Maze solving: Difference between revisions
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=={{header|Red}}== |
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(imports maze generation code, see http://rosettacode.org/wiki/Maze_generation#Red) |
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<lang Red>Red ["Maze solver"] |
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do %mazegen.red |
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print [ |
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"start:" start: random size - 1x1 |
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"end:" end: random size - 1x1 |
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] |
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isnew?: function [pos] [not find visited pos] |
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open?: function [pos d] [ |
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o: pos/y * size/x + pos/x + 1 |
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0 = pick walls/:o d |
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] |
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expand: function [pos][ |
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either any [ |
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all [pos/x > 0 isnew? p: pos - 1x0 open? p 1] |
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all [pos/x < (size/x - 1) isnew? p: pos + 1x0 open? pos 1] |
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all [pos/y > 0 isnew? p: pos - 0x1 open? p 2] |
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all [pos/y < (size/y - 1) isnew? p: pos + 0x1 open? pos 2] |
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][append visited p insert path p][remove path] |
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path/1 |
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] |
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path: reduce [start] |
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visited: [] |
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until [end = expand path/1] |
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print reverse path</lang> |
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{{out}} |
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<pre>Maze width: 15 |
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Maze height: 15 |
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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |
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|_ _ _ _|_ _|_ _|_ _|_ _ _ _|_| |
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start: 2x4 end: 12x3 |
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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 |
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</pre> |
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=={{header|Ruby}}== |
=={{header|Ruby}}== |
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Revision as of 10:49, 11 September 2020
You are encouraged to solve this task according to the task description, using any language you may know.
For a maze generated by this task, write a function that finds (and displays) the shortest path between two cells. Note that because these mazes are generated by the Depth-first search algorithm, they contain no circular paths, and a simple depth-first tree search can be used.
Ada
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).
<lang Ada>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;</lang>
- Example output
- :
(using a maze generated by the Ada implementation of the maze generation task as the input):
> ./maze_solver < maze.txt The Maze: +- -+---+---+---+---+---+---+---+---+---+---+ | | | + + +---+---+---+---+---+---+---+ + + | | | | | | + +---+---+ +---+ + +---+---+---+ + | | | | | | | +---+ +---+---+ +---+ + + +---+ + | | | | | | | + +---+ +---+---+ +---+ + + +---+ | | | | | | +---+---+ + +---+---+---+---+ +---+ + | | | | | | + + +---+---+ +---+ + +---+---+ + | | | | | + +---+ +---+---+---+---+---+---+---+ + | | | +---+---+---+---+---+---+---+---+---+---+- -+ Solution found! +-*-+---+---+---+---+---+---+---+---+---+---+ | * * * * * * * * * * * * * * * * * * * | | + + +---+---+---+---+---+---+---+ * + + | | | | * * * * * * * | | + +---+---+ +---+ + * +---+---+---+ + | | | | * | | | +---+ +---+---+ +---+ * + + +---+ + | | | * * * | | | | + +---+ +---+---+ * +---+ + + +---+ | | | * * * * * | | | +---+---+ + * +---+---+---+---+ +---+ + | | * * * | * * * | | | + + +---+---+ * +---+ * + * +---+---+ + | | | * * * * * | * * * * * * * | + +---+ +---+---+---+---+---+---+---+ * + | | * | +---+---+---+---+---+---+---+---+---+---+-*-+
AutoHotkey
Generator and solver combined. <lang AutoHotkey>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</lang>
Outputs:
+---+---+---+---+---+---+---+---+---+---+ | ¦¦¦¦¦ | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦¦¦¦¦ | +---+ ¦ +---+ ¦ + ¦ +---+ ¦ +---+---+ ¦ + | | ¦ | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ | + + ¦ + ¦ +---+---+---+---+ ¦ + ¦ + ¦ + | ¦¦¦¦¦ | ¦ | ¦¦¦¦¦¦¦¦¦¦¦¦¦ | ¦ | ¦¦¦¦¦ | + ¦ +---+ ¦ + ¦ +---+---+ ¦ + ¦ +---+---+ | ¦ | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | | + ¦ +---+---+---+ ¦ +---+---+---+ ¦ + + | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | +---+ ¦ + ¦ +---+---+ +---+---+---+ ¦ + | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | | ¦¦¦¦¦ | | ¦ | + ¦ +---+---+---+ ¦ +---+ ¦ + ¦ + + ¦ + | ¦¦¦¦¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ | ¦¦¦¦¦ | +---+ ¦ + ¦ +---+---+ ¦ +---+ ¦ + ¦ +---+ | ¦¦¦¦¦ | ¦ | ¦¦¦¦¦¦¦¦¦ | ¦¦¦¦¦ | ¦ | | + ¦ +---+ ¦ + ¦ +---+---+ ¦ +---+ ¦ + + | ¦ | ¦¦¦¦¦ | ¦¦¦¦¦ | | ¦¦¦¦¦ | + ¦ +---+---+---+---+ ¦ +---+ +---+ ¦ + | ¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦ | ¦ | +---+---+---+---+---+---+---+---+---+---+
BBC BASIC
Maze generation code also included. <lang bbcbasic> MazeWidth% = 11
MazeHeight% = 9
MazeCell% = 50
VDU 23,22,MazeWidth%*MazeCell%/2+3;MazeHeight%*MazeCell%/2+3;8,16,16,128
VDU 23,23,3;0;0;0; : REM Line thickness
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</lang>
C
See Maze generation for combined gen/solve code.
