectors of neighbors.

Dijkstra_equal_weights =: 4 : 0
dist =. previous =. #&_ n =. # graph =. y [ source =. x
dist =. 0 source } dist
Q =. 0
while. #Q do.
u =. {.Q
Q =. }.Q
if. _ = u{dist do. break. end.
for_v. >u{graph do.
if. -. v e. previous do.
alt =. >: u { dist
if. alt < v { dist do.
dist =. alt v } dist
previous =. u v } previous
if. v e. Q do.
echo 'belch'
else.
Q =. Q,v
end.
end.
end.
end.
end.
dist;previous
)

path =: 3 : 0
p =. <:#y
while. _ > {:p do.
p =. p,y{~{:p
end.
|.}:p
)

solve=:3 :0
NB. convert walls to graph
shape =. }.@\$@:>
ew =. (,.&0 ,: 0&,.)@>@{.  NB. east west doors
ns =. (, &0 ,: 0&, )@>@{:
cell_offsets =. 1 _1 1 _1 * 2 # 1 , {:@shape
cell_numbers =. i.@shape
neighbors =. (cell_numbers +"_ _1 cell_offsets *"_1 (ew , ns))y
graph =. (|:@(,/"_1) <@-."1 0 ,@i.@shape)neighbors NB. list of boxed neighbors
NB. solve it
path , > {: 0 Dijkstra_equal_weights graph
)

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
:
a=. display y
size=. >.&\$&>/y
columns=. {: size
cells =. <"1(1 2&p.@<.@(%&columns) ,.  2 4&p.@(columns&|))x
'o' cells } a  NB. exercise, replace cells with a gerund to draw arrows on the path.
)

Example:

4 (display~ solve)@maze 20
+   +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| o   o   o | o   o   o   o     | o   o   o   o   o   o   o   o |               |
+---+---+   +   +---+---+   +---+   +---+---+   +---+---+---+   +   +   +---+   +
| o   o | o | o |       | o   o   o     |       |           | o |   |       |   |
+   +   +   +   +   +   +---+---+---+   +   +---+---+   +   +   +---+   +---+   +
| o | o   o | o |   |   |           |   |           |   |   | o   o |   | o   o |
+   +---+---+   +   +   +   +---+   +---+---+---+   +   +---+---+   +---+   +   +
| o   o   o   o     |   |   |                       |             o   o   o | o
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

## Java

import java.io.*;
import java.util.*;

public class MazeSolver
{
/**
* Reads a file into an array of strings, one per line.
*/
private static String[] readLines (InputStream f) throws IOException
{
ArrayList<String> lines = new ArrayList<String>();
String line;
while ((line = r.readLine()) != null)
return lines.toArray(new String[0]);
}

/**
* Makes the maze half as wide (i. e. "+---+" becomes "+-+"), so that
* each cell in the maze is the same size horizontally as vertically.
* (Versus the expanded version, which looks better visually.)
* Also, converts each line of the maze from a String to a
* char[], because we'll want mutability when drawing the solution later.
*/
private static char[][] decimateHorizontally (String[] lines)
{
final int width = (lines[0].length() + 1) / 2;
char[][] c = new char[lines.length][width];
for (int i = 0  ;  i < lines.length  ;  i++)
for (int j = 0  ;  j < width  ;  j++)
c[i][j] = lines[i].charAt (j * 2);
return c;
}

/**
* Given the maze, the x and y coordinates (which must be odd),
* and the direction we came from, return true if the maze is
* solvable, and draw the solution if so.
*/
private static boolean solveMazeRecursively (char[][] maze,
int x, int y, int d)
{
boolean ok = false;
for (int i = 0  ;  i < 4  &&  !ok  ;  i++)
if (i != d)
switch (i)
{
// 0 = up, 1 = right, 2 = down, 3 = left
case 0:
if (maze[y-1][x] == ' ')
ok = solveMazeRecursively (maze, x, y - 2, 2);
break;
case 1:
if (maze[y][x+1] == ' ')
ok = solveMazeRecursively (maze, x + 2, y, 3);
break;
case 2:
if (maze[y+1][x] == ' ')
ok = solveMazeRecursively (maze, x, y + 2, 0);
break;
case 3:
if (maze[y][x-1] == ' ')
ok = solveMazeRecursively (maze, x - 2, y, 1);
break;
}
// check for end condition
if (x == 1  &&  y == 1)
ok = true;
// once we have found a solution, draw it as we unwind the recursion
if (ok)
{
maze[y][x] = '*';
switch (d)
{
case 0:
maze[y-1][x] = '*';
break;
case 1:
maze[y][x+1] = '*';
break;
case 2:
maze[y+1][x] = '*';
break;
case 3:
maze[y][x-1] = '*';
break;
}
}
return ok;
}

/**
* Solve the maze and draw the solution.  For simplicity,
* assumes the starting point is the lower right, and the
* ending point is the upper left.
*/
private static void solveMaze (char[][] maze)
{
solveMazeRecursively (maze, maze[0].length - 2, maze.length - 2, -1);
}

/**
* Opposite of decimateHorizontally().  Adds extra characters to make
* the maze "look right", and converts each line from char[] to
* String at the same time.
*/
private static String[] expandHorizontally (char[][] maze)
{
char[] tmp = new char[3];
String[] lines = new String[maze.length];
for (int i = 0  ;  i < maze.length  ;  i++)
{
StringBuilder sb = new StringBuilder(maze[i].length * 2);
for (int j = 0  ;  j < maze[i].length  ;  j++)
if (j % 2 == 0)
sb.append (maze[i][j]);
else
{
tmp[0] = tmp[1] = tmp[2] = maze[i][j];
if (tmp[1] == '*')
tmp[0] = tmp[2] = ' ';
sb.append (tmp);
}
lines[i] = sb.toString();
}
return lines;
}

/**
* Accepts a maze as generated by:
* http://rosettacode.org/wiki/Maze_generation#Java
* in a file whose name is specified as a command-line argument,
* or on standard input if no argument is specified.
*/
public static void main (String[] args) throws IOException
{
InputStream f = (args.length > 0
?  new FileInputStream (args[0])
:  System.in);
String[] lines = readLines (f);
char[][] maze = decimateHorizontally (lines);
solveMaze (maze);
String[] solvedLines = expandHorizontally (maze);
for (int i = 0  ;  i < solvedLines.length  ;  i++)
System.out.println (solvedLines[i]);
}
}
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| * |           |               |         * * * * * |           |
+ * +   +   +---+   +---+---+   +   +---+ * +---+ * +---+   +---+
| * |   |       |   | * * * |   |       | * * * | * * * |       |
+ * +   +---+   +   + * + * +   +---+   +---+ * +---+ * +---+   +
| * |       |       | * | * |           | * * * |   | * |       |
+ * +---+---+   +---+ * + * +---+---+   + * +---+   + * +   +   +
| * | * * * |       | * | * | * * * |   | * |       | * |   |   |
+ * + * + * +---+   + * + * + * + * +---+ * +---+   + * +   +---+
| * * * | * |       | * | * * * | * * * * * |       | * |       |
+---+---+ * +---+---+ * +---+---+---+---+---+   +---+ * +---+   +
|       | * * * | * * * |               |           | * * * |   |
+   +---+---+ * + * +---+   +---+---+   +   +---+   +---+ * +   +
| * * * * * * * | * |   |           |   |   |   |       | * * * |
+ * +---+---+---+ * +   +   +---+   +---+   +   +   +---+---+ * +
| * * * * * * * * * |           |               |             * |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

### Animated version

Uses code from maze generation task

Works with: Java version 8
import java.awt.*;
import java.awt.event.*;
import java.awt.geom.Path2D;
import java.util.*;
import javax.swing.*;

public class MazeGenerator extends JPanel {
enum Dir {
N(1, 0, -1), S(2, 0, 1), E(4, 1, 0), W(8, -1, 0);
final int bit;
final int dx;
final int dy;
Dir opposite;

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

Dir(int bit, int dx, int dy) {
this.bit = bit;
this.dx = dx;
this.dy = dy;
}
};
final int nCols;
final int nRows;
final int cellSize = 25;
final int margin = 25;
final int[][] maze;

public MazeGenerator(int size) {
setPreferredSize(new Dimension(650, 650));
setBackground(Color.white);
nCols = size;
nRows = size;
maze = new int[nRows][nCols];
solution = new LinkedList<>();
generateMaze(0, 0);

@Override
public void mousePressed(MouseEvent e) {
new Thread(() -> {
solve(0);
}).start();
}
});
}

@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);

g.setStroke(new BasicStroke(5));
g.setColor(Color.black);

// draw maze
for (int r = 0; r < nRows; r++) {
for (int c = 0; c < nCols; c++) {

int x = margin + c * cellSize;
int y = margin + r * cellSize;

if ((maze[r][c] & 1) == 0) // N
g.drawLine(x, y, x + cellSize, y);

if ((maze[r][c] & 2) == 0) // S
g.drawLine(x, y + cellSize, x + cellSize, y + cellSize);

if ((maze[r][c] & 4) == 0) // E
g.drawLine(x + cellSize, y, x + cellSize, y + cellSize);

if ((maze[r][c] & 8) == 0) // W
g.drawLine(x, y, x, y + cellSize);
}
}

// draw pathfinding animation
int offset = margin + cellSize / 2;

