Maze solving

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

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[edit]

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![edit]

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:

Screenshot from Atari 8-bit computer

Ada[edit]

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).

with Ada.Text_IO;

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
         Ada.Text_IO.Put_Line(Message);
      end if;
      for I in M'Range loop
         Ada.Text_IO.Put_Line(M(I));
      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
      Maze(I) := Ada.Text_IO.Get_Line;
   end loop;
   Maze(Y_Start)(X_Start)   := ' '; -- Start from
   Maze(Y_Finish)(X_Finish) := ' '; -- Go_To
   Output_Maze(Maze, "The Maze:");
   Ada.Text_IO.New_Line;

   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[edit]

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[edit]

Mazesolve bbc.gif

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[edit]

See Maze generation for combined gen/solve code.

C++[edit]

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

Maze solving cpp.png

#include <windows.h>
#include <iostream>
#include <string>

//--------------------------------------------------------------------------------------------------
using namespace std;

//--------------------------------------------------------------------------------------------------
const int BMP_SIZE = 512, CELL_SIZE = 8;

//--------------------------------------------------------------------------------------------------
enum directions { NONE, NOR = 1, EAS = 2, SOU = 4, WES = 8 };

//--------------------------------------------------------------------------------------------------
class myBitmap
{
public:
    myBitmap() : pen( NULL ) {}
    ~myBitmap()
    {
	DeleteObject( pen );
	DeleteDC( hdc );
	DeleteObject( bmp );
    }

    bool create( int w, int h )
    {
	BITMAPINFO	bi;
	ZeroMemory( &bi, sizeof( bi ) );
	bi.bmiHeader.biSize	   = sizeof( bi.bmiHeader );
	bi.bmiHeader.biBitCount	   = sizeof( DWORD ) * 8;
	bi.bmiHeader.biCompression = BI_RGB;
	bi.bmiHeader.biPlanes	   = 1;
	bi.bmiHeader.biWidth	   =  w;
	bi.bmiHeader.biHeight	   = -h;

	HDC dc = GetDC( GetConsoleWindow() );
	bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
	if( !bmp ) return false;

	hdc = CreateCompatibleDC( dc );
	SelectObject( hdc, bmp );
	ReleaseDC( GetConsoleWindow(), dc ); 
	width = w; height = h;

	return true;
    }

    void clear()
    {
	ZeroMemory( pBits, width * height * sizeof( DWORD ) );
    }

    void setPenColor( DWORD clr )
    {
	if( pen ) DeleteObject( pen );
	pen = CreatePen( PS_SOLID, 1, clr );
	SelectObject( hdc, pen );
    }

    void saveBitmap( string path )
    {
	BITMAPFILEHEADER fileheader;
	BITMAPINFO	 infoheader;
	BITMAP		 bitmap;
	DWORD		 wb;

	GetObject( bmp, sizeof( bitmap ), &bitmap );

	DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
	ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
	ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
	ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

	infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
	infoheader.bmiHeader.biCompression = BI_RGB;
	infoheader.bmiHeader.biPlanes = 1;
	infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
	infoheader.bmiHeader.biHeight = bitmap.bmHeight;
	infoheader.bmiHeader.biWidth = bitmap.bmWidth;
	infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

	fileheader.bfType    = 0x4D42;
	fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
	fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

	GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

	HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL );
	WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
	WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
	WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
	CloseHandle( file );

	delete [] dwpBits;
    }

    HDC getDC() const     { return hdc; }
    int getWidth() const  { return width; }
    int getHeight() const { return height; }

private:
    HBITMAP bmp;
    HDC	    hdc;
    HPEN    pen;
    void    *pBits;
    int	    width, height;
};
//--------------------------------------------------------------------------------------------------
class mazeGenerator
{
public:
    mazeGenerator()
    {
	_world = 0; 
	_bmp.create( BMP_SIZE, BMP_SIZE ); 
	_bmp.setPenColor( RGB( 0, 255, 0 ) ); 
    }

    ~mazeGenerator() { killArray(); }

    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[edit]

(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[edit]

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[edit]

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));
  ReadLn;
end;

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

EasyLang[edit]

Run it

size = 20
n = 2 * size + 1
endpos = n * n - 1
startpos = n + 2
# 
f = 100 / (n - 0.5)
len m[] n * n
# 
background 000
func show_maze . .
  clear
  for i = 1 to len m[]
    if m[i] = 0
      x = (i - 1) mod n
      y = (i - 1) div n
      color 777
      move x * f - f / 2 y * f - f / 2
      rect f * 1.5 f * 1.5
    .
  .
  sleep 0.001
.
offs[] = [ 1 n -1 (-n) ]
brdc[] = [ n - 2 -1 1 -1 ]
brdr[] = [ -1 n - 2 -1 1 ]
# 
func m_maze pos . .
  m[pos] = 0
  call show_maze
  d[] = [ 1 2 3 4 ]
  for i = 4 downto 1
    d = random i
    dir = d[d]
    d[d] = d[i]
    r = (pos - 1) div n
    c = (pos - 1) mod n
    posn = pos + 2 * offs[dir]
    if c <> brdc[dir] and r <> brdr[dir] and m[posn] <> 0
      posn = pos + 2 * offs[dir]
      m[(pos + posn) div 2] = 0
      call m_maze posn
    .
  .
.
func make_maze . .
  for i = 1 to len m[]
    m[i] = 1
  .
  call m_maze startpos
  m[endpos] = 0
.
call make_maze
call show_maze
# 
func 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 / 4
.
func solve dir0 pos . found .
  call mark pos 900
  sleep 0.05
  if pos = endpos
    found = 1
  else
    for dir = 1 to 4
      posn = pos + offs[dir]
      if dir <> dir0 and m[posn] = 0 and found = 0
        call solve (dir + 1) mod 4 + 1 posn found
        if found = 0
          call mark posn 777
          sleep 0.05
        .
      .
    .
  .
.
sleep 2
call solve 0 startpos found