C++
Generator and solver combined. The generator is the same found in Maze generation
<lang cpp>
- include <windows.h>
- include <iostream>
- include <string>
//-------------------------------------------------------------------------------------------------- using namespace std;
//-------------------------------------------------------------------------------------------------- const int BMP_SIZE = 512, CELL_SIZE = 8;
//-------------------------------------------------------------------------------------------------- enum directions { NONE, NOR = 1, EAS = 2, SOU = 4, WES = 8 };
//-------------------------------------------------------------------------------------------------- class myBitmap { public:
myBitmap() : pen( NULL ) {}
~myBitmap()
{
DeleteObject( pen ); DeleteDC( hdc ); DeleteObject( bmp );
}
bool create( int w, int h )
{
BITMAPINFO bi; ZeroMemory( &bi, sizeof( bi ) ); bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h;
HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false;
hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc ); width = w; height = h;
return true;
}
void clear()
{
ZeroMemory( pBits, width * height * sizeof( DWORD ) );
}
void setPenColor( DWORD clr )
{
if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, 1, clr ); SelectObject( hdc, pen );
}
void saveBitmap( string path )
{
BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD wb;
GetObject( bmp, sizeof( bitmap ), &bitmap );
DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );
delete [] dwpBits;
}
HDC getDC() const { return hdc; }
int getWidth() const { return width; }
int getHeight() const { return height; }
private:
HBITMAP bmp; HDC hdc; HPEN pen; void *pBits; int width, height;
}; //-------------------------------------------------------------------------------------------------- class mazeGenerator { public:
mazeGenerator()
{
_world = 0; _bmp.create( BMP_SIZE, BMP_SIZE ); _bmp.setPenColor( RGB( 0, 255, 0 ) );
}
~mazeGenerator() { killArray(); }
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;
} //-------------------------------------------------------------------------------------------------- </lang>
Clojure
<lang clojure>(ns small-projects.find-shortest-way
(:require [clojure.string :as str]))
- Misk functions
(defn cell-empty? [maze coords]
(= :empty (get-in maze coords)))
(defn wall? [maze coords]
(= :wall (get-in maze coords)))
(defn track? [maze coords]
(= :track (get-in maze coords)))
(defn get-neighbours [maze [y x cell]]
[[y (dec x)] [(inc y) x] [y (inc x)] [(dec y) x]])
(defn get-difference [coll1 filter-coll]
(filter #(not (contains? filter-coll %)) coll1))
(defn get-empties [maze cell]
(->> (get-neighbours maze cell)
(filter (partial cell-empty? maze))))
(defn possible-ways [maze cell filter-coll]
(-> (get-empties maze cell)
(get-difference filter-coll)))
(defn replace-cells [maze coords v]
(if (empty? coords) maze (recur (assoc-in maze (first coords) v) (rest coords) v)))
- Print and parse functions
(def cell-code->str
[" " " " " " " " "· " "╵ " "╴ " "┘ " " " " " " " " " "╶─" "└─" "──" "┴─" " " " " " " " " "╷ " "│ " "┐ " "┤ " " " " " " " " " "┌─" "├─" "┬─" "┼─" " " " " " " " " "■ " "╹ " "╸ " "┛ " " " " " " " " " "╺━" "┗━" "━━" "┻━" " " " " " " " " "╻ " "┃ " "┓ " "┫ " " " " " " " " " "┏━" "┣━" "┳━" "╋━" " "])
(defn get-cell-code [maze coords]
(let [mode (if (track? maze coords) 1 0)
check (if (zero? mode) wall? track?)]
(transduce
(comp
(map (partial check maze))
(keep-indexed (fn [idx test] (when test idx)))
(map (partial bit-shift-left 1)))
(completing bit-or)
(bit-shift-left mode 5)
(sort (conj (get-neighbours maze coords) coords)))))
(defn code->str [cell-code]
(nth cell-code->str cell-code))
(defn maze->str-symbols [maze]
(for [y (range (count maze))]
(for [x (range (count (nth maze y)))]
(code->str (get-cell-code maze [y x])))))
(defn maze->str [maze]
(->> (maze->str-symbols maze)
(map str/join)
(str/join "\n")))
(defn parse-pretty-maze [maze-str]
(->> (str/split-lines maze-str)
(map (partial take-nth 2))
(map (partial map #(if (= \space %) :empty :wall)))
(map vec)
(vec)))
- Core
(defn find-new-border [maze border old-border]
(apply conj (map (fn [cell]
(zipmap (possible-ways maze cell (conj border old-border))
(repeat cell)))
(keys border))))
(defn backtrack [visited route]
(let [cur-cell (get visited (first route))]
(if (= cur-cell :start)
route
(recur visited (conj route cur-cell)))))
(defn breadth-first-search [maze start-cell end-cell]
(loop [visited {start-cell :start}
border {start-cell :start}
old-border {start-cell :start}]
(if (contains? old-border end-cell)
(backtrack visited (list end-cell))
(recur
(conj visited border)
(find-new-border maze border old-border)
border))))
(def maze (parse-pretty-maze maze-str))
(def solved-maze
(replace-cells maze (breadth-first-search maze [1 1] [19 19]) :track))
(println (maze->str solved-maze))</lang>
- Input:
┌───────────┬───────┬───────┬───────────┐ │ │ │ │ │ │ ╶───────┘ ╷ ╵ ╷ ╵ ┌───╴ │ │ │ │ │ │ │ ╶───────┬───┴───┬───┴───┬───┘ ╷ │ │ │ │ │ │ │ ├───────╴ │ ╷ ╵ ╷ │ ┌───┘ │ │ │ │ │ │ │ │ │ ┌───┬───┘ ├───────┤ │ ├───────┤ │ │ │ │ │ │ │ │ │ ╵ ╵ ╶───┴───┐ │ │ ╵ ╷ │ │ │ │ │ │ │ ├───────────────┐ ╵ │ │ ╶───┤ │ │ │ │ │ │ │ │ ╶───┐ ┌───┴───╴ │ │ ┌───┘ │ │ │ │ │ │ │ │ ├───╴ │ │ ╶───┬───┤ └───┤ ╶───┤ │ │ │ │ │ │ │ │ ╶───┤ └───╴ ╵ └───┐ └───╴ │ │ │ │ │ └───────┴───────────────────┴───────────┘
- Output:
┌───────────┬───────┬───────┬───────────┐ │ ╻ │ │ │ │ │ ┃ ╶───────┘ ╷ ╵ ╷ ╵ ┌───╴ │ │ ┃ │ │ │ │ │ ┃ ╶───────┬───┴───┬───┴───┬───┘ ╷ │ │ ┗━━━━━━━┓ │ ┏━━━┓ │ ┏━━━┓ │ │ │ ├───────╴ ┃ │ ┃ ╷ ┃ ╵ ┃ ╷ ┃ │ ┌───┘ │ │ ┏━━━━━━━┛ │ ┃ │ ┗━━━┛ │ ┃ │ │ │ │ ┃ ┌───┬───┘ ┃ ├───────┤ ┃ │ ├───────┤ │ ┃ │ │ ┏━━━┛ │ │ ┃ │ │ │ │ ┃ ╵ ╵ ┃ ╶───┴───┐ │ ┃ │ ╵ ╷ │ │ ┗━━━━━━━┛ │ │ ┃ │ │ │ ├───────────────┐ ╵ │ ┃ │ ╶───┤ │ │ │ │ ┃ │ │ │ │ ╶───┐ ┌───┴───╴ │ ┃ │ ┌───┘ │ │ │ │ │ ┃ │ │ │ ├───╴ │ │ ╶───┬───┤ ┃ └───┤ ╶───┤ │ │ │ │ │ ┗━━━┓ │ │ │ ╶───┤ └───╴ ╵ └───┐ ┃ └───╴ │ │ │ │ ┗━━━━━━━╸ │ └───────┴───────────────────┴───────────┘