Path2D path = new Path2D.Float();
path.moveTo(offset, offset);

for (int pos : solution) {
int x = pos % nCols * cellSize + offset;
int y = pos / nCols * cellSize + offset;
path.lineTo(x, y);
}

g.setColor(Color.orange);
g.draw(path);

g.setColor(Color.blue);
g.fillOval(offset - 5, offset - 5, 10, 10);

g.setColor(Color.green);
int x = offset + (nCols - 1) * cellSize;
int y = offset + (nRows - 1) * cellSize;
g.fillOval(x - 5, y - 5, 10, 10);

}

void generateMaze(int r, int c) {
Dir[] dirs = Dir.values();
Collections.shuffle(Arrays.asList(dirs));
for (Dir dir : dirs) {
int nc = c + dir.dx;
int nr = r + dir.dy;
if (withinBounds(nr, nc) && maze[nr][nc] == 0) {
maze[r][c] |= dir.bit;
maze[nr][nc] |= dir.opposite.bit;
generateMaze(nr, nc);
}
}
}

boolean withinBounds(int r, int c) {
return c >= 0 && c < nCols && r >= 0 && r < nRows;
}

boolean solve(int pos) {
if (pos == nCols * nRows - 1)
return true;

int c = pos % nCols;
int r = pos / nCols;

for (Dir dir : Dir.values()) {
int nc = c + dir.dx;
int nr = r + dir.dy;
if (withinBounds(nr, nc) && (maze[r][c] & dir.bit) != 0
&& (maze[nr][nc] & 16) == 0) {

int newPos = nr * nCols + nc;

maze[nr][nc] |= 16;

animate();

if (solve(newPos))
return true;

animate();

solution.removeLast();
maze[nr][nc] &= ~16;
}
}

return false;
}

void animate() {
try {
} catch (InterruptedException ignored) {
}
repaint();
}

public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Maze Generator");
f.setResizable(false);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}

## JavaScript

Animated: generating and solving.
To start solving, click to choose a 'start' and an 'end' points.
Go here to see it in action.

var ctx, wid, hei, cols, rows, maze, stack = [], start = {x:-1, y:-1}, end = {x:-1, y:-1}, grid = 8;
function drawMaze() {
for( var i = 0; i < cols; i++ ) {
for( var j = 0; j < rows; j++ ) {
switch( maze[i][j] ) {
case 0: ctx.fillStyle = "black"; break;
case 1: ctx.fillStyle = "green"; break;
case 2: ctx.fillStyle = "red"; break;
case 3: ctx.fillStyle = "yellow"; break;
case 4: ctx.fillStyle = "#500000"; break;
}
ctx.fillRect( grid * i, grid * j, grid, grid  );
}
}
}
function getFNeighbours( sx, sy, a ) {
var n = [];
if( sx - 1 > 0 && maze[sx - 1][sy] == a ) {
n.push( { x:sx - 1, y:sy } );
}
if( sx + 1 < cols - 1 && maze[sx + 1][sy] == a ) {
n.push( { x:sx + 1, y:sy } );
}
if( sy - 1 > 0 && maze[sx][sy - 1] == a ) {
n.push( { x:sx, y:sy - 1 } );
}
if( sy + 1 < rows - 1 && maze[sx][sy + 1] == a ) {
n.push( { x:sx, y:sy + 1 } );
}
return n;
}
function solveMaze() {
if( start.x == end.x && start.y == end.y ) {
for( var i = 0; i < cols; i++ ) {
for( var j = 0; j < rows; j++ ) {
switch( maze[i][j] ) {
case 2: maze[i][j] = 3; break;
case 4: maze[i][j] = 0; break;
}
}
}
drawMaze();
return;
}
var neighbours = getFNeighbours( start.x, start.y, 0 );
if( neighbours.length ) {
stack.push( start );
start = neighbours[0];
maze[start.x][start.y] = 2;
} else {
maze[start.x][start.y] = 4;
start = stack.pop();
}

drawMaze();
requestAnimationFrame( solveMaze );
}
function getCursorPos( event ) {
var rect = this.getBoundingClientRect();
var x = Math.floor( ( event.clientX - rect.left ) / grid ),
y = Math.floor( ( event.clientY - rect.top  ) / grid );
if( maze[x][y] ) return;
if( start.x == -1 ) {
start = { x: x, y: y };
} else {
end = { x: x, y: y };
maze[start.x][start.y] = 2;
solveMaze();
}
}
function getNeighbours( sx, sy, a ) {
var n = [];
if( sx - 1 > 0 && maze[sx - 1][sy] == a && sx - 2 > 0 && maze[sx - 2][sy] == a ) {
n.push( { x:sx - 1, y:sy } ); n.push( { x:sx - 2, y:sy } );
}
if( sx + 1 < cols - 1 && maze[sx + 1][sy] == a && sx + 2 < cols - 1 && maze[sx + 2][sy] == a ) {
n.push( { x:sx + 1, y:sy } ); n.push( { x:sx + 2, y:sy } );
}
if( sy - 1 > 0 && maze[sx][sy - 1] == a && sy - 2 > 0 && maze[sx][sy - 2] == a ) {
n.push( { x:sx, y:sy - 1 } ); n.push( { x:sx, y:sy - 2 } );
}
if( sy + 1 < rows - 1 && maze[sx][sy + 1] == a && sy + 2 < rows - 1 && maze[sx][sy + 2] == a ) {
n.push( { x:sx, y:sy + 1 } ); n.push( { x:sx, y:sy + 2 } );
}
return n;
}
function createArray( c, r ) {
var m = new Array( c );
for( var i = 0; i < c; i++ ) {
m[i] = new Array( r );
for( var j = 0; j < r; j++ ) {
m[i][j] = 1;
}
}
return m;
}
function createMaze() {
var neighbours = getNeighbours( start.x, start.y, 1 ), l;
if( neighbours.length < 1 ) {
if( stack.length < 1 ) {
drawMaze(); stack = [];
start.x = start.y = -1;
document.getElementById( "canvas" ).addEventListener( "mousedown", getCursorPos, false );
return;
}
start = stack.pop();
} else {
var i = 2 * Math.floor( Math.random() * ( neighbours.length / 2 ) )
l = neighbours[i]; maze[l.x][l.y] = 0;
l = neighbours[i + 1]; maze[l.x][l.y] = 0;
start = l
stack.push( start )
}
drawMaze();
requestAnimationFrame( createMaze );
}
function createCanvas( w, h ) {
var canvas = document.createElement( "canvas" );
wid = w; hei = h;
canvas.width = wid; canvas.height = hei;
canvas.id = "canvas";
ctx = canvas.getContext( "2d" );
ctx.fillStyle = "black"; ctx.fillRect( 0, 0, wid, hei );
document.body.appendChild( canvas );
}
function init() {
cols = 73; rows = 53;
createCanvas( grid * cols, grid * rows );
maze = createArray( cols, rows );
start.x = Math.floor( Math.random() * ( cols / 2 ) );
start.y = Math.floor( Math.random() * ( rows / 2 ) );
if( !( start.x & 1 ) ) start.x++; if( !( start.y & 1 ) ) start.y++;
maze[start.x][start.y] = 0;
createMaze();
}

HTML to test.

<!DOCTYPE html>
<title>Maze</title>

## Julia

Works with: Julia version 0.6
Translation of: Python
"""
+   +---+---+
| 1   2   3 |
+---+   +   +
| 4   5 | 6
+---+---+---+

julia> const graph = [
0 1 0 0 0 0;
1 0 1 0 1 0;
0 1 0 0 0 1;
0 0 0 0 1 0;
0 1 0 1 0 0;
0 0 1 0 0 0]

julia> dist, path = dijkstra(graph, 1)
(Dict(4=>3,2=>1,3=>2,5=>2,6=>3,1=>0), Dict(4=>5,2=>1,3=>2,5=>2,6=>3,1=>0))

julia> printpath(path, 6) # Display solution of the maze
1 -> 2 -> 3 -> 6

"""
function dijkstra(graph, source::Int=1)
# ensure that the adjacency matrix is squared
@assert size(graph, 1) == size(graph, 2)
inf = typemax(Int64)
n   = size(graph, 1)

Q    = IntSet(1:n)                  # Set of unvisited nodes
dist = Dict(n => inf for n in Q)    # Unknown distance function from source to v
prev = Dict(n => 0   for n in Q)    # Previous node in optimal path from source
dist[source] = 0                    # Distance from source to source

function _minimumdist(nodes) # Find the less distant node among nodes
kmin, vmin = nothing, inf
for (k, v) in dist
if k  nodes && v  vmin
kmin, vmin = k, v
end
end
return kmin
end
# Until all nodes are visited...
while !isempty(Q)
u = _minimumdist(Q)         # Vertex in Q with smallest dist[]
pop!(Q, u)
if dist[u] == inf break end # All remaining vertices are inaccessible from source
for v in 1:n                # Each neighbor v of u
if graph[u, v] != 0 && v  Q # where v has not yet been visited
alt = dist[u] + graph[u, v]
if alt < dist[v]    # Relax (u, v, a)
dist[v] = alt
prev[v] = u
end
end
end
end

return dist, prev
end

function printpath(prev::Dict, target::Int)
path = "\$target"
while prev[target] != 0
target = prev[target]
path = "\$target -> " * path
end
println(path)
end

const graph = [
0 1 0 0 0 0;
1 0 1 0 1 0;
0 1 0 0 0 1;
0 0 0 0 1 0;
0 1 0 1 0 0;
0 0 1 0 0 0]

dist, path = dijkstra(graph)
printpath(path, 6)