EGL[edit]

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[edit]

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)))

(defun read-maze (file-name)
  (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[edit]

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 ).

-export( [task/0] ).

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.

task() ->
    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],
        receive
        {ok, Cells} -> {ok, Cells}
        end.
Output:
8> maze_solving:task().
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|     .   .   .   . | .   .   .   . | .   .   .   . |           |
+---+   +---+---+   +   +---+---+   +   +---+---+   +   +---+   +
| .   . |       | .   . |       | .   . |       | .   . |       |
+   +---+   +   +---+---+   +---+---+---+   +   +---+   +---+   +
| . |       |           |                   |       | . |   |   |
+   +---+   +---+---+   +   +   +---+---+   +---+---+   +   +---+
| .   . |   |       |   |   |   |           | .   . | . |       |
+   +   +   +   +   +---+   +   +---+---+---+   +   +   +---+   +
|   | . |       |           |             S   . | .   .     |   |
+---+   +---+---+   +---+---+---+   +---+---+---+   +---+---+   +
| .   . | .   . |       | .   . |   |           |   |           |
+   +   +   +   +---+   +   +   +   +   +---+   +   +   +---+---+
| . |   | . | . |       | . | . |   | G   . |   |   |           |
+   +---+   +   +---+---+   +   +---+---+   +   +---+---+---+   +
| .   .   . | .   .   .   . | .   .   .   . |                   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Frege[edit]

Translation of: Haskell
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[edit]

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

Haskell[edit]

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.

#!/usr/bin/runhaskell

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[edit]

The following code works with the solution from Maze Generation.

20x20 solved start @ red

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)
    thread {
        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[edit]

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[edit]

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
    {
        BufferedReader r =
            new BufferedReader (new InputStreamReader (f, "US-ASCII"));
        ArrayList<String> lines = new ArrayList<String>();
        String line;
        while ((line = r.readLine()) != null)
            lines.add (line);
        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[edit]

Maze java.png

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;
    LinkedList<Integer> solution;

    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);

        addMouseListener(new MouseAdapter() {
            @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;

                solution.add(newPos);
                maze[nr][nc] |= 16;

                animate();

                if (solve(newPos))
                    return true;

                animate();

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

        return false;
    }

    void animate() {
        try {
            Thread.sleep(50L);
        } 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.add(new MazeGenerator(24), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }
}

JavaScript[edit]

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>
<html><head><meta charset="UTF-8">
<title>Maze</title>
<script src="maze.js"></script></head><body onload="init()"></body></html>

Julia[edit]

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[edit]

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[edit]

Graph[edit]

Solving the maze generated in Maze_generation#Graph:

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

MathematicaMazeGraphSolving.png

Nim[edit]

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:
    result.cells.add newString(cols)
    result.hwalls.add h
    result.vwalls.add v


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:
      discard
    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:
        result.add HWall
      else:
        result.add HOpen
        if h notin {'-', '\0'}: result[^2] = h
    result.add RightCorner

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

  for _ in 1..maze.hwalls[0].len:
    result.add HWall
  result.add RightCorner


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

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[edit]

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[edit]

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
 
function heads()
    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)
if heads() then
    {dy,dx} = {rand(h)*2,heads()*w*4+1}
    grid[dy][dx] = ' '
else
    {dy,dx} = {heads()*h*2+1,rand(w)*4-1}
    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[edit]

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[edit]

(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[edit]

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 : Prolog-Maze-solved.jpg

PureBasic[edit]

;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
      AddElement(path())
      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
      
      AddElement(path())
      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[edit]

# 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[edit]

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 (read-maze file)
  (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[edit]

(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]);
	@neighbors.pick or DeadEnd;
    }
 
    sub move ($dir, @cur) {
	my ($x,$y) = @cur;
	given $dir {
	    when Up    { @maze[--$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y--][$x+1] -= W; }
	    when Down  { @maze[++$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y++][$x+1] -= W; }
	    when Left  { @maze[$y][--$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x--] -= N; }
	    when Right { @maze[$y][++$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x++] -= N; }
	} 
	@maze[$y][$x] = 0;
	[$x,$y];
    }
}
 
sub display (@maze) {
    for @maze -> @y {
	for @y.rotor(2) -> ($w, $c) {
	    print @ch[abs $w];
	    if $c >= 0 { print @ch[$c] x 3 } 
	    else { print ' ', @ch[abs $c], ' ' }
	}
	say @ch[@y[*-1]];
    }
}
 