D
This entry reads a maze generated by http://rosettacode.org/wiki/Maze_generation#D and chooses two random start-end points. <lang d>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);
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | . . . . . . . . . | + + +---+---+ + +---+ + . +---+---+---+ . + + | | | | . . . | | . | | +---+---+---+---+---+---+---+ +---+ . +---+ + . +---+ | | | | . . . . . | E | + +---+---+---+ + + +---+ +---+---+ . +---+---+ | | . . . | | | | | . . . | | +---+ + . + . + + +---+---+---+ + +---+ . + + | | . | . | | . . . | | . . . | | + +---+ . + . +---+---+ . + . +---+---+---+ . +---+ + | . . . . . | . | . . . . . | . . . . . . . | . . . . . | + . +---+---+ . + . +---+---+---+---+---+ . +---+---+ . + | . . . | | . . . | | | . | . | +---+ . + +---+---+ + +---+ + + . +---+---+ . + | | . . . . . . . | | | | . | . . . . . | + +---+---+---+ . + +---+ +---+ + . + . +---+---+ | | . . . . . . . | | | | | . . . | | + + . +---+---+---+---+ +---+ + +---+---+ + + | . . . . . . S | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+
EasyLang
<lang>intvars size = 20 n = 2 * size + 1 endpos = n * n - n - 3 startpos = 2 * n + 2 f# = 100 / n
func draw_square pos col . .
x = pos mod n y = pos / n color col move x * f# y * f# rect f# * 1.05 f# * 1.05
. func mark pos . .
x = pos mod n y = pos / n color 900 move x * f# + f# / 2 y * f# + f# / 2 circle f# / 4
. len m[] n * n
func show_maze . .
color 000
rect 100 100
for i range len m[]
if m[i] = 0
call draw_square i 777
.
.
call draw_square startpos 900
. offs[] = [ 1 n -1 (-n) ] func visited pos . r .
r = 0 for i range 4 r += m[pos + 2 * offs[i]] .
. func m_maze pos . .
m[pos] = 0
repeat
call visited pos res
until res = 0
dir = random 4
posn = pos + 2 * offs[dir]
if m[posn] <> 0
m[pos + offs[dir]] = 0
call m_maze posn
.
.
. func make_maze . .
for i range len m[] m[i] = 1 . for i range n m[i] = 0 m[n * i] = 0 m[n * i + n - 1] = 0 m[n * (n - 1) + i] = 0 . call m_maze startpos m[endpos] = 0
. func solve dir0 pos . found .
call mark pos
sleep 0.05
if pos = endpos
found = 1
else
for dir range 4
posn = pos + offs[dir]
if dir <> dir0 and m[posn] = 0 and found = 0
call solve (dir + 2) mod 4 posn found
if found = 0
call draw_square posn 777
sleep 0.05
.
.
.
.
.
call make_maze call show_maze sleep 1 call solve -1 startpos found</lang>
EGL
<lang EGL>program MazeGenAndSolve
// First and last columns/rows are "dead" cells. Makes generating // a maze with border walls much easier. Therefore, a visible // 20x20 maze has a maze size of 22. mazeSize int = 22;
south boolean[][]; west boolean[][]; visited boolean[][];
// Solution variables solution Dictionary; done boolean; startingRow, startingCol, endingRow, endingCol int;
function main()
initMaze();
generateMaze();
drawMaze(false); // Draw maze without solution
solveMaze();
drawMaze(true); // Draw maze with solution
end
private function initMaze()
visited = createBooleanArray(mazeSize, mazeSize, false);
// Initialize border cells as already visited
for(col int from 1 to mazeSize)
visited[col][1] = true;
visited[col][mazeSize] = true;
end
for(row int from 1 to mazeSize)
visited[1][row] = true;
visited[mazeSize][row] = true;
end
// Initialize all walls as present
south = createBooleanArray(mazeSize, mazeSize, true);
west = createBooleanArray(mazeSize, mazeSize, true);
end
private function createBooleanArray(col int in, row int in, initialState boolean in) returns(boolean[][])
newArray boolean[][] = new boolean[0][0];
for(i int from 1 to col)
innerArray boolean[] = new boolean[0];
for(j int from 1 to row)
innerArray.appendElement(initialState);
end
newArray.appendElement(innerArray);
end
return(newArray);
end
private function createIntegerArray(col int in, row int in, initialValue int in) returns(int[][])
newArray int[][] = new int[0][0];
for(i int from 1 to col)
innerArray int[] = new int[0];
for(j int from 1 to row)
innerArray.appendElement(initialValue);
end
newArray.appendElement(innerArray);
end
return(newArray);
end
private function generate(col int in, row int in)
// Mark cell as visited
visited[col][row] = true;
// Keep going as long as there is an unvisited neighbor
while(!visited[col][row + 1] || !visited[col + 1][row] ||
!visited[col][row - 1] || !visited[col - 1][row])
while(true)
r float = MathLib.random(); // Choose a random direction
case
when(r < 0.25 && !visited[col][row + 1]) // Go south
south[col][row] = false; // South wall down
generate(col, row + 1);
exit while;
when(r >= 0.25 && r < 0.50 && !visited[col + 1][row]) // Go east
west[col + 1][row] = false; // West wall of neighbor to the east down
generate(col + 1, row);
exit while;
when(r >= 0.5 && r < 0.75 && !visited[col][row - 1]) // Go north
south[col][row - 1] = false; // South wall of neighbor to the north down
generate(col, row - 1);
exit while;
when(r >= 0.75 && r < 1.00 && !visited[col - 1][row]) // Go west
west[col][row] = false; // West wall down
generate(col - 1, row);
exit while;
end
end
end
end
private function generateMaze()
// Pick random start position (within the visible maze space)
randomStartCol int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
randomStartRow int = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
generate(randomStartCol, randomStartRow);
end
private function drawMaze(solve boolean in)
line string;
// Iterate over wall arrays (skipping dead border cells as required).