## Kotlin

Translation of: Java
// Version 1.2.31

import java.io.File

typealias Maze = List<CharArray>

/**
* Makes the maze half as wide (i. e. "+---+" becomes "+-+"), so that
* each cell in the maze is the same size horizontally as vertically.
* (Versus the expanded version, which looks better visually.)
* Also, converts each line of the maze from a String to a
* char[], because we'll want mutability when drawing the solution later.
*/
fun decimateHorizontally(lines: List<String>): Maze {
val width = (lines[0].length + 1) / 2
val c = List(lines.size) { CharArray(width) }
for (i in 0 until lines.size) {
for (j in 0 until width) c[i][j] = lines[i][j * 2]
}
return c
}

/**
* Given the maze, the x and y coordinates (which must be odd),
* and the direction we came from, return true if the maze is
* solvable, and draw the solution if so.
*/
fun solveMazeRecursively(maze: Maze, x: Int, y: Int, d: Int): Boolean {
var ok = false
var i = 0
while (i < 4 && !ok) {
if (i != d) {
// 0 = up, 1 = right, 2 = down, 3 = left
when(i) {
0 -> if (maze[y - 1][x] == ' ') ok = solveMazeRecursively (maze, x, y - 2, 2)
1 -> if (maze[y][x + 1] == ' ') ok = solveMazeRecursively (maze, x + 2, y, 3)
2 -> if (maze[y + 1][x] == ' ') ok = solveMazeRecursively (maze, x, y + 2, 0)
3 -> if (maze[y][x - 1] == ' ') ok = solveMazeRecursively (maze, x - 2, y, 1)
else -> {}
}
}
i++
}

// check for end condition
if (x == 1 && y == 1) ok = true

// once we have found a solution, draw it as we unwind the recursion
if (ok) {
maze[y][x] = '*'
when (d) {
0 -> maze[y - 1][x] = '*'
1 -> maze[y][x + 1] = '*'
2 -> maze[y + 1][x] = '*'
3 -> maze[y][x - 1] = '*'
else -> {}
}
}
return ok
}

/**
* Solve the maze and draw the solution. For simplicity,
* assumes the starting point is the lower right, and the
* ending point is the upper left.
*/
fun solveMaze(maze: Maze) =
solveMazeRecursively(maze, maze[0].size - 2, maze.size - 2, -1)

/**
* Opposite of decimateHorizontally(). Adds extra characters to make
* the maze "look right", and converts each line from char[] to
* String at the same time.
*/
fun expandHorizontally(maze: Maze): Array<String> {
val tmp = CharArray(3)
val lines = Array<String>(maze.size) { "" }
for (i in 0 until maze.size) {
val sb = StringBuilder(maze[i].size * 2)
for (j in 0 until maze[i].size) {
if (j % 2 == 0)
sb.append(maze[i][j])
else {
for (k in 0..2) tmp[k] = maze[i][j]
if (tmp[1] == '*') {
tmp[0] = ' '
tmp[2] = ' '
}
sb.append(tmp)
}
}
lines[i] = sb.toString()
}
return lines
}

/**
* Accepts a maze as generated by:
* http://rosettacode.org/wiki/Maze_generation#Kotlin
* in a file whose name is specified as a command-line argument.
*/
fun main(args: Array<String>) {
if (args.size != 1) {
println("The maze file to be read should be passed as a single command line argument.")
return
}
val f = File(args[0])
if (!f.exists()) {
println("Sorry \${args[0]} does not exist.")
return
}
val lines = f.readLines(Charsets.US_ASCII)
val maze = decimateHorizontally(lines)
solveMaze(maze)
val solvedLines = expandHorizontally(maze)
println(solvedLines.joinToString("\n"))
}
Output:

Maze (maze.txt) produced by the maze generation program:

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

Solution generated by this program when passed maze.txt - follow *'s from bottom right (start) to top left (finish):

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

## Mathematica /Wolfram Language

### Graph

Solving the maze generated in Maze_generation#Graph:

HighlightGraph[maze, PathGraph@FindShortestPath[maze, 1, 273]]
Output:

## Nim

Translation of: Go
import random, strutils

type

Direction {.pure.} = enum None, Up, Left, Down, Right

Maze = object
cells: seq[string]
hwalls: seq[string]
vwalls: seq[string]

####################################################################################################
# Maze creation.

func initMaze(rows, cols: Positive): Maze =
## Initialize a maze description.
var h = repeat('-', cols)
var v = repeat("|", cols)
for i in 0..<rows:

proc gen(maze: var Maze; r, c: Natural) =
## Generate a maze starting from point (r, c).

maze.cells[r][c] = ' '
var dirs = [Up, Left, Down, Right]
dirs.shuffle()
for dir in dirs:
case dir
of None:
of Up:
if r > 0 and maze.cells[r-1][c] == '\0':
maze.hwalls[r][c] = chr(0)
maze.gen(r-1, c)
of Left:
if c > 0 and maze.cells[r][c-1] == '\0':
maze.vwalls[r][c] = chr(0)
maze.gen(r, c-1)
of Down:
if r < maze.cells.high and maze.cells[r+1][c] == '\0':
maze.hwalls[r+1][c] = chr(0)
maze.gen(r+1, c)
of Right:
if c < maze.cells[0].high and maze.cells[r][c+1] == '\0':
maze.vwalls[r][c+1] = chr(0)
maze.gen(r, c+1)

proc gen(maze: var Maze) =
## Generate a maze, choosing a random starting point.
maze.gen(rand(maze.cells.high), rand(maze.cells[0].high))

####################################################################################################
# Maze solving.

proc solve(maze: var Maze; ra, ca, rz, cz: Natural) =
## Solve a maze by finding the path from point (ra, ca) to point (rz, cz).

proc rsolve(maze: var Maze; r, c: Natural; dir: Direction): bool {.discardable.} =
## Recursive solver.

if r == rz and c == cz:
maze.cells[r][c] = 'F'
return true

if dir != Down and maze.hwalls[r][c] == '\0':
if maze.rSolve(r-1, c, Up):
maze.cells[r][c] = '^'
maze.hwalls[r][c] = '^'
return true

if dir != Up and r < maze.hwalls.high and maze.hwalls[r+1][c] == '\0':
if maze.rSolve(r+1, c, Down):
maze.cells[r][c] = 'v'
maze.hwalls[r+1][c] = 'v'
return true

if dir != Left and c < maze.vwalls[0].high and maze.vwalls[r][c+1] == '\0':
if maze.rSolve(r, c+1, Right):
maze.cells[r][c] = '>'
maze.vwalls[r][c+1] = '>'
return true

if dir != Right and maze.vwalls[r][c] == '\0':
if maze.rSolve(r, c-1, Left):
maze.cells[r][c] = '<'
maze.vwalls[r][c] = '<'
return true

maze.rsolve(ra, ca, None)
maze.cells[ra][ca] = 'S'

####################################################################################################
# Maze display.

func `\$`(maze: Maze): string =
## Return the string representation fo a maze.

const
HWall = "+---"
HOpen = "+   "
VWall = "|   "
VOpen = "    "
RightCorner = "+\n"
RightWall = "|\n"

for r, hw in maze.hwalls:

for h in hw:
if h == '-' or r == 0:
else:
if h notin {'-', '\0'}: result[^2] = h

for c, vw in maze.vwalls[r]:
if vw == '|' or c == 0:
else:
if vw notin {'|', '\0'}: result[^4] = vw
if maze.cells[r][c] != '\0': result[^2] = maze.cells[r][c]

for _ in 1..maze.hwalls[0].len:

#———————————————————————————————————————————————————————————————————————————————————————————————————

when isMainModule:

const
Width = 8
Height = 8

randomize()
var maze = initMaze(Width, Height)
maze.gen()
var ra, rz = rand(Width - 1)
var ca, cz = rand(Height - 1)
while rz == ra and cz == ca:
# Make sur starting and ending points are different.
rz = rand(Width - 1)
cz = rand(Height - 1)
maze.solve(ra, ca , rz, cz)
echo maze
Output:
+---+---+---+---+---+---+---+---+
|   | > > > > > > > > > > v     |
+   + ^ +---+---+---+---+ v +   +
|   | ^ < < |           | v |   |
+   +---+ ^ +   +---+   + v +---+
|       | ^ |       |   | > > v |
+   +---+ ^ +---+---+   +---+ v +
|       | ^ |               | v |
+---+   + ^ +   +   +---+---+ v +
|       | ^     |   |       | v |
+   +---+ ^ +---+---+   +   + v +
| > > > > ^ |       |   |   | v |
+ ^ +---+---+   +   +---+   + v +
| ^ < < | F     |           | v |
+---+ ^ + ^ +---+---+---+---+ v +
|     S | ^ < < < < < < < < < < |
+---+---+---+---+---+---+---+---+

## Perl

This example includes maze generation code.