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]);
	@neighbors.pick or DeadEnd;
    }

    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[edit]

(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[edit]

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[edit]

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

use rand::{thread_rng, Rng, rngs::ThreadRng};
 
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
    thread_rng: ThreadRng,                  //Random numbers generator
}
 
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],
            thread_rng: thread_rng(),
        }
    }
 
    ///Randomly chooses the starting cell
    fn first(&mut self) -> Cell {
        Cell::from(self.thread_rng.gen_range(0, WIDTH), self.thread_rng.gen_range(0, HEIGHT))
    }
 
    ///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 {
            while let Some(cell) = self.neighbor(&next) {
                cell_stack.push(cell);
                next = cell;
            }
            match cell_stack.pop() {
                Some(cell) => next = cell,
                None => break,
            }
        }
    }
 
    ///MAZE SOLVING: Find the starting cell of the solution
    fn solution_first(&self) -> Option<Cell> {
        for (i, wall) in self.walls_h[0].iter().enumerate() {
            if !wall {
                return Some(Cell::from(i, 0));
            }
        }
        for (i, wall) in self.walls_v.iter().enumerate() {
            if !wall[0] {
                return Some(Cell::from(0, i));
            }
        }
        None
    }

    ///MAZE SOLVING: Find the last cell of the solution
    fn solution_last(&self) -> Option<Cell> {
        for (i, wall) in self.walls_h[HEIGHT].iter().enumerate() {
            if !wall {
                return Some(Cell::from(i, HEIGHT - 1));
            }
        }
        for (i, wall) in self.walls_v.iter().enumerate() {
            if !wall[WIDTH] {
                return Some(Cell::from(WIDTH - 1, i));
            }
        }
        None
    }

    ///MAZE SOLVING: Get the next candidate cell
    fn solution_next(&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] && !self.walls_v[cell.row][cell.col] { neighbors.push(Cell::from(cell.col - 1, cell.row)); }
        if cell.row > 0 && self.cells[cell.col][cell.row - 1] && !self.walls_h[cell.row][cell.col] { neighbors.push(Cell::from(cell.col, cell.row - 1)); }
        if cell.col < WIDTH - 1 && self.cells[cell.col + 1][cell.row] && !self.walls_v[cell.row][cell.col + 1] { neighbors.push(Cell::from(cell.col + 1, cell.row)); }
        if cell.row < HEIGHT - 1 && self.cells[cell.col][cell.row + 1] && !self.walls_h[cell.row + 1][cell.col] { 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();
            Some(*next)
        }
    }

    ///MAZE SOLVING: solve the maze
    ///Uses self.cells to store the solution cells (true)
    fn solve(&mut self) {
        self.cells = [[true; HEIGHT]; WIDTH];
        let mut solution: Vec<Cell> = Vec::new();
        let mut next = self.solution_first().unwrap();
        solution.push(next);
        let last = self.solution_last().unwrap();
        'main: loop {
            while let Some(cell) = self.solution_next(&next) {
                solution.push(cell);
                if cell == last {
                    break 'main;
                }
                next = cell;
            }
            solution.pop().unwrap();
            next = *solution.last().unwrap();
        }
        self.cells = [[false; HEIGHT]; WIDTH];
        for cell in solution {
            self.cells[cell.col][cell.row] = true;
        }
    }

    ///MAZE SOLVING: Ask if cell is part of the solution (cells[col][row] == true)
    fn is_solution(&self, col: usize, row: usize) -> bool {
        self.cells[col][row]
    }

    ///Displays a wall
    ///MAZE SOLVING: Leave space for printing '*' if cell is part of the solution 
    /// (only when painting vertical walls)
    /// 
    // fn paint_wall(h_wall: bool, active: bool) {
    //     if h_wall {
    //         print!("{}", if active { "+---" } else { "+   " });
    //     } else {
    //         print!("{}", if active { "|   " } else { "    " });
    //     }
    // }
    fn paint_wall(h_wall: bool, active: bool, with_solution: bool) {
        if h_wall {
            print!("{}", if active { "+---" } else { "+   " });
        } else {
            print!("{}{}", if active { "|" } else { " " }, if with_solution { "" } else { "   " });
        }
    }
    
    ///MAZE SOLVING: Paint * if cell is part of the solution
    fn paint_solution(is_part: bool) {
        print!("{}", if is_part { " * " } else {"   "});
    }

    ///Displays a final wall for a row
    fn paint_close_wall(h_wall: bool) {
        if h_wall { println!("+") } else { println!() }
    }
 
    ///Displays a whole row of walls
    ///MAZE SOLVING: Displays a whole row of walls and, optionally, the included solution cells.
    // fn paint_row(&self, h_walls: bool, index: usize) {
    //     let iter = if h_walls { self.walls_h[index].iter() } else { self.walls_v[index].iter() };
    //     for &wall in iter {
    //         Maze::paint_wall(h_walls, wall);
    //     }
    //     Maze::paint_close_wall(h_walls);
    // }
    fn paint_row(&self, h_walls: bool, index: usize, with_solution: bool) {
        let iter = if h_walls { self.walls_h[index].iter() } else { self.walls_v[index].iter() };
        for (col, &wall) in iter.enumerate() {
            Maze::paint_wall(h_walls, wall, with_solution);
            if !h_walls && with_solution && col < WIDTH  {
                Maze::paint_solution(self.is_solution(col, index));
            }
        }
        Maze::paint_close_wall(h_walls);
    }