// Construct a row at a time and output to console.
for(row int from 1 to mazeSize - 1)
if(row > 1)
line = "";
for(col int from 2 to mazeSize)
if(west[col][row])
line ::= cellTest(col, row, solve);
else
line ::= cellTest(col, row, solve);
end
end
Syslib.writeStdout(line);
end
line = "";
for(col int from 2 to mazeSize - 1)
if(south[col][row])
line ::= "+---";
else
line ::= "+ ";
end
end
line ::= "+";
SysLib.writeStdout(line);
end
end
private function cellTest(col int in, row int in, solve boolean in) returns(string)
wall string;
// Determine cell wall structure. If in solve mode, show start, end and
// solution markers.
if(!solve)
if(west[col][row])
wall = "| ";
else
wall = " ";
end
else
if(west[col][row])
case
when(col == startingCol and row == startingRow)
wall = "| S ";
when(col == endingCol and row == endingRow)
wall = "| E ";
when(solution.containsKey("x=" + col + "y=" + row))
wall = "| * ";
otherwise
wall = "| ";
end
else
case
when(col == startingCol and row == startingRow)
wall = " S ";
when(col == endingCol and row == endingRow)
wall = " E ";
when(solution.containsKey("x=" + col + "y=" + row))
wall = " * ";
otherwise
wall = " ";
end
end
end
return(wall); end
private function solve(col int in, row int in)
if(col == 1 || row == 1 || col == mazeSize || row == mazeSize)
return;
end
if(done || visited[col][row])
return;
end
visited[col][row] = true;
solution["x=" + col + "y=" + row] = true;
// Reached the end point
if(col == endingCol && row == endingRow)
done = true;
end
if(!south[col][row]) // Go South
solve(col, row + 1);
end
if(!west[col + 1][row]) // Go East
solve(col + 1, row);
end
if(!south[col][row - 1]) // Go North
solve(col, row - 1);
end
if(!west[col][row]) // Go West
solve(col - 1, row);
end
if(done)
return;
end
solution.removeElement("x=" + col + "y=" + row);
end
private function solveMaze()
for(col int from 1 to mazeSize)
for(row int from 1 to mazeSize)
visited[col][row] = false;
end
end
solution = new Dictionary(false, OrderingKind.byInsertion);
done = false;
// Pick random start position on first visible row
startingCol = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
startingRow = 2;
// Pick random end position on last visible row
endingCol = MathLib.floor((MathLib.random() *(mazeSize - 2)) + 2);
endingRow = mazeSize - 1;
solve(startingCol, startingRow); end
end</lang>
- Output example (for 10x10 maze):
+---+---+---+---+---+---+---+---+---+---+ | | | | | + +---+ +---+---+ + + +---+ + | | | | | | | | +---+ + +---+ +---+---+ + + + | | | | | | | + +---+---+ + + + +---+---+ + | | | | | | | + + + + + +---+---+---+ + + | | | | | | | + +---+---+---+ + +---+ +---+ + | | | | | | +---+ +---+ +---+ + +---+ + + | | | | | | | + + + +---+ +---+---+---+---+ + | | | | | | | + + + + +---+---+---+---+ + + | | | | | | | | + + + + +---+---+ + + + + | | | | +---+---+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+---+---+ | | * * S | | | + +---+ +---+---+ + + +---+ + | | * | | | | | | +---+ + +---+ +---+---+ + + + | | * * | * * | | | | + +---+---+ + + + +---+---+ + | | * * | * | * | * * * * | | + + + + + +---+---+---+ + + | * * | * * | * | | * * | | + +---+---+---+ + +---+ +---+ + | * * | * * | | * * | | +---+ +---+ +---+ + +---+ + + | | * | * * | * * * | | | + + + +---+ +---+---+---+---+ + | | * | * | | * * * * * | | + + + + +---+---+---+---+ + + | | * | * | | * * | * | | + + + + +---+---+ + + + + | * * | E | * * | +---+---+---+---+---+---+---+---+---+---+
Emacs Lisp
file: maze.el <lang lisp>(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)))
(provide 'maze) </lang> file: maze-solve <lang lisp>#!/usr/bin/env emacs -script
- -*- lexical-binding
- t -*-
- > Solve mazes generated by maze-generator.