#!perl
use strict;
use warnings;

my (\$width, \$height) = @ARGV;
\$_ ||= 10 for \$width, \$height;

my %visited;

my \$h_barrier = "+" . ("--+" x \$width) . "\n";
my \$v_barrier = "|" . ("  |" x \$width) . "\n";
my @output = (\$h_barrier, \$v_barrier) x \$height;
push @output, \$h_barrier;
my @dx = qw(-1 1 0 0);
my @dy = qw(0 0 -1 1);

sub visit {
my (\$x, \$y) = @_;
\$visited{\$x, \$y} = 1;
my \$rand = int rand 4;
for my \$n ( \$rand .. 3, 0 .. \$rand-1 ) {
my (\$xx, \$yy) = (\$x + \$dx[\$n], \$y + \$dy[\$n]);
next if \$visited{ \$xx, \$yy };
next if \$xx < 0 or \$xx >= \$width;
next if \$yy < 0 or \$yy >= \$height;

my \$row = \$y * 2 + 1 + \$dy[\$n];
my \$col = \$x * 3 + 1 + \$dx[\$n];
substr( \$output[\$row], \$col, 2, '  ' );

no warnings 'recursion';
visit( \$xx, \$yy );
}
}

visit( int rand \$width, int rand \$height );

print "Here is the maze:\n";
print @output;

%visited = ();

my @d = ('>>', '<<', 'vv', '^^');
sub solve {
my (\$x, \$y) = @_;
return 1 if \$x == 0 and \$y == 0;
\$visited{ \$x, \$y } = 1;
my \$rand = int rand 4;
for my \$n ( \$rand .. 3, 0 .. \$rand-1 ) {
my (\$xx, \$yy) = (\$x + \$dx[\$n], \$y + \$dy[\$n]);
next if \$visited{ \$xx, \$yy };
next if \$xx < 0 or \$xx >= \$width;
next if \$yy < 0 or \$yy >= \$height;

my \$row = \$y * 2 + 1 + \$dy[\$n];
my \$col = \$x * 3 + 1 + \$dx[\$n];

my \$b = substr( \$output[\$row], \$col, 2 );
next if "  " ne \$b;

no warnings 'recursion';
next if not solve( \$xx, \$yy );

substr( \$output[\$row], \$col, 2, \$d[\$n] );
substr( \$output[\$row-\$dy[\$n]], \$col-\$dx[\$n], 2, \$d[\$n] );
return 1;
}
0;
}

if( solve( \$width-1, \$height-1 ) ) {
print "Here is the solution:\n";
substr( \$output[1], 1, 2, '**' );
print @output;
} else {
print "Could not solve!\n";
}
Output:
Here is the maze:
+--+--+--+--+--+--+--+--+--+--+
|  |                    |     |
+  +  +--+--+--+  +--+  +  +  +
|     |        |  |        |  |
+  +--+--+  +  +  +--+--+--+  +
|           |  |     |     |  |
+--+--+--+--+  +--+  +--+  +  +
|           |  |  |     |     |
+  +  +--+  +  +  +--+  +--+  +
|  |     |  |  |     |     |  |
+--+--+  +--+  +  +  +--+  +--+
|        |     |  |  |  |     |
+  +--+--+  +--+--+  +  +--+  +
|  |     |  |        |        |
+  +  +  +  +  +--+--+--+--+--+
|  |  |     |  |     |        |
+  +  +--+--+  +  +  +  +--+  +
|  |  |     |     |        |  |
+  +  +  +  +--+--+--+--+--+  +
|        |                    |
+--+--+--+--+--+--+--+--+--+--+
Here is the solution:
+--+--+--+--+--+--+--+--+--+--+
|**|                    |     |
+vv+  +--+--+--+  +--+  +  +  +
|vv   |   ^^>>>|  |        |  |
+vv+--+--+^^+vv+  +--+--+--+  +
|vv>>>>>>>>>|vv|     |     |  |
+--+--+--+--+vv+--+  +--+  +  +
|           |vv|  |     |     |
+  +  +--+  +vv+  +--+  +--+  +
|  |     |  |vv|     |     |  |
+--+--+  +--+vv+  +  +--+  +--+
|        |<<<vv|  |  |  |     |
+  +--+--+vv+--+--+  +  +--+  +
|  |<<<^^|vv|        |        |
+  +vv+^^+vv+  +--+--+--+--+--+
|  |vv|<<<vv|  |     |        |
+  +vv+--+--+  +  +  +  +--+  +
|  |vv|^^>>>|     |        |  |
+  +vv+^^+vv+--+--+--+--+--+  +
|   vv>>>|vv>>>>>>>>>>>>>>>>>>|
+--+--+--+--+--+--+--+--+--+--+

## Phix

Combined generator and solver.

--
-- demo\rosetta\Maze_solving.exw
-- =============================
--
with javascript_semantics
constant w = 11, h = 8

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

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

integer dx, dy -- door location (in a wall!)

function solve_maze(integer x, y)
sequence p = {{x-4,y},{x,y+2},{x+4,y},{x,y-2}}
for d=1 to length(p) do
integer {nx,ny} = p[d]
integer {wx,wy} = {(x+nx)/2,(y+ny)/2}
if grid[wy][wx]=' ' then
grid[wy][wx] = "-:-:"[d]        -- mark path
if {wx,wy}={dx,dy} then return true end if
if grid[ny][nx]=' ' then
grid[ny][nx] = 'o'          -- mark cell
if solve_maze(nx,ny) then return true end if
grid[ny][nx] = ' '          -- unmark cell
end if
grid[wy][wx] = ' '              -- unmark path
end if
end for
return false
end function

return rand(2)=1 -- toin coss 50:50 true(1)/false(0)
end function

integer {x,y} = {(rand(w)*4)-1,rand(h)*2}
amaze(x,y)
-- mark start pos
grid[y][x] = '*'
-- add a random door (heads=rhs/lhs, tails=top/btm)
grid[dy][dx] = ' '
else
grid[dy][dx-1..dx+1] = ' '
end if
{} = solve_maze(x,y)
puts(1,join(grid,'\n'))
Output:
+---+---+---+---+---+---+---+---+---+---+---+
| o - o - o |     o - o - o - o |   |       |
+ : +---+ : +---+ : +---+---+ : +   +   +   +
| o - o | o | o - o |   | o - o |       |   |
+---+ : + : + : +---+   + : +---+---+---+   +
| o - o | o - o |       | o - o | o - o - o |
+ : +---+---+---+   +---+---+ : + : +---+ : +
| o |                       | o - o |   | o |
+ : +   +---+---+---+---+   +---+---+   + : +
| o |           |   |           |         o -
+ : +---+---+   +   +   +---+---+   +---+---+
| o |               |               |       |
+ : +---+---+---+   +---+   +---+---+   +   +
| o - o - o |       | * |   |           |   |
+   +---+ : +---+---+ : +   +---+---+   +   +
|       | o - o - o - o |               |   |
+---+---+---+---+---+---+---+---+---+---+---+

## Picat

main =>
Maze0 = ["+---+---+---+---+---+---+---+---+",
"|   |       |       |           |",
"+   +   +   +---+   +   +---+   +",
"|       |   |       |       |   |",
"+---+---+   +   +---+---+   +   +",
"|       |   |               |   |",
"+---+   +   +   +---+---+---+   +",
"|       |   |               |   |",
"+   +   +   +---+---+---+   +   +",
"|   |   |   |               |   |",
"+   +   +   +---+   +---+---+   +",
"|   |   |       |           |   |",
"+   +---+---+   +---+---+---+   +",
"|           |       |           |",
"+   +---+   +---+   +   +---+   +",
"|       |               |       |",
"+---+---+---+---+---+---+---+---+"],
MaxR = len(Maze0) div 2,
MaxC = len(Maze0[1]) div 4,
Maze = new_array(MaxR,MaxC),
foreach (R in 1..MaxR, C in 1..MaxC)
Maze[R,C] = 0
end,
fill_maze(Maze0,Maze,1),
solve_maze(Maze,(1,1),(MaxR,MaxC),Cost,Plan),
OutputMaze = new_array(MaxR,MaxC),
foreach ((R,C) in Plan)
OutputMaze[R,C] = '*'
end,
output_maze(Maze0,OutputMaze,1).

fill_maze([Line1,Line2|Maze0],Maze,R) =>
fill_maze_cols(Line1,Maze,R,1),
fill_maze_cols(Line2,Maze,R,1),
fill_maze(Maze0,Maze,R+1).
fill_maze(_,_,_) =>    true.

fill_maze_cols(['+',' ',' ',' '|Line],Maze,R,C) =>
Maze[R,C] := Maze[R,C] \/ 4,     % up
Maze[R-1,C] := Maze[R-1,C] \/ 8, % down
fill_maze_cols(Line,Maze,R,C+1).
fill_maze_cols([' ',' ',' ',' '|Line],Maze,R,C) =>
Maze[R,C] := Maze[R,C] \/ 1,     % left
Maze[R,C-1] := Maze[R,C-1] \/ 2, % right
fill_maze_cols(Line,Maze,R,C+1).
fill_maze_cols([_,_,_,_|Line],Maze,R,C) =>
fill_maze_cols(Line,Maze,R,C+1).
fill_maze_cols(_,_,_,_) => true.