    ///Paints the maze
    ///MAZE SOLVING: Displaying the solution is an option
    // fn paint(&self) {
    //     for i in 0 .. HEIGHT {
    //         self.paint_row(true, i);
    //         self.paint_row(false, i);
    //     }
    //     self.paint_row(true, HEIGHT);
    // }
    fn paint(&self, with_solution: bool) {
        for i in 0 .. HEIGHT {
            self.paint_row(true, i, with_solution);
            self.paint_row(false, i, with_solution);
        }
        self.paint_row(true, HEIGHT, with_solution);
    }
}

fn main() {
    let mut maze = Maze::new();
    maze.build();
    maze.open_doors();
    
    println!("The maze:");
    maze.paint(false);

    maze.solve();
    println!("The maze, solved:");
    maze.paint(true);
}
Output:
The maze:
+---+---+---+---+---+---+---+---+---+---+---+---+---+   +---+---+
|       |       |                                       |       |
+   +---+   +   +   +---+   +   +---+---+---+---+---+   +   +   +
|           |       |       |   |               |   |       |   |
+---+---+---+---+   +   +---+   +   +---+---+   +   +---+---+   +
|               |   |       |   |   |       |   |               |
+   +---+---+   +   +---+   +   +   +   +   +   +   +---+---+---+
|           |   |   |       |   |       |   |   |               |
+   +---+   +   +   +   +---+---+---+---+   +   +---+---+---+   +
|   |       |   |   |       |           |   |           |   |   |
+---+   +---+   +---+---+   +   +---+   +   +---+---+   +   +   +
|       |                   |   |   |   |       |   |   |   |   |
+   +---+---+---+---+---+   +   +   +   +---+   +   +   +   +   +
|           |           |   |       |   |       |   |   |       |
+   +---+   +   +---+   +---+---+   +   +   +---+   +   +---+---+
|   |   |   |   |   |   |           |       |       |       |   |
+   +   +   +   +   +   +   +---+---+---+---+   +   +---+   +   +
|       |       |   |       |           |       |       |   |   |
+---+   +---+---+   +---+---+   +---+---+   +---+---+   +   +   +
|   |   |                   |                   |       |       |
+   +   +---+---+---+   +---+   +---+---+---+   +   +---+---+---+
|   |               |               |       |   |               |
+   +---+---+---+   +---+   +---+---+   +   +---+---+   +---+   +
|               |       |       |       |               |   |   |
+   +   +   +---+---+   +---+---+   +---+---+---+---+---+   +   +
|   |   |   |           |           |   |               |       |
+   +   +---+   +---+---+   +---+---+   +   +---+---+   +   +---+
|   |       |               |           |       |   |       |   |
+   +---+   +---+---+---+---+   +---+   +---+   +   +---+---+   +
|       |   |           |           |   |       |               |
+---+   +   +   +   +---+   +---+   +---+   +---+---+---+---+   +
|       |       |               |                               |
+   +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
The maze, solved:
+---+---+---+---+---+---+---+---+---+---+---+---+---+   +---+---+
|       |       |         *   *   *   *   *   *   *   * |       |
+   +---+   +   +   +---+   +   +---+---+---+---+---+   +   +   +
|           |       | *   * |   |               |   |       |   |
+---+---+---+---+   +   +---+   +   +---+---+   +   +---+---+   +
| *   *   *   * |   | *   * |   |   |       |   |               |
+   +---+---+   +   +---+   +   +   +   +   +   +   +---+---+---+
| *   *   * | * |   | *   * |   |       |   |   |               |
+   +---+   +   +   +   +---+---+---+---+   +   +---+---+---+   +
|   | *   * | * |   | *   * |           |   |           |   |   |
+---+   +---+   +---+---+   +   +---+   +   +---+---+   +   +   +
| *   * |     *   *   *   * |   |   |   |       |   |   |   |   |
+   +---+---+---+---+---+   +   +   +   +---+   +   +   +   +   +
| *         |           |   |       |   |       |   |   |       |
+   +---+   +   +---+   +---+---+   +   +   +---+   +   +---+---+
| * |   |   |   |   |   |           |       |       |       |   |
+   +   +   +   +   +   +   +---+---+---+---+   +   +---+   +   +
| *   * |       |   |       |           |       |       |   |   |
+---+   +---+---+   +---+---+   +---+---+   +---+---+   +   +   +
|   | * |                   |                   |       |       |
+   +   +---+---+---+   +---+   +---+---+---+   +   +---+---+---+
|   | *   *   *   * |               | *   * |   |     *   *   * |
+   +---+---+---+   +---+   +---+---+   +   +---+---+   +---+   +
| *   *         | *   * |       | *   * | *   *   *   * |   | * |
+   +   +   +---+---+   +---+---+   +---+---+---+---+---+   +   +
| * | * |   | *   *   * | *   *   * |   | *   *   *   * | *   * |
+   +   +---+   +---+---+   +---+---+   +   +---+---+   +   +---+
| * | *   * | *   *   *   * |           | *   * |   | *   * |   |
+   +---+   +---+---+---+---+   +---+   +---+   +   +---+---+   +
| *   * | * | *   *     | *   *   * |   | *   * |               |
+---+   +   +   +   +---+   +---+   +---+   +---+---+---+---+   +
| *   * | *   * | *   *   *     | *   *   *                     |
+   +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Swift[edit]