- > Example
- ./maze-solve maze.txt
(add-to-list 'load-path (file-name-directory load-file-name)) (require 'maze)
(solve (elt command-line-args-left 0)) </lang>
- Output:
+ +---+---+---+---+---+---+---+---+---+ | * * * | | | | +---+---+ + +---+---+ +---+---+ + | | * | | | | | | + + + + +---+ + + +---+ + | | * * * * | | | +---+---+---+---+---+ +---+---+ + + | | | | | * * | | | | + +---+ + + +---+ + + + + | | | | | * * | | + + + + +---+ + + +---+ + | | | | | | * * * | + + + +---+---+---+ +---+---+ + | | | | | | * | + + +---+---+ + + + + + + | | | | | | * | + + + +---+---+---+---+---+ + + | | | | | * | + +---+---+ + + +---+---+---+ + | | | * | +---+---+---+---+---+---+---+---+---+ +
Erlang
Using the maze from Maze_generation. When the path splits each possibility gets its own process that checks if it is the correct one or a dead end. It is intentional that the receive statement in loop_stop/5 only selects successful result. <lang Erlang> -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.
</lang>
- Output:
8> maze_solving:task(). +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | . . . . | . . . . | . . . . | | +---+ +---+---+ + +---+---+ + +---+---+ + +---+ + | . . | | . . | | . . | | . . | | + +---+ + +---+---+ +---+---+---+ + +---+ +---+ + | . | | | | | . | | | + +---+ +---+---+ + + +---+---+ +---+---+ + +---+ | . . | | | | | | | . . | . | | + + + + + +---+ + +---+---+---+ + + +---+ + | | . | | | S . | . . | | +---+ +---+---+ +---+---+---+ +---+---+---+ +---+---+ + | . . | . . | | . . | | | | | + + + + +---+ + + + + +---+ + + +---+---+ | . | | . | . | | . | . | | G . | | | | + +---+ + +---+---+ + +---+---+ + +---+---+---+ + | . . . | . . . . | . . . . | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Frege
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.
<lang frege>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</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | * | * * * * * | | | | | | + * +---+---+ * +---+ * +---+ + + + +---+---+---+ + + + + + | * | * * * * * | | * | | | | * * * * * | | | | + * + * +---+---+ + * + +---+ +---+---+ * +---+ * + +---+---+---+ + | * * * | | | * | | | * * * * * | * * * | | * * * * * | | +---+---+ + + + * + + +---+ * +---+---+ * +---+---+ * +---+ * + + | | | * | | | * | | * * * | * * * * * | * * * | | + + +---+---+---+ * + +---+ + * + + * +---+ * +---+---+ * +---+ + | | | * * * * * * * | | * | * * * * * | | * * * * * | + + + * +---+---+---+---+---+---+ * +---+---+---+---+ + +---+---+ * + | | | * * * | * * * * * | * * * | * * * | * * * | | | * | + +---+---+ * + * +---+ * + * + * +---+ * + * + * +---+ +---+ + + * + | | | * | * | * * * | * | * * * | * * * | * * * | | | | | * | + + + + * + * + * +---+ * +---+ * +---+---+---+ * + + + +---+ * + | | * * * | * * * * * | * * * * * * * * * | | * | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ runtime 0.249 wallclock seconds.
Go
Generates maze, picks start and finish cells randomly, solves, prints. <lang go>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'
}</lang>
- Example output
- :
+---+---+---+---+---+---+---+ | | v < < < < < < | + +---+ + v + +---+ ^ + | | F < < | | ^ | +---+---+---+---+ +---+ ^ + | | | ^ | + +---+---+ +---+ + ^ + | | | S | +---+---+---+---+---+---+---+
Haskell
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.
<lang haskell>#!/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_
</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+ | * | | | | + * + +---+ + +---+ +---+ +---+ + | * | | | | | | | + * +---+ + +---+ +---+ +---+---+ + | * | | | | | | + * +---+---+---+ +---+ + + + + + | * * * * * * * | | | | | +---+---+---+ * +---+ +---+---+---+ + + | | * * * | | | | | + +---+ +---+ * + + +---+ + +---+ | | | * * * | | | | | +---+---+ + * +---+---+---+ + +---+ + | | * * * * * | | | | + +---+---+---+---+ * +---+ +---+---+ + | * * * * * * * * * * * | +---+---+---+---+---+---+---+---+---+---+---+
Icon and Unicon
The following code works with the solution from Maze Generation.
Replace the main with this: <lang Icon>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</lang>
And include this after the Generator and Display procedures. <lang Icon>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</lang>
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.
<lang unicon>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</lang>
J
Due to reports that the program failed, the generation and solver are shown together. The display verb was extended to include a dyadic definition. The complete program was tested with j 8.0.2 on linux using no profile, the command $ ijconsole -jprofile <lang J> maze=:4 :0
assert.0<:n=.<:x*y
horiz=. 0$~x,y-1
verti=. 0$~(x-1),y
path=.,:here=. ?x,y
unvisited=.0 (<here+1)} 0,0,~|:0,0,~1$~y,x
while.n do.
neighbors=. here+"1 (,-)=0 1
neighbors=. neighbors #~ (<"1 neighbors+1) {unvisited
if.#neighbors do.
n=.n-1
next=. ({~ ?@#) neighbors
unvisited=.0 (<next+1)} unvisited
if.{.next=here
do. horiz=.1 (<-:here+next-0 1)} horiz
else. verti=. 1 (<-:here+next-1 0)} verti end.
path=.path,here=.next
else.
here=.{:path
path=.}:path
end.
end.
horiz;verti
)
NB. source Dijkstra_equal_weights graph NB. NB. + +---+---+ NB. | 0 1 2 | (sample cell numbers) NB. +---+ + + NB. | 3 4 | 5 NB. +---+---+---+ NB. NB. graph =: 1;0 2 4;1 5;4;1 3;2 NB. The graph is a vector of boxed vectors of neighbors.
Dijkstra_equal_weights =: 4 : 0
dist =. previous =. #&_ n =. # graph =. y [ source =. x
dist =. 0 source } dist
Q =. 0
while. #Q do.
u =. {.Q
Q =. }.Q
if. _ = u{dist do. break. end.
for_v. >u{graph do.
if. -. v e. previous do.
alt =. >: u { dist
if. alt < v { dist do.
dist =. alt v } dist
previous =. u v } previous
if. v e. Q do.
echo 'belch'
else.