table (+,+,+,min,-)
solve_maze(_Maze,FPos,FPos,Cost,Plan) =>
Cost = 0,
Plan = [FPos].
solve_maze(Maze,Pos@(R,C),FPos,Cost,Plan) ?=>
Maze[R,C] /\ 1 == 1,             % left
solve_maze(Maze,(R,C-1),FPos,Cost1,Plan1),
Plan = [Pos|Plan1],
Cost = Cost1+1.
solve_maze(Maze,Pos@(R,C),FPos,Cost,Plan) ?=>
Maze[R,C] /\ 2 == 2,             % right
solve_maze(Maze,(R,C+1),FPos,Cost1,Plan1),
Plan = [Pos|Plan1],
Cost = Cost1+1.
solve_maze(Maze,Pos@(R,C),FPos,Cost,Plan) ?=>
Maze[R,C] /\ 4 == 4,             % up
solve_maze(Maze,(R-1,C),FPos,Cost1,Plan1),
Plan = [Pos|Plan1],
Cost = Cost1+1.
solve_maze(Maze,Pos@(R,C),FPos,Cost,Plan) ?=>
Maze[R,C] /\ 8 == 8,             % down
solve_maze(Maze,(R+1,C),FPos,Cost1,Plan1),
Plan = [Pos|Plan1],
Cost = Cost1+1.

output_maze([Line1,Line2|Maze0],Maze,R) =>
output_maze_cols(Line1,Maze,R,1),
output_maze_cols(Line2,Maze,R,1),
output_maze(Maze0,Maze,R+1).
output_maze([Line],_,_) =>    println(Line).

output_maze_cols([' ',' ',' ',' '|Line],Maze,R,C) =>
if Maze[R,C] == '*' then
print("  * ")
else
print("    ")
end,
output_maze_cols(Line,Maze,R,C+1).
output_maze_cols(['|',' ',' ',' '|Line],Maze,R,C) =>
if Maze[R,C] == '*' then
print("| * ")
else
print("|   ")
end,
output_maze_cols(Line,Maze,R,C+1).
output_maze_cols(['+',' ',' ',' '|Line],Maze,R,C) =>
if Maze[R,C] == '*' && Maze[R-1,C] == '*' then
print("+ * ")
else
print("+   ")
end,
output_maze_cols(Line,Maze,R,C+1).
output_maze_cols([C1,C2,C3,C4|Line],Maze,R,C) =>
printf("%c%c%c%c",C1,C3,C3,C4),
output_maze_cols(Line,Maze,R,C+1).
output_maze_cols(Line,_,_,_) => println(Line).
Output:
+---+---+---+---+---+---+---+---+
| * | *   * |       |           |
+ * + * + * +---+   +   +---+   +
| *   * | * |       |       |   |
+---+---+ * +   +---+---+   +   +
|       | * |               |   |
+---+   + * +   +---+---+---+   +
|       | * |               |   |
+   +   + * +---+---+---+   +   +
|   |   | * |               |   |
+   +   + * +---+   +---+---+   +
|   |   | *   * |           |   |
+   +---+---+ * +---+---+---+   +
|           | *   * | *   *   * |
+   +---+   +---+ * + * +---+ * +
|       |         *   * |     * |
+---+---+---+---+---+---+---+---+

## PicoLisp

(de shortestPath (Goal This Maze)
(let (Path NIL  Best NIL  Dir " > ")
(recur (This Path Dir)
(when (and This (not (: mark)))
(push 'Path (cons This Dir))
(if (== Goal This)
(unless (and Best (>= (length Path) (length Best)))
(setq Best Path) )
(=: mark T)
(recurse (: west) Path " > ")
(recurse (: east) Path " < ")
(recurse (: south) Path " \^ ")
(recurse (: north) Path " v ")
(=: mark NIL) ) ) )
(disp Maze 0
'((Fld) (if (asoq Fld Best) (cdr @) "   ")) ) ) )

Using the maze produced in Maze generation#PicoLisp, this finds the shortest path from the top-left cell 'a8' to the bottom-right exit 'k1':

: (shortestPath 'a8 'k1 (maze 11 8))
+   +---+---+---+---+---+---+---+---+---+---+
8 | >   >   v | >   v |                       |
+   +   +   +   +   +   +---+   +---+---+   +
7 |   |   | >   ^ | v |   |       |       |   |
+---+   +---+---+   +   +   +---+   +   +   +
6 |   |       |     v |   |           |   |   |
+   +---+   +---+   +---+---+---+   +   +---+
5 |       |       | >   >   >   v |   |       |
+---+   +---+   +---+---+---+   +---+---+   +
4 |   |       |       |       | v | >   >   v |
+   +---+   +---+   +---+   +   +   +---+   +
3 |       |       |   |       | v | ^   < | v |
+   +---+---+   +   +   +   +   +---+   +   +
2 |       |       |   |   |   | v | >   ^ | v |
+   +   +   +---+   +   +---+   +   +---+   +
1 |   |               |         >   ^ |     >
+---+---+---+---+---+---+---+---+---+---+---+
a   b   c   d   e   f   g   h   i   j   k

## Prolog

Works with SWI-Prolog and XPCE.

:- dynamic cell/2.
:- dynamic maze/3.
:- dynamic path/1.

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

% initialisation of the neighbours of the cells
forall(between(0, Lig, I),
(   forall(between(0, Col, J), assert(maze(I, J, []))))),

% creation of the window of the maze
new(D, window('Maze')),
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))),
L0 is random(Lig),
C0 is random(Col),
assert(cell(L0, C0)),
\+search(D, Lig, Col, L0, C0),
send(D, open),

% we look for a path from cell(0, 0) to cell(Lig-1, Col-1)
% creation of the entrance
erase_line(D, -1, 0, 0, 0),

% creation of the exit
Lig1 is Lig-1,
Col1 is Col-1,
erase_line(D, Lig1, Col1, Lig, Col1),

% seraching the path
assert(path([[0, 0], [-1, 0]])),
walk(Lig, Col),
path(P),
display_path(D, P).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
walk(Lig, Col) :-
path([[L, C] | _R]),
L is Lig - 1,
C is Col - 1,
retract(path(P)),
assert(path([[Lig, C]|P])).

walk(Lig, Col) :-
retract(path([[L, C] | R])),
maze(L, C, Edge),
member([L1, C1], Edge),
\+member([L1, C1], R),
assert(path([[L1,C1], [L, C] | R])),
walk(Lig, Col).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
display_path(_, []).

display_path(D, [[L, C] | R]):-
new(B, box(10,10)),
send(B, fill_pattern, new(_, colour(@default, 0,0,0))),
X is C * 30 + 60,
Y is L * 30 + 60,
send(D, display, B, point(X,Y)),
display_path(D, R).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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)),

retract(maze(L, C, Edge)),
assert(maze(L, C, [[L1, C1] | Edge])),
retract(maze(L1, C1, Edge1)),
assert(maze(L1, C1, [[L, C] | Edge1])),

erase_line(D, L, C, L1, C1),
search(D, Lig, Col, L1, C1).

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

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

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

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

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

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

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

output :

## PureBasic

;code from the maze generation task is place here in its entirety before the rest of the code

Procedure displayMazePath(Array maze(2), List Path.POINT())
Protected x, y, vWall.s, hWall.s
Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2)
Protected Dim mazeOutput.mazeOutput(mazeHeight)
Protected Dim mazeRow.mazeOutput(0)
Static pathChars.s = "@^>v<"

For y = 0 To mazeHeight
makeDisplayMazeRow(mazeRow(), maze(), y): mazeOutput(y) = mazeRow(0)
Next

If ListSize(path())
FirstElement(path())
Protected prevPath.POINT = path()

While NextElement(path())
x = path()\x - prevPath\x
y = path()\y - prevPath\y
Select x
Case -1: dirTaken = #dir_W
Case 1: dirTaken = #dir_E
Default
If y < 0
dirTaken = #dir_N
Else
dirTaken = #dir_S
EndIf
EndSelect
hWall = mazeOutput(prevPath\y)\hWall
mazeOutput(prevPath\y)\hWall = Left(hWall, prevPath\x * #cellDWidth + 2) + Mid(pathChars, dirTaken + 1, 1) + Right(hWall, Len(hWall) - (prevPath\x * #cellDWidth + 3))
prevPath = path()
Wend
hWall = mazeOutput(prevPath\y)\hWall
mazeOutput(prevPath\y)\hWall = Left(hWall, prevPath\x * #cellDWidth + 2) + Mid(pathChars, #dir_ID + 1, 1) + Right(hWall, Len(hWall) - (prevPath\x * #cellDWidth + 3))

For y = 0 To mazeHeight
PrintN(mazeOutput(y)\vWall): PrintN(mazeOutput(y)\hWall)
Next
EndIf
EndProcedure

Procedure solveMaze(Array maze(2), *start.POINT, *finish.POINT, List Path.POINT())
Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2)
Dim visited(mazeWidth + 1, mazeHeight + 1) ;includes padding for easy border detection

Protected i
;mark outside border as already visited (off limits)
For i = 1 To mazeWidth
visited(i, 0) = #True: visited(i, mazeHeight + 1) = #True
Next
For i = 1 To mazeHeight
visited(0, i) = #True: visited(mazeWidth + 1, i) = #True
Next