Works with: Swift version 3

The following requires the use of the implementation for generation task. Assumes there will be no circular paths through the maze as the problem suggests.

enum errors: Error {
    //Occurs when a start or end position is given that is outside of bounds
    case IndexOutsideMazeBoundary
}
///Used to solve any maze generated by the swift implementation of maze generator at:
///https://www.rosettacode.org/wiki/Maze_generation#Swift
class MazeSolver {
    ///your starting index position in the maze
    var startPos: (Int, Int)
    /// the end index position you are trying to reach within the maze
    var endPos: (Int, Int)
    /// a maze of [[INT]] where each value is between 1 and 14.
    /// each number representing a
    var maze: [[Int]]
    var visitedSpaces: [(Int, Int)]
    
    init(maze: [[Int]]) {
        self.startPos = (0, 0)
        self.endPos = (0, 0)
        /// a maze that consists of a array of ints from 1-14 organized to
        /// create a maze like structure.
        /// Each number represents where the walls and paths will be
        /// ex. 2 only has a path south and 12 has paths E or W
        self.maze = maze
        /// spaces each branch has visited to stop from searching previously explored
        /// areas of the maze
        self.visitedSpaces = []
    }

    /// determine if the user has previously visited the given location within the maze
    func visited(position: (Int, Int)) -> Bool {
        return visitedSpaces.contains(where: {$0 == position})
    }
    
    /// used to translate the mazes number scheme to a list of directions available
    ///  for each number. DirectionDiff for N would be  (0, -1) for example
    func getDirections(positionValue: Int) -> [(Int, Int)] {
        
        switch positionValue {
        case 1:
            return [Direction.north.diff]
        case 2:
            return [Direction.south.diff]
        case 3:
            return [Direction.north.diff, Direction.south.diff]
        case 4:
            return [Direction.east.diff]
        case 5:
            return [Direction.north.diff, Direction.east.diff]
        case 6:
            return [Direction.south.diff, Direction.east.diff]
        case 7:
            return [Direction.north.diff, Direction.east.diff, Direction.south.diff]
        case 8:
            return [Direction.west.diff]
        case 9:
            return [Direction.north.diff, Direction.west.diff]
        case 10:
            return [Direction.west.diff, Direction.south.diff]
        case 11:
            return [Direction.north.diff, Direction.south.diff, Direction.west.diff]
        case 12:
            return [Direction.west.diff, Direction.east.diff]
        case 13:
            return [Direction.north.diff, Direction.east.diff, Direction.west.diff]
        case 14:
            return [Direction.east.diff, Direction.south.diff, Direction.west.diff]
        default:
            return []
        }
    }
    
    /// calculate and return all paths branching from the current position that haven't been explored yet
    func availablePaths(currentPosition: (Int, Int), lastPos: (Int, Int)) -> [(Int, Int)] {
        /// all available paths to be returned
        var paths: [(Int, Int)] = []
        /// the maze contents at the given position (ie the maze number)
        let positionValue = maze[currentPosition.0][ currentPosition.1]
        /// used to build the new path positions and check them before they
        /// are added to paths
        var workingPos: (Int, Int)
        
        // is the maze at a dead end and not our first position
        if ([1, 2, 4, 8].contains(positionValue) && currentPosition != lastPos) {
            return []
        }
        
        /// the directions available based on the maze contents of our
        /// current position
        let directions: [(Int, Int)] = getDirections(positionValue: positionValue)
        
        /// build the paths
        for pos in directions {
            workingPos = (currentPosition.0 + pos.0, currentPosition.1 + pos.1)
            
            if (currentPosition == lastPos || (workingPos != lastPos && !visited(position: workingPos))) {
                paths.append(workingPos)
            }
        }
        
        return paths
    }
    
    /// prints a model of the maze with
    /// O representing the start point
    /// X representing the end point
    /// * representing traveled space
    /// NOTE: starting pos and end pos represent indexes and thus start at 0
    func solveAndDisplay(startPos: (Int, Int), endPos: (Int, Int)) throws {
        if (startPos.0 >= maze.count || startPos.1 >= maze[0].count) {
            throw errors.IndexOutsideMazeBoundary
        }
        
        /// the position you are beginning at in the maze
        self.startPos = startPos
        /// the position you wish to get to within the maze
        self.endPos = endPos
        /// spaces each branch has visited to stop from searching previously explored
        /// areas of the maze
        self.visitedSpaces = []
        
        self.displaySolvedMaze(finalPath: solveMaze(startpos: startPos, pathSoFar: [])!)
        