Q =. Q,v
end.
end.
end.
end.
end.
dist;previous
)
path =: 3 : 0
p =. <:#y
while. _ > {:p do.
p =. p,y{~{:p
end.
|.}:p
)
solve=:3 :0
NB. convert walls to graph
shape =. }.@$@:>
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.
) </lang>
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
<lang java>import java.io.*; import java.util.*;
public class MazeSolver {
/**
* Reads a file into an array of strings, one per line.
*/
private static String[] readLines (InputStream f) throws IOException
{
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]);
}
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | * | | | * * * * * | | + * + + +---+ +---+---+ + +---+ * +---+ * +---+ +---+ | * | | | | * * * | | | * * * | * * * | | + * + +---+ + + * + * + +---+ +---+ * +---+ * +---+ + | * | | | * | * | | * * * | | * | | + * +---+---+ +---+ * + * +---+---+ + * +---+ + * + + + | * | * * * | | * | * | * * * | | * | | * | | | + * + * + * +---+ + * + * + * + * +---+ * +---+ + * + +---+ | * * * | * | | * | * * * | * * * * * | | * | | +---+---+ * +---+---+ * +---+---+---+---+---+ +---+ * +---+ + | | * * * | * * * | | | * * * | | + +---+---+ * + * +---+ +---+---+ + +---+ +---+ * + + | * * * * * * * | * | | | | | | | * * * | + * +---+---+---+ * + + +---+ +---+ + + +---+---+ * + | * * * * * * * * * | | | * | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Animated version
Uses code from maze generation task
<lang java>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);
});
}
}</lang>
JavaScript
Animated: generating and solving.
To start solving, click to choose a 'start' and an 'end' points.
Go here to see it in action.
<lang javascript>
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();
} </lang> 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
<lang julia>"""
+ +---+---+ | 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)</lang>
Kotlin
<lang scala>// 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 ${args[0]} does not exist.")
return
}
val lines = f.readLines(Charsets.US_ASCII)
val maze = decimateHorizontally(lines)
solveMaze(maze)
val solvedLines = expandHorizontally(maze)
println(solvedLines.joinToString("\n"))
}</lang>
- Output:
Maze (maze.txt) produced by the maze generation program:
+---+---+---+---+---+---+---+---+ | | | | +---+---+ + + +---+ + + | | | | | | | + + + +---+ + +---+ + | | | | | | + + + + +---+---+---+ + | | | | | | +---+ + +---+---+---+ + + | | | | | | + +---+ + +---+ + + + | | | | | | + + +---+---+ +---+---+ + | | | | | + +---+ + +---+ + +---+ | | | | +---+---+---+---+---+---+---+---+
Solution generated by this program when passed maze.txt - follow *'s from bottom right (start) to top left (finish):
+---+---+---+---+---+---+---+---+ | * * * * * | * * * * * | | +---+---+ * + + * +---+ * + + | | * | | * | | * * * | + + + * +---+ * + +---+ * + | | | * | * * * | * | + + + * + * +---+---+---+ * + | | | * | * * * * * * * | * | +---+ + * +---+---+---+ * + * + | | * | * * * * * | * | * | + +---+ * + * +---+ * + * + * + | | * * * | * * * | * * * | * | + + * +---+---+ * +---+---+ * + | * * * | * * * | * * * | * * * | + * +---+ * + * +---+ * + * +---+ | * * * * * | * * * * * | * * * | +---+---+---+---+---+---+---+---+
Mathematica
Graph
Solving the maze generated in Maze_generation#Graph: <lang mathematica>HighlightGraph[maze, PathGraph@FindShortestPath[maze, 1, 273]]</lang>
- Output:
Perl
This example includes maze generation code. <lang perl>
- !perl
use strict; use warnings;
my ($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";
} </lang>
- Output:
Here is the maze: +--+--+--+--+--+--+--+--+--+--+ | | | | + + +--+--+--+ +--+ + + + | | | | | | + +--+--+ + + +--+--+--+ + | | | | | | +--+--+--+--+ +--+ +--+ + + | | | | | | + + +--+ + + +--+ +--+ + | | | | | | | | +--+--+ +--+ + + +--+ +--+ | | | | | | | + +--+--+ +--+--+ + +--+ + | | | | | | + + + + + +--+--+--+--+--+ | | | | | | | + + +--+--+ + + + +--+ + | | | | | | | + + + + +--+--+--+--+--+ + | | | +--+--+--+--+--+--+--+--+--+--+ Here is the solution: +--+--+--+--+--+--+--+--+--+--+ |**| | | +vv+ +--+--+--+ +--+ + + + |vv | ^^>>>| | | | +vv+--+--+^^+vv+ +--+--+--+ + |vv>>>>>>>>>|vv| | | | +--+--+--+--+vv+--+ +--+ + + | |vv| | | | + + +--+ +vv+ +--+ +--+ + | | | |vv| | | | +--+--+ +--+vv+ + +--+ +--+ | |<<<vv| | | | | + +--+--+vv+--+--+ + +--+ + | |<<<^^|vv| | | + +vv+^^+vv+ +--+--+--+--+--+ | |vv|<<<vv| | | | + +vv+--+--+ + + + +--+ + | |vv|^^>>>| | | | + +vv+^^+vv+--+--+--+--+--+ + | vv>>>|vv>>>>>>>>>>>>>>>>>>| +--+--+--+--+--+--+--+--+--+--+
Phix
Combined generator and solver. <lang Phix>-- demo\rosetta\Maze_solving.exw 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, integer 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'))</lang>
- 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 | | | +---+---+---+---+---+---+---+---+---+---+---+
PicoLisp
<lang PicoLisp>(de shortestPath (Goal This Maze)
(let (Path NIL Best NIL Dir " > ")
(recur (This Path Dir)
(when (and This (not (: mark)))
(push 'Path (cons This Dir))
(if (== Goal This)
(unless (and Best (>= (length Path) (length Best)))
(setq Best Path) )
(=: mark T)
(recurse (: west) Path " > ")
(recurse (: east) Path " < ")
(recurse (: south) Path " \^ ")
(recurse (: north) Path " v ")
(=: mark NIL) ) ) )
(disp Maze 0
'((Fld) (if (asoq Fld Best) (cdr @) " ")) ) ) )</lang>
Using the maze produced in Maze generation#PicoLisp, this finds the shortest path from the top-left cell 'a8' to the bottom-right exit 'k1':
: (shortestPath 'a8 'k1 (maze 11 8))
+ +---+---+---+---+---+---+---+---+---+---+
8 | > > v | > v | |
+ + + + + + +---+ +---+---+ +
7 | | | > ^ | v | | | | |
+---+ +---+---+ + + +---+ + + +
6 | | | v | | | | |
+ +---+ +---+ +---+---+---+ + +---+
5 | | | > > > v | | |
+---+ +---+ +---+---+---+ +---+---+ +
4 | | | | | v | > > v |
+ +---+ +---+ +---+ + + +---+ +
3 | | | | | v | ^ < | v |
+ +---+---+ + + + + +---+ + +
2 | | | | | | v | > ^ | v |
+ + + +---+ + +---+ + +---+ +
1 | | | > ^ | >
+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j k
Prolog
Works with SWI-Prolog and XPCE.