Protected x = *start\x, y = *start\y, nextCellDir
visited(x + offset(#visited, #dir_ID)\x, y + offset(#visited, #dir_ID)\y) = #True

ClearList(path())
Repeat
If x = *finish\x And y = *finish\y
path()\x = x: path()\y = y
Break ;success
EndIf

nextCellDir = #firstDir - 1
For i = #firstDir To #numDirs
If Not visited(x + offset(#visited, i)\x, y + offset(#visited, i)\y)
If maze(x + offset(#wall, i)\x, y + offset(#wall, i)\y) & wallvalue(i) <> #Null
nextCellDir = i: Break ;exit for/next search
EndIf
EndIf
Next

If nextCellDir >= #firstDir
visited(x + offset(#visited, nextCellDir)\x, y + offset(#visited, nextCellDir)\y) = #True

path()\x = x: path()\y = y

x + offset(#maze, nextCellDir)\x: y + offset(#maze, nextCellDir)\y
ElseIf ListSize(path()) > 0
x = path()\x: y = path()\y
DeleteElement(path())
Else
Break
EndIf
ForEver

EndProcedure

;demonstration
If OpenConsole()
Define.POINT start, finish
start\x = Random(mazeWidth - 1): start\y = Random(mazeHeight - 1)
finish\x = Random(mazeWidth - 1): finish\y = Random(mazeHeight - 1)
NewList Path.POINT()
solveMaze(maze(), start, finish, path())
If ListSize(path()) > 0
PrintN("Solution found for path between (" + Str(start\x) + ", " + Str(start\y) + ") and (" + Str(finish\x) + ", " + Str(finish\y) + ")")
displayMazePath(maze(), path())
Else
PrintN("No solution found for path between (" + Str(start\x) + ", " + Str(start\y) + ") and (" + Str(finish\x) + ", " + Str(finish\y) + ")")
EndIf

Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf

Using the maze produced in Maze generation#PureBasic, this additional code will find and display the path between two random maze cells. A working example requires combining the two code listings by placing the 'maze generation' code at the beginning of the 'maze solving' code.

Sample output:

Solution found for path between (3, 2) and (7, 1)
+---+---+---+---+---+---+---+---+---+---+
| v   <   <   <   < |   | v   <   <     |
+   +---+---+---+   +   +   +---+   +---+
| >   v         | ^ |   | v | @ | ^   < |
+---+   +---+---+   +   +   +   +---+   +
|   | v |     >   ^ |     v | ^     | ^ |
+   +   +   +---+---+---+   +   +---+   +
| v   < |               | >   ^ | >   ^ |
+   +---+---+---+---+   +---+   +   +   +
| v |       |           |       | ^ |   |
+   +---+   +   +---+---+---+---+   +---+
| >   >   v |       |     >   v | ^   < |
+---+---+   +---+---+---+   +   +---+   +
|         >   >   >   >   ^ | >   >   ^ |
+---+---+---+---+---+---+---+---+---+---+

## Python

# python 3

def Dijkstra(Graph, source):
'''
+   +---+---+
| 0   1   2 |
+---+   +   +
| 3   4 | 5
+---+---+---+

>>> graph = (        # or ones on the diagonal
...     (0,1,0,0,0,0,),
...     (1,0,1,0,1,0,),
...     (0,1,0,0,0,1,),
...     (0,0,0,0,1,0,),
...     (0,1,0,1,0,0,),
...     (0,0,1,0,0,0,),
... )
...
>>> Dijkstra(graph, 0)
([0, 1, 2, 3, 2, 3], [1e+140, 0, 1, 4, 1, 2])
>>> display_solution([1e+140, 0, 1, 4, 1, 2])
5<2<1<0
'''
# Graph[u][v] is the weight from u to v (however 0 means infinity)
infinity = float('infinity')
n = len(graph)
dist = [infinity]*n   # Unknown distance function from source to v
previous = [infinity]*n # Previous node in optimal path from source
dist[source] = 0        # Distance from source to source
Q = list(range(n)) # All nodes in the graph are unoptimized - thus are in Q
while Q:           # The main loop
u = min(Q, key=lambda n:dist[n])                 # vertex in Q with smallest dist[]
Q.remove(u)
if dist[u] == infinity:
break # all remaining vertices are inaccessible from source
for v in range(n):               # each neighbor v of u
if Graph[u][v] and (v in Q): # where v has not yet been visited
alt = dist[u] + Graph[u][v]
if alt < dist[v]:       # Relax (u,v,a)
dist[v] = alt
previous[v] = u
return dist,previous

def display_solution(predecessor):
cell = len(predecessor)-1
while cell:
print(cell,end='<')
cell = predecessor[cell]
print(0)

## Racket

Following function returns a path between two cells in a maze which is created by the build-maze function (See Maze generation).

;; Returns a path connecting two given cells in the maze
;; find-path :: Maze Cell Cell -> (Listof Cell)
(define (find-path m p1 p2)
(match-define (maze N M tbl) m)
(define (alternatives p prev) (remove prev (connections tbl p)))
(define (dead-end? p prev) (empty? (alternatives p prev)))
(define ((next-turn route) p)
(define prev (car route))
(cond
[(equal? p p2) (cons p2 route)]
[(dead-end? p prev) '()]
[else (append-map (next-turn (cons p route))
(alternatives p prev))]))
(reverse
(append-map (next-turn (list p1))
(alternatives p1 (list p1)))))

Reading a maze from a file

;; Reads the maze from the textual form
;; read-maze :: File-path -> Maze
(define tbl (make-hash))
(with-input-from-file file
(λ ()
; the first line gives us the width of the maze
(define N (/ (- (string-length (read-line)) 1) 4))
; while reading other lines we get the height of the maze
(define M
(for/sum ([h (in-lines)] [v (in-lines)] [j (in-naturals)])
(for ([i (in-range N)])
(when (eq? #\space (string-ref h (* 4 (+ 1 i))))
(connect! tbl (list i j) (list (+ i 1) j)))
(when (eq? #\space (string-ref v (+ 1 (* 4 i))))
(connect! tbl (list i j) (list i (+ j 1)))))
1))
(maze N M tbl))))

Printing out a maze with a path between two given cells

;; Shows a maze with a path connecting two given cells
(define (show-path m p1 p2)
(match-define (maze N M tbl) m)
(define route (find-path m p1 p2))
(for ([i N]) (display "+---"))
(displayln "+")
(for ([j M])
(display "|")
(for ([i (- N 0)])
(if (member (list i j) route)
(display " *")
(display "  "))
(if (connected? tbl (list i j) (list (+ 1 i) j))
(display "  ")
(display " |")))
(newline)
(for ([i N])
(if (connected? tbl (list i j) (list i (+ j 1)))
(display "+   ")
(display "+---")))
(displayln "+"))
(newline))

Example:

-> (define m (build-maze 14 7))
-> (with-output-to-file "maze" (λ () (show-maze m)))
-> (show-maze (read-maze "maze"))
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|                       |           |           |       |
+   +---+---+---+---+   +   +   +   +---+   +---+   +   +
|       |           |   |   |   |   |       |       |   |
+---+   +   +---+   +---+   +   +   +   +---+   +---+   +
|       |   |   |           |   |   |       |   |       |
+   +   +   +   +---+---+---+   +   +   +   +   +   +---+
|   |   |   |       |           |   |   |       |       |
+   +---+   +   +   +   +---+---+   +   +---+---+---+   +
|   |       |   |   |           |   |           |   |   |
+   +   +---+---+   +---+---+   +   +---+---+   +   +   +
|   |               |   |       |           |       |   |
+   +---+---+---+   +   +   +---+---+---+   +---+---+   +
|                   |       |                           |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

-> (show-path m '(0 0) '(13 6))
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| *                     | *   *   * |           |       |
+   +---+---+---+---+   +   +   +   +---+   +---+   +   +
| *   * | *   *   * |   | * |   | * |       |       |   |
+---+   +   +---+   +---+   +   +   +   +---+   +---+   +
| *   * | * |   | *   *   * |   | * |       |   |       |
+   +   +   +   +---+---+---+   +   +   +   +   +   +---+
| * |   | * |       |           | * |   |       |       |
+   +---+   +   +   +   +---+---+   +   +---+---+---+   +
| * | *   * |   |   |           | * |           |   |   |
+   +   +---+---+   +---+---+   +   +---+---+   +   +   +
| * | *   *   *   * |   |       | *   *   * |       |   |
+   +---+---+---+   +   +   +---+---+---+   +---+---+   +
| *   *   *   *   * |       |             *   *   *   * |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

## Raku

(formerly Perl 6)

Works with: Rakudo version 2017.02

(Includes maze generation code.)