    }
    
    /// recursively solves our maze
    private func solveMaze(startpos: (Int, Int), pathSoFar: [(Int, Int)]) -> [(Int, Int)]? {
        /// marks our current position in the maze
        var currentPos: (Int, Int) = startpos
        /// saves the spaces visited on this current branch
        var currVisitedSpaces : [(Int, Int)] = [startpos]
        /// the final path (or the path so far if the end pos has not been reached)
        /// from the start position to the end position
        var finalPath: [(Int, Int)] = pathSoFar
        
        /// all possible paths from our current position that have not been explored
        var possiblePaths: [(Int, Int)] = availablePaths(currentPosition: startpos, lastPos: pathSoFar.last ?? startpos)
                
        // move through the maze until you come to a position that has been explored, the end position, or a dead end (the 
        // possible paths array is empty)
        while (!possiblePaths.isEmpty) {
            // found the final path
            guard (currentPos != self.endPos) else {
                finalPath.append(contentsOf: currVisitedSpaces)
                return finalPath
            }
            // multiple valid paths from current position found
            // recursively call new branches for each valid path
            if (possiblePaths.count > 1) {
                visitedSpaces.append(contentsOf: currVisitedSpaces)
                finalPath.append(contentsOf: currVisitedSpaces)
                // for each valid path recursively call each path
                // and if it contains the final path
                // ie it found the endpoint, return that path
                for pos in possiblePaths {
                    let path = solveMaze(startpos: pos, pathSoFar: finalPath)
                    
                    if (path != nil) {
                        return path
                    }
                }
                // otherwise this branch and it's sub-branches
                // are dead-ends so kill this branch
                return nil
            }
            // continue moving along the only path available
            else {
                // update current path to our only available next
                // position
                currentPos = possiblePaths[0]
                
                // calculate the available paths from our new
                // current position
                possiblePaths = availablePaths(currentPosition: currentPos, lastPos: currVisitedSpaces.last ?? currentPos)
                // update the visited spaces for this branch
                currVisitedSpaces.append(currentPos)
            }
        }
        
        // if our new current position is the endpos return our final path
        if (currentPos == self.endPos) {
            finalPath.append(contentsOf: currVisitedSpaces)
            return finalPath
        }
        else {
            return nil
        }
    }
    
    // Reference: https://www.rosettacode.org/wiki/Maze_generation#Swift
    // adapts the display method used in the swift implementation of the maze generator we used for this app to display the maze 
    // solved
    func displaySolvedMaze(finalPath: [(Int, Int)]) {
        /// all cells are 3 wide in the x axis
        let cellWidth = 3
        for j in 0..<y {
            // Draw top edge
            // if mark corner with +, add either (cell width) spaces or - to the topedge var dependin on if it is a wall or not
            var topEdge = ""
            for i in 0..<x {
                topEdge += "+"
                topEdge += String(repeating: (maze[i][j] & Direction.north.rawValue) == 0 ? "-" : " ", count: cellWidth)
            }
            topEdge += "+"
            print(topEdge)

            // Draw left edge
            //through the center of the cell if is a wall add |  if not a space
            // then if it is travelled add " * " otherwise just 3 spaces then
            //cap it with a | at the end for the right most wall
            var leftEdge = ""
            for i in 0..<x {
                leftEdge += (maze[i][j] & Direction.west.rawValue) == 0 ? "|" : " "
                
                if (finalPath.first! == (i, j)) {
                    leftEdge += " O "
                }
                else if (finalPath.last! == (i, j)) {
                    leftEdge += " X "
                }
                else {
                    if (finalPath.contains(where: {$0 == (i, j)})) {
                        leftEdge += " * "
                    }
                    else {
                        leftEdge += String(repeating: " ", count: cellWidth)
                    }
                }
            }
            leftEdge += "|"
            print(leftEdge)
        }

        // Draw bottom edge
        // adds + on corners and _ everywhere else
        var bottomEdge = ""
        for _ in 0..<x {
            bottomEdge += "+"
            bottomEdge += String(repeating: "-", count: cellWidth)
        }
        bottomEdge += "+"
        print(bottomEdge)
    }

}
example implementation using the aforementioned maze generator code for the swift implementation on rosettaCode

let x = 20
let y = 10
let maze = MazeGenerator(x, y)
var solver: MazeSolver =  MazeSolver(maze: maze.maze)
do {
         // making sure the start and end pos are within the maze boundary
         try solver.solveAndDisplay(startPos: (0, 0), endPos: (5, 5))
     }
     catch errors.IndexOutsideMazeBoundary {
         print("[ERROR] given start or end point outside of bounds")
     }
Output:

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | O * | | * * | * * | * * * * * * * * * | | +---+ + +---+ + + + + +---+---+---+---+---+---+---+ + +---+ + | * * | | * | * * | * | * | | * * | * * * * | | | + +---+---+ + +---+---+ + +---+ + + + +---+---+---+---+ + + | * | | * | | * * | * * * | * | * * | | | + +---+ + + + + +---+---+---+ + +---+---+---+ +---+---+---+ + | * | | | * * | * * | * * | * * * * | | | + + +---+ +---+ +---+ + + +---+---+---+---+ + +---+ +---+ + | * | | | * * | * | | * | * * * | * * | | | | | + + + +---+ +---+ + +---+ + +---+ + +---+ + + + +---+ | * | | | | X * | * * | * | * | * * | | | | | | + + +---+ +---+ +---+---+ + + +---+---+---+ + + +---+---+ + | * | | | | | * | * | * * * | | | | + +---+ +---+ +---+---+ + + +---+---+ + +---+---+---+ + + + | * * | | * * | * * * | | | | | +---+ + +---+---+---+---+---+---+---+ +---+---+ + +---+ + +---+ + | | * | | * * * * | * * | * * | | | | | | | + + +---+---+ +---+---+ + + +---+ + + + + +---+---+---+ + | * * * * | * * | * * * | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Tcl[edit]