<lang Prolog>:- 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).
</lang>
output : 
PureBasic
<lang PureBasic>;code from the maze generation task is place here in its entirety before the rest of the code
Procedure displayMazePath(Array maze(2), List Path.POINT())
Protected x, y, vWall.s, hWall.s
Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2)
Protected Dim mazeOutput.mazeOutput(mazeHeight)
Protected Dim mazeRow.mazeOutput(0)
Static pathChars.s = "@^>v<"
For y = 0 To mazeHeight
makeDisplayMazeRow(mazeRow(), maze(), y): mazeOutput(y) = mazeRow(0)
Next
If ListSize(path())
FirstElement(path())
Protected prevPath.POINT = path()
While NextElement(path())
x = path()\x - prevPath\x
y = path()\y - prevPath\y
Select x
Case -1: dirTaken = #dir_W
Case 1: dirTaken = #dir_E
Default
If y < 0
dirTaken = #dir_N
Else
dirTaken = #dir_S
EndIf
EndSelect
hWall = mazeOutput(prevPath\y)\hWall
mazeOutput(prevPath\y)\hWall = Left(hWall, prevPath\x * #cellDWidth + 2) + Mid(pathChars, dirTaken + 1, 1) + Right(hWall, Len(hWall) - (prevPath\x * #cellDWidth + 3))
prevPath = path()
Wend
hWall = mazeOutput(prevPath\y)\hWall
mazeOutput(prevPath\y)\hWall = Left(hWall, prevPath\x * #cellDWidth + 2) + Mid(pathChars, #dir_ID + 1, 1) + Right(hWall, Len(hWall) - (prevPath\x * #cellDWidth + 3))
For y = 0 To mazeHeight
PrintN(mazeOutput(y)\vWall): PrintN(mazeOutput(y)\hWall)
Next
EndIf
EndProcedure
Procedure solveMaze(Array maze(2), *start.POINT, *finish.POINT, List Path.POINT())
Protected mazeWidth = ArraySize(maze(), 1), mazeHeight = ArraySize(maze(), 2)
Dim visited(mazeWidth + 1, mazeHeight + 1) ;includes padding for easy border detection
Protected i
;mark outside border as already visited (off limits)
For i = 1 To mazeWidth
visited(i, 0) = #True: visited(i, mazeHeight + 1) = #True
Next
For i = 1 To mazeHeight
visited(0, i) = #True: visited(mazeWidth + 1, i) = #True
Next
Protected x = *start\x, y = *start\y, nextCellDir
visited(x + offset(#visited, #dir_ID)\x, y + offset(#visited, #dir_ID)\y) = #True
ClearList(path())
Repeat
If x = *finish\x And y = *finish\y
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</lang> 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
<lang Python>
- python 3
def Dijkstra(Graph, source):
+ +---+---+
| 0 1 2 |
+---+ + +
| 3 4 | 5
+---+---+---+
>>> graph = ( # or ones on the diagonal
... (0,1,0,0,0,0,),
... (1,0,1,0,1,0,),
... (0,1,0,0,0,1,),
... (0,0,0,0,1,0,),
... (0,1,0,1,0,0,),
... (0,0,1,0,0,0,),
... )
...
>>> Dijkstra(graph, 0)
([0, 1, 2, 3, 2, 3], [1e+140, 0, 1, 4, 1, 2])
>>> display_solution([1e+140, 0, 1, 4, 1, 2])
5<2<1<0
# Graph[u][v] is the weight from u to v (however 0 means infinity)
infinity = float('infinity')
n = len(graph)
dist = [infinity]*n # Unknown distance function from source to v
previous = [infinity]*n # Previous node in optimal path from source
dist[source] = 0 # Distance from source to source
Q = list(range(n)) # All nodes in the graph are unoptimized - thus are in Q
while Q: # The main loop
u = min(Q, key=lambda n:dist[n]) # vertex in Q with smallest dist[]
Q.remove(u)
if dist[u] == infinity:
break # all remaining vertices are inaccessible from source
for v in range(n): # each neighbor v of u
if Graph[u][v] and (v in Q): # where v has not yet been visited
alt = dist[u] + Graph[u][v]
if alt < dist[v]: # Relax (u,v,a)
dist[v] = alt
previous[v] = u
return dist,previous
def display_solution(predecessor):
cell = len(predecessor)-1
while cell:
print(cell,end='<')
cell = predecessor[cell]
print(0)
</lang>
Racket
Following function returns a path between two cells in a maze which is created by the build-maze function (See Maze generation).