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]);
}

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]];
}
}

sub solve (@maze is copy, @from = [1, 1], @to = [@maze[0] - 2, @maze - 2]) {
my (\$x, \$y) = @from;
my (\$xto, \$yto) = @to;
my @stack;

sub drop-crumb(\$x,\$y,\$c) { @maze[\$y][\$x] = -\$c }
drop-crumb(\$x,\$y,N);

loop {
my \$dir = pick_direction([\$x,\$y]);
if \$dir {
(\$x, \$y) = move(\$dir, [\$x,\$y]);
return @maze if \$x == \$xto and \$y == \$yto;
}
else {
@maze[\$y][\$x] = -TRIED;
(\$x,\$y) = @stack.pop;
@maze[\$y][\$x] = -TRIED;
(\$x,\$y) = @stack.pop;
}
}

sub pick_direction([\$x,\$y]) {
my @neighbors =
(Up    unless @maze[\$y - 1][\$x]),
(Down  unless @maze[\$y + 1][\$x]),
(Left  unless @maze[\$y][\$x - 1]),
(Right unless @maze[\$y][\$x + 1]);
}

sub move (\$dir, @cur) {
my (\$x,\$y) = @cur;
given \$dir {
when Up    { for ^2 { push @stack, \$[\$x,\$y--]; drop-crumb \$x,\$y,S; } }
when Down  { for ^2 { push @stack, \$[\$x,\$y++]; drop-crumb \$x,\$y,N; } }
when Left  { for ^2 { push @stack, \$[\$x--,\$y]; drop-crumb \$x,\$y,E; } }
when Right { for ^2 { push @stack, \$[\$x++,\$y]; drop-crumb \$x,\$y,W; } }
}
\$x,\$y;
}
}

display solve gen_maze( 29, 19 );
Output:
┌ ╵ ────┬───────────────┬───────────────┬───────────────────────────────┬───────────┬───────────────┬───────────────┐
│ ╵ · · │ ╷ ╴ ╴ ╴ ╴     │               │ ╷ ╴ ╴ · · · · · · · · · · · · │ ╷ ╴ ╴ · · │ · · · · · · · │ · · · · · · · │
│ ╵ ╶───┘ ╷ ╶───┐ ╵ ╷   │   ╷   ╶───────┤ ╷ ╷ ╵ ╶───────┬───────┐ · ┌───┘ ╷ ╷ ╵ ╷ · │ · ╶───┬───╴ · │ · ╷ · ┌───╴ · │
│ ╵ ╴ ╴ ╴ ╴ · · │ ╵ │   │   │           │ ╷ │ ╵ ╴ ╴ ╴ ╴ │ ╷ ╴ ╴ │ · │ ╷ ╴ ╴ │ ╵ │ · │ · · · │ · · · │ · │ · │ · · · │
│ · ┌───────────┤ ╵ │   └───┴───────╴   │ ╷ ├───────┐ ╵ ╵ ╷ ╷ ╵ └───┘ ╷ ┌───┘ ╵ │ · │ · ╷ · │ · ┌───┴───┘ · │ · ╶───┤
│ · │ ╶ ╶ ╶ ╶ ╷ │ ╵ │                   │ ╷ │       │ ╵ ╴ ╴ │ ╵ ╴ ╴ ╴ ╴ │ ╶ ╶ ╵ │ · │ · │ · │ · │ · · · · · │ · · · │
│ · │ ╵ ╶───┐ ╷ ╵ ╵ ├───────────────╴   │ ╷ └───╴   └───────┼───┬───────┤ ╵ ┌───┤ · ├───┘ · │ · │ · ╷ · ┌───┴───┐ · │
│ · │ ╵ ╴ ╴ │ ╶ ╶ ╵ │                   │ ╶ ╶ ╶ ╶ ╶ ╶ ╶ ╶ ╷ │ · │ ╶ ╶ ╷ │ ╵ │ · │ · │ · · · │ · │ · │ · │ · · · │ · │
│ · └───┐ ╵ ├───────┴───────┐   ╶───────┴───────┬───────╴ ╷ │ · │ ╵ ╷ ╷ │ ╵ │ · │ · │ · ┌───┤ · │ · │ · │ · ╷ · ╵ · │
│ · · · │ ╵ │ ╷ ╴ ╴ ╴ ╴ ╴ ╴ │                   │ ╷ ╴ ╴ ╴ ╴ │ · │ ╵ │ ╷ │ ╵ │ · │ · │ · │ · │ · │ · │ · │ · │ · · · │
├───╴ · │ ╵ │ ╷ ╶───────┐ ╵ ├───────────────┐   │ ╷ ╶───┬───┘ · │ ╵ │ ╷ ╵ ╵ │ · ╵ · ╵ · │ · ╵ · └───┘ · │ · ├───────┤
│ · · · │ ╵ │ ╶ ╶ ╶ ╶ ╷ │ ╵ │ ╷ ╴ ╴ ╴ ╴ ╴ ╴ │   │ ╶ ╶ ╷ │ · · · │ ╵ │ ╶ ╶ ╵ │ · · · · · │ · · · · · · · │ · │ · · · │
│ · ┌───┤ ╵ └───────╴ ╷ │ ╵ ╵ ╷ ┌───────┐ ╵ │   └───┐ ╷ └───┐ · │ ╵ ├───────┼───────┬───┴───────┬───┬───┘ · ├───╴ · │
│ · │ · │ ╵ ╴ ╴ ╴ ╴ ╴ ╴ │ ╵ ╴ ╴ │ · · · │ ╵ │       │ ╶ ╶ ╷ │ · │ ╵ │ ╷ ╴ ╴ │ ╷ ╴ ╴ │ ╷ ╴ ╴ ╴ ╴ │ · │ · · · │ · · · │
│ · ╵ · ├───────────────┴───────┴───┐ · │ ╵ └───────┴───┐ ╷ │ · │ ╵ ╵ ╷ ╷ ╵ ╵ ╷ ╷ ╵ │ ╷ ┌───╴ ╵ │ · │ · ╶───┤ · ╶───┤
│ · · · │ · · · · · · · · · · · · · │ · │ ╵ ╴ ╴ ╴ ╴ · · │ ╷ │ · │ ╵ ╴ ╴ │ ╵ ╴ ╴ │ ╵ │ ╷ │ ╶ ╶ ╵ │ · │ · · · │ · · · │
├───┐ · │ · ┌───────────╴ · ┌───┐ · │ · └───┬───╴ ╵ ┌───┘ ╷ │ · ├───────┴───────┤ ╵ ╵ ╷ │ ╵ ╶───┤ · └───┐ · │ · ╷ · │
│ · │ · │ · │ · · · · · · · │ · │ · │ · · · │ ╶ ╶ ╵ │ ╷ ╴ ╴ │ · │ · · · · · · · │ ╵ ╴ ╴ │ ╵ ╴ ╴ │ · · · │ · │ · │ · │
│ · │ · └───┘ · ┌───────────┘ · │ · ├───╴ · │ ╵ ┌───┘ ╷ ┌───┘ · │ · ╷ · ┌───╴ · └───────┴───┐ ╵ └───┐ · ╵ · ├───┘ · │
│ · │ · · · · · │ · · · · · · · │ · │ · · · │ ╵ │ ╷ ╴ ╴ │ · · · │ · │ · │ · · · · · · · · · │ ╵ ╴ ╴ │ · · · │ · · · │
│ · ├───────╴ · ├───┐ · ┌───┐ · ╵ · │ · ╶───┤ ╵ ╵ ╷ ┌───┘ · ╶───┤ · │ · └───┬───╴ · ┌───────┤ · ╷ ╵ │ · ╶───┘ · ╷ · │
│ · │ · · · · · │   │ · │ · │ · · · │ · · · │ ╵ ╴ ╴ │ · · · · · │ · │ · · · │ · · · │ ╶ ╶ ╷ │ · │ ╵ │ · · · · · │ · │
│ · ╵ · ┌───────┘   │ · ╵ · └───────┤ · ╷ · └───────┴───────┐ · ╵ · └───┐ · └───┐ · │ ╵ ╷ ╷ └───┘ ╵ ├───────────┤ · │
│ · · · │           │ · · · · · · · │ · │ · · · · · · · · · │ · · · · · │ · · · │ · │ ╵ │ ╶ ╶ ╶ ╶ ╵ │ ╷ ╴ ╴ ╴ ╴ │ · │
│ · ╶───┤   ╶───────┴───┬───────┐ · ├───┘ · ┌───────────┐ · ├───────────┴───╴ · │ · │ ╵ └───────┐ · │ ╷ ┌───╴ ╵ │ · │
│ · · · │               │ · · · │ · │ · · · │ · · · · · │ · │ · · · · · · · · · │ · │ ╵ ╴ ╴ ╴ ╴ │ · │ ╷ │ ╶ ╶ ╵ │ · │
├───┐ · ├───────┬───╴   │ · ╷ · │ · │ · ┌───┤ · ╶───────┤ · │ · ╶───────┬───┐ · ├───┴───────┐ ╵ └───┘ ╷ │ ╵ ┌───┴───┤
│ · │ · │       │       │ · │ · │ · │ · │ · │ · · · · · │ · │ · · · · · │ · │ · │           │ ╵ ╴ ╴ ╴ ╴ │ ╵ │ ╷ ╴ ╴ │
│ · │ · │   ╷   ╵   ┌───┘ · │ · ╵ · ╵ · │ · ╵ · ┌───┐ · ╵ · └───────╴ · │ · ╵ · │   ┌───╴   └───────┐ · │ ╵ ╵ ╷ ╷ ╵ │
│ · │ · │   │       │ · · · │ · · · · · │ · · · │ · │ · · · · · · · · · │ · · · │   │               │ · │ ╵ ╴ ╴ │ ╵ │
│ · │ · │   └───┬───┴───────┴───┬───────┤ · ┌───┘ · ├───────────────────┴───────┤   └───────────┐   └───┴───────┤ ╵ │
│ · │ · │       │               │       │ · │ · · · │                           │               │               │ ╵ │
│ · ╵ · ├───┐   │   ╶───────┐   ╵   ╷   │ · ╵ · ╷ · │   ╶───────────────────┐   └───┬───────┐   └───────┬───┐   │ ╵ │
│ · · · │ · │   │           │       │   │ · · · │ · │                       │       │       │           │   │   │ ╵ │
│ · ╶───┤ · │   └───────┐   ├───────┤   └───┬───┴───┼───────────┬───────┐   ├───┐   ╵   ╷   ├───────┐   │   │   │ ╵ │
│ · · · │ · │           │   │       │       │       │           │       │   │   │       │   │       │   │   │   │ ╵ │
├───╴ · ╵ · └───────┐   ╵   │   ╷   └───╴   ╵   ╷   ╵   ┌───╴   ╵   ╷   ╵   │   └───────┘   ╵   ╷   ╵   │   ╵   ╵ ╵ │
│ · · · · · · · · · │       │   │               │       │           │       │                   │       │         ╵ │
└───────────────────┴───────┴───┴───────────────┴───────┴───────────┴───────┴───────────────────┴───────┴──────── │ ┘

## Red

(imports maze generation code, see http://rosettacode.org/wiki/Maze_generation#Red)

Red ["Maze solver"]

do %mazegen.red
print [
"start:" start: random size - 1x1
"end:" end: random size - 1x1
]
isnew?: function [pos] [not find visited pos]
open?: function [pos d] [
o: pos/y * size/x + pos/x + 1
0 = pick walls/:o d
]
expand: function [pos][
either any [
all [pos/x > 0 isnew? p: pos - 1x0 open? p 1]
all [pos/x < (size/x - 1) isnew? p: pos + 1x0 open? pos 1]
all [pos/y > 0 isnew? p: pos - 0x1 open? p 2]
all [pos/y < (size/y - 1) isnew? p: pos + 0x1 open? pos 2]
][append visited p insert path p][remove path]
path/1
]
path: reduce [start]
visited: []
until [end = expand path/1]
print reverse path
Output:
Maze width: 15
Maze height: 15
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _
| |   |   |  _  |_  |    _ _ _|
|  _|_| |_ _| | |  _| |_  |   |
| |_   _|  _ _| |  _ _ _|_ _| |
|_  |_  | |  _ _|_ _|  _  |   |
|  _|  _| | |    _ _ _|_   _|_|
|_ _ _|  _ _| |_|  _ _  |_|   |
|  _|  _|_ _ _  | |  _|_ _ _| |
| |  _|  _ _  |_  |_   _  | | |
|  _|  _|  _|_  |_ _ _|_   _| |
|_  | |  _  |  _|  _ _  |_|   |
| |_ _| |   |_ _ _|   | |  _| |
| |  _ _| |_ _ _  | |_ _|_  |_|
| |_  | |_  |_ _ _|_ _ _  |_  |
|  _| |   |_  |   |   |  _|   |
|_ _ _ _|_ _|_ _|_ _|_ _ _ _|_|
start: 2x4 end: 12x3
2x4 3x4 3x3 2x3 2x2 3x2 3x1 3x0 4x0 4x1 5x1 5x0 6x0 7x0 7x1 7x2 7x3 6x3 5x3 5x4 5x5 4x5 3x5 3x6 2x6 2x7 1x7 1x8 0x8 0x9 1x9 1x10 2x10 2x9 2x8 3x8 3x7 4x7 5x7 6x7 6x8 7x8 7x9 6x9 6x10 7x10 8x10 8x9 9x9 10x9 11x9 11x10 11x11 10x11 10x10 9x10 9x11 9x12 10x12 11x12 12x12 12x13 11x13 11x14 12x14 13x14 13x13 14x13 14x12 13x12 13x11 12x11 12x10 13x10 13x9 14x9 14x8 14x7 14x6 14x5 13x5 13x6 12x6 11x6 11x5 10x5 9x5 8x5 8x6 8x7 7x7 7x6 6x6 6x5 6x4 7x4 8x4 9x4 10x4 10x3 11x3 12x3

## Ruby

This solution extends the maze generator script. To get a working script, copy & paste both parts into one file.

class Maze
# Solve via breadth-first algorithm.
# Each queue entry is a path, that is list of coordinates with the
# last coordinate being the one that shall be visited next.
def solve

# Clean up.
reset_visiting_state

# Enqueue start position.
@queue = []
enqueue_cell([], @start_x, @start_y)

# Loop as long as there are cells to visit and no solution has
# been found yet.
path = nil
until path || @queue.empty?
path = solve_visit_cell
end

if path
# Mark the cells that make up the shortest path.
for x, y in path
@path[x][y] = true
end
else
puts "No solution found?!"
end
end

private

# Maze solving visiting method.
def solve_visit_cell
# Get the next path.
path = @queue.shift
# The cell to visit is the last entry in the path.
x, y = path.last

# Have we reached the end yet?
return path  if x == @end_x && y == @end_y

# Mark cell as visited.
@visited[x][y] = true

for dx, dy in DIRECTIONS
if dx.nonzero?
# Left / Right
new_x = x + dx
if move_valid?(new_x, y) && !@vertical_walls[ [x, new_x].min ][y]
enqueue_cell(path, new_x, y)
end
else
# Top / Bottom
new_y = y + dy
if move_valid?(x, new_y) && !@horizontal_walls[x][ [y, new_y].min ]
enqueue_cell(path, x, new_y)
end
end
end

nil         # No solution yet.
end

# Enqueue a new coordinate to visit.
def enqueue_cell(path, x, y)
# Add new coordinates to the current path and enqueue the new path.
@queue << path + [[x, y]]
end
end

# Demonstration:
maze = Maze.new 20, 10
maze.solve
maze.print

Example output:

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

## Rust

This solution reuses the maze generator Rust code. The modified and new parts are marked with the label "MAZE SOLVING".Uses the rand library.

const WIDTH: usize = 16;
const HEIGHT: usize = 16;

#[derive(Clone, Copy, PartialEq)]
struct Cell {
col: usize,
row: usize,
}

impl Cell {
fn from(col: usize, row: usize) -> Cell {
Cell {col, row}
}
}

struct Maze {
cells: [[bool; HEIGHT]; WIDTH],         //cell visited/non visited
walls_h: [[bool; WIDTH]; HEIGHT + 1],   //horizontal walls existing/removed
walls_v: [[bool; WIDTH + 1]; HEIGHT],   //vertical walls existing/removed
}

impl Maze {

///Inits the maze, with all the cells unvisited and all the walls active
fn new() -> Maze {
Maze {
cells: [[true; HEIGHT]; WIDTH],
walls_h: [[true; WIDTH]; HEIGHT + 1],
walls_v: [[true; WIDTH + 1]; HEIGHT],
}
}

///Randomly chooses the starting cell
fn first(&mut self) -> Cell {
}

///Opens the enter and exit doors
fn open_doors(&mut self) {
let from_top: bool = self.thread_rng.gen();
let limit = if from_top { WIDTH } else { HEIGHT };
let door = self.thread_rng.gen_range(0, limit);
let exit = self.thread_rng.gen_range(0, limit);
if from_top {
self.walls_h[0][door] = false;
self.walls_h[HEIGHT][exit] = false;
} else {
self.walls_v[door][0] = false;
self.walls_v[exit][WIDTH] = false;
}
}

///Removes a wall between the two Cell arguments
fn remove_wall(&mut self, cell1: &Cell, cell2: &Cell) {
if cell1.row == cell2.row {
self.walls_v[cell1.row][if cell1.col > cell2.col { cell1.col } else { cell2.col }] = false;
} else {
self.walls_h[if cell1.row > cell2.row { cell1.row } else { cell2.row }][cell1.col] = false;
};
}

///Returns a random non-visited neighbor of the Cell passed as argument
fn neighbor(&mut self, cell: &Cell) -> Option<Cell> {
self.cells[cell.col][cell.row] = false;
let mut neighbors = Vec::new();
if cell.col > 0 && self.cells[cell.col - 1][cell.row] { neighbors.push(Cell::from(cell.col - 1, cell.row)); }
if cell.row > 0 && self.cells[cell.col][cell.row - 1] { neighbors.push(Cell::from(cell.col, cell.row - 1)); }
if cell.col < WIDTH - 1 && self.cells[cell.col + 1][cell.row] { neighbors.push(Cell::from(cell.col + 1, cell.row)); }
if cell.row < HEIGHT - 1 && self.cells[cell.col][cell.row + 1] { neighbors.push(Cell::from(cell.col, cell.row + 1)); }
if neighbors.is_empty() {
None
} else {
let next = neighbors.get(self.thread_rng.gen_range(0, neighbors.len())).unwrap();
self.remove_wall(cell, next);
Some(*next)
}
}

///Builds the maze (runs the Depth-first search algorithm)
fn build(&mut self) {
let mut cell_stack: Vec<Cell> = Vec::new();
let mut next = self.first();
loop {