Works with: Tcl version 8.6

This script assumes that the contents of the generation task have already been sourced. Note that the algorithm implemented here does not assume that the maze is free of circuits, and in the case that there are multiple routes, it finds the shortest one because it is a breadth-first search (by virtue of the queue variable being used as a queue).

oo::define maze {
    method solve {} {
	### Initialization of visited matrix and location/path queue
	set visited [lrepeat $x [lrepeat $y 0]]
	set queue {0 0 {}}

	### Loop to do the searching ###
	while 1 {
	    # Check for running out of path; an error in maze construction
	    if {[llength $queue] == 0} {
		error "cannot reach finish"
	    }
	    # Visit the next square from the queue
	    set queue [lassign $queue cx cy path]
	    if {[lindex $visited $cx $cy]} continue
	    lset visited $cx $cy 1
	    lappend path $cx $cy
	    # Check for reaching the goal
	    if {$cx == $x-1 && $cy == $y-1} break
	    # Add the square in each direction to the queue if a move there is legal
	    foreach {dx dy} {0 1  1 0  0 -1  -1 0} {
		set nx [expr {$cx + $dx}]; set ny [expr {$cy + $dy}]
		if {
		    $nx >= 0 && $nx < $x && $ny >= 0 && $ny < $y
		    && ($dx && idx($verti, min($cx,$nx), $cy) ||
			$dy && idx($horiz, $cx, min($cy,$ny)))
		} then {
		    lappend queue $nx $ny $path
		}
	    }
	}

	### Loop to set up the path rendering ###
	# (-2,-2) is just a marker that isn't next to the maze at all, so
	# guaranteeing the use of the last 'else' clause
	foreach {cx cy} $path {nx ny} [concat [lrange $path 2 end] -2 -2] {
	    if {$nx-$cx == 1} {
		lset content $cx $cy "v"
	    } elseif {$nx-$cx == -1} {
		lset content $cx $cy "^"
	    } elseif {$ny-$cy == -1} {
		lset content $cx $cy "<"
	    } else {
		lset content $cx $cy ">"
	    }
	}

	### Return the path ###
	return $path
    }
}

# Do the solution (we ignore the returned path here...)
m solve
# Print it out
puts [m view]

Example output:

+   +---+---+---+---+---+---+---+---+---+---+
| v     |                                   |
+   +---+   +---+---+---+---+---+---+---+   +
| v |       | >   v | >   v |   |           |
+   +   +---+   +   +   +   +   +   +---+   +
| v     | >   ^ | v | ^ | v |   |       |   |
+   +---+   +---+   +   +   +   +---+   +---+
| v | >   ^ | v   < | ^ | v |       |   |   |
+   +   +---+   +---+   +   +   +---+   +   +
| >   ^ | v   < | >   ^ | v |       |       |
+---+---+   +---+   +---+   +---+   +---+---+
| v   <   < | >   ^ | v   < | >   >   >   v |
+   +---+---+   +---+   +---+   +---+---+   +
| >   v |     ^   < | >   >   ^ |       | v |
+---+   +---+---+   +---+---+---+   +   +   +
|     >   >   >   ^ |               |     >  
+---+---+---+---+---+---+---+---+---+---+---+

Wren[edit]

Translation of: Kotlin
Library: Wren-ioutil
import "os" for Process
import "/ioutil" for File, FileUtil

/*
    * 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
    * character list, because we'll want mutability when drawing the solution later.
*/
var decimateHorizontally = Fn.new { |lines|
    var width = ((lines[0].count + 1)/2).floor
    var c = List.filled(lines.count, null)
    for (i in 0...lines.count) {
        c[i] = List.filled(width, null)
        for (j in 0...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.
*/
var solveMazeRecursively  // recursive function
solveMazeRecursively = Fn.new { |maze, x, y, d|
    var ok = false
    var i = 0
    while (i < 4 && !ok) {
        if (i != d) {
            // 0 = up, 1 = right, 2 = down, 3 = left
            if (i == 0) {
                if (maze[y - 1][x] == " ") ok = solveMazeRecursively.call(maze, x, y - 2, 2)
            } else if (i == 1) {
                if (maze[y][x + 1] == " ") ok = solveMazeRecursively.call(maze, x + 2, y, 3)
            } else if (i == 2) {
                if (maze[y + 1][x] == " ") ok = solveMazeRecursively.call(maze, x, y + 2, 0)
            } else if (i == 3) {
                if (maze[y][x - 1] == " ") ok = solveMazeRecursively.call(maze, x - 2, y, 1)
            }
        }
        i = i + 1
    }