<lang racket>
- 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)))))
</lang>
Reading a maze from a file <lang racket>
- 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))))
</lang>
Printing out a maze with a path between two given cells <lang racket>
- 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))
</lang>
Example:
-> (define m (build-maze 14 7)) -> (with-output-to-file "maze" (λ () (show-maze m))) -> (show-maze (read-maze "maze")) +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | | | | + +---+---+---+---+ + + + +---+ +---+ + + | | | | | | | | | | +---+ + +---+ +---+ + + + +---+ +---+ + | | | | | | | | | | + + + + +---+---+---+ + + + + + +---+ | | | | | | | | | | + +---+ + + + +---+---+ + +---+---+---+ + | | | | | | | | | | + + +---+---+ +---+---+ + +---+---+ + + + | | | | | | | | + +---+---+---+ + + +---+---+---+ +---+---+ + | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ -> (show-path m '(0 0) '(13 6)) +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | * | * * * | | | + +---+---+---+---+ + + + +---+ +---+ + + | * * | * * * | | * | | * | | | | +---+ + +---+ +---+ + + + +---+ +---+ + | * * | * | | * * * | | * | | | | + + + + +---+---+---+ + + + + + +---+ | * | | * | | | * | | | | + +---+ + + + +---+---+ + +---+---+---+ + | * | * * | | | | * | | | | + + +---+---+ +---+---+ + +---+---+ + + + | * | * * * * | | | * * * | | | + +---+---+---+ + + +---+---+---+ +---+---+ + | * * * * * | | * * * * | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Raku
(formerly Perl 6)
(Includes maze generation code.) <lang perl6>constant mapping = :OPEN(' '), :N< ╵ >, :E< ╶ >, :NE< └ >, :S< ╷ >, :NS< │ >, :ES< ┌ >, :NES< ├ >, :W< ╴ >, :NW< ┘ >, :EW< ─ >, :NEW< ┴ >, :SW< ┐ >, :NSW< ┤ >, :ESW< ┬ >, :NESW< ┼ >, :TODO< x >, :TRIED< · >;
enum Sym (mapping.map: *.key); my @ch = mapping.map: *.value;
enum Direction <DeadEnd Up Right Down Left>;
sub gen_maze ( $X,
$Y,
$start_x = (^$X).pick * 2 + 1,
$start_y = (^$Y).pick * 2 + 1 )
{
my @maze;
push @maze, $[ flat ES, -N, (ESW, EW) xx $X - 1, SW ];
push @maze, $[ flat (NS, TODO) xx $X, NS ];
for 1 ..^ $Y {
push @maze, $[ flat NES, EW, (NESW, EW) xx $X - 1, NSW ]; push @maze, $[ flat (NS, TODO) xx $X, NS ];
}
push @maze, $[ flat NE, (EW, NEW) xx $X - 1, -NS, NW ];
@maze[$start_y][$start_x] = OPEN;
my @stack;
my $current = [$start_x, $start_y];
loop {
if my $dir = pick_direction( $current ) {
@stack.push: $current;
$current = move( $dir, $current );
}
else {
last unless @stack;
$current = @stack.pop;
}
}
return @maze;
sub pick_direction([$x,$y]) {
my @neighbors = (Up if @maze[$y - 2][$x]), (Down if @maze[$y + 2][$x]), (Left if @maze[$y][$x - 2]), (Right if @maze[$y][$x + 2]); @neighbors.pick or DeadEnd;
}
sub move ($dir, @cur) {
my ($x,$y) = @cur; given $dir { when Up { @maze[--$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y--][$x+1] -= W; } when Down { @maze[++$y][$x] = OPEN; @maze[$y][$x-1] -= E; @maze[$y++][$x+1] -= W; } when Left { @maze[$y][--$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x--] -= N; } when Right { @maze[$y][++$x] = OPEN; @maze[$y-1][$x] -= S; @maze[$y+1][$x++] -= N; } } @maze[$y][$x] = 0; [$x,$y];
}
}
sub display (@maze) {
for @maze -> @y {
for @y.rotor(2) -> ($w, $c) { print @ch[abs $w]; if $c >= 0 { print @ch[$c] x 3 } else { print ' ', @ch[abs $c], ' ' } } say @ch[@y[*-1]];
}
}
sub solve (@maze is copy, @from = [1, 1], @to = [@maze[0] - 2, @maze - 2]) {
my ($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 );</lang>
- Output:
┌ ╵ ────┬───────────────┬───────────────┬───────────────────────────────┬───────────┬───────────────┬───────────────┐ │ ╵ · · │ ╷ ╴ ╴ ╴ ╴ │ │ ╷ ╴ ╴ · · · · · · · · · · · · │ ╷ ╴ ╴ · · │ · · · · · · · │ · · · · · · · │ │ ╵ ╶───┘ ╷ ╶───┐ ╵ ╷ │ ╷ ╶───────┤ ╷ ╷ ╵ ╶───────┬───────┐ · ┌───┘ ╷ ╷ ╵ ╷ · │ · ╶───┬───╴ · │ · ╷ · ┌───╴ · │ │ ╵ ╴ ╴ ╴ ╴ · · │ ╵ │ │ │ │ ╷ │ ╵ ╴ ╴ ╴ ╴ │ ╷ ╴ ╴ │ · │ ╷ ╴ ╴ │ ╵ │ · │ · · · │ · · · │ · │ · │ · · · │ │ · ┌───────────┤ ╵ │ └───┴───────╴ │ ╷ ├───────┐ ╵ ╵ ╷ ╷ ╵ └───┘ ╷ ┌───┘ ╵ │ · │ · ╷ · │ · ┌───┴───┘ · │ · ╶───┤ │ · │ ╶ ╶ ╶ ╶ ╷ │ ╵ │ │ ╷ │ │ ╵ ╴ ╴ │ ╵ ╴ ╴ ╴ ╴ │ ╶ ╶ ╵ │ · │ · │ · │ · │ · · · · · │ · · · │ │ · │