    // 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] = "*"
        if (d == 0) {
            maze[y - 1][x] = "*"
        } else if (d == 1) {
            maze[y][x + 1] = "*"
        } else if (d == 2) {
            maze[y + 1][x] = "*"
        } else if (d == 3) {
            maze[y][x - 1] = "*"
        }
    }
    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.
*/
var solveMaze = Fn.new { |maze|
    solveMazeRecursively.call(maze, maze[0].count - 2, maze.count - 2, -1)
}

/*
    * Opposite of decimateHorizontally(). Adds extra characters to make
    * the maze "look right", and converts each line from a char list to a
    * string at the same time.
*/
var expandHorizontally = Fn.new { |maze|
    var tmp = List.filled(3, " ")
    var lines = List.filled(maze.count, null)
    for (i in 0...maze.count) {
        var sb = ""
        for (j in 0...maze[i].count) {
            if (j % 2 == 0) {
                sb = sb + maze[i][j]
            } else {
                for (k in 0..2) tmp[k] = maze[i][j]
                if (tmp[1] == "*") {
                    tmp[0] = " "
                    tmp[2] = " "
                }
                sb = sb + tmp.join()
            }
        }
        lines[i] = sb
    }
    return lines
}

/*
    * Accepts a maze as generated by:
    * http://rosettacode.org/wiki/Maze_generation#Wren
    * in a file whose name is specified as a command-line argument.
*/
var args = Process.arguments
if (args.count != 1) {
    System.print("The maze file to be read should be passed as a single command line argument.")
    return
}
if (!File.exists(args[0])) {
    System.print("Sorry %(args[0]) does not exist.")
    return
}
var lines = FileUtil.readLines(args[0]).where { |l| l != "" }.toList
var maze = decimateHorizontally.call(lines)
solveMaze.call(maze)
var solvedLines = expandHorizontally.call(maze)
System.print(solvedLines.join("\n"))
Output:

Using the same maze.txt as the Kotlin example:

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

zkl[edit]

This entry parses a maze generated by http://rosettacode.org/wiki/Maze_generation#zkl and chooses random start/end points. Parsing the maze and switching between row major (h,w) and row minor (x,y) makes for some pretty vile code.

ver,hor:=make_maze();  // see above link for this code

fcn munge(a,b){ String(a[0,2],b,a[3,*]) } // "+---" --> "+-*-"

fcn solveMaze(ver,hor, a,b, u,v, w,h){
   if (a==u and b==v) return(True);

   sh:=hor[b][a]; sv:=ver[b][a];
   hor[b][a]=munge(sh,"*"); ver[b][a]=munge(sv,"*");   // drop breadcrumb

   foreach dx,dy in (T( T(0,-1),T(1,0),T(0,1),T(-1,0) )){
      x:=a+dx; y:=b+dy; hy:=hor[y]; vy:=ver[y];
      if ( (0<=x<w) and (0<=y<h) and // (x,y) in bounds
	   (dx==0 or (dx== 1 and vy[x]=="    ") or   // horizontal
		     (dx==-1 and vy[a][0]==" " and vy[x][2]!="*")) and
	   (dy==0 or (dy== 1 and hy[x]=="+   ") or   // vertical
		     (dy==-1 and hor[b][a][1]==" " and hy[x][2]!="*"))
         )
      {
	 sh:=hy[x];
	 if(solveMaze(ver,hor, x,y, u,v, w,h)){
	    hy[x]=sh; // remove splat on wall but not floor while backing out
	    return(True); 
	 }
      }
   }
   hor[b][a]=sh; ver[b][a]=sv;  // pick up breadcrumb when backtracking
   return(False);
}

w:=(hor[0].len() - 1); h:=(hor.len() - 1);
startx:=(0).random(w); starty:=(0).random(h);
endx  :=(0).random(w); endy  :=(0).random(h);

sh:=hor[starty][startx];
if (not solveMaze(ver,hor, startx,starty, endx,endy, w,h))
   println("No solution path found.");
else{
   hor[starty][startx]=sh;
   ver[starty][startx]=munge(ver[starty][startx],"S");
   ver[endy][endx]    =munge(ver[endy][endx],"E");
   foreach a,b in (hor.zip(ver)) { println(a.concat(),"\n",b.concat()) }
}
Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|           | *   *         | *   * | *   *   *   *   *   * |   |
+---+---+   +   +   +---+   +   +   +   +   +---+---+---+   +   +
|           | * | * |       | * | *   * |   | *   *   * | * | S |
+   +---+   +   +   +---+---+   +---+---+   +   +---+   +   +   +
|   |       | * | * | *   * | *     |       | * | *   * | * | * |
+   +   +---+   +   +   +   +   +---+   +---+   +   +---+   +   +
|   |       | * | *   * | *   * |       | *   * | * | *   * | * |
+   +   +---+   +---+---+---+---+   +---+   +---+   +   +---+   +
|   |   | *   * |           |       | *   * |   | *   * | *   * |
+   +---+   +---+   +   +   +   +---+   +---+   +---+---+   +---+
| E   *   * |       |   |   |   |   | * | *   *   *   *   * |   |
+   +---+---+---+---+   +   +   +   +   +   +---+---+---+---+   +
|   |       |       |   |   |   |     *   * |               |   |
+   +   +   +   +   +   +   +   +---+---+---+   +---+---+   +   +
|       |       |       |   |                           |       |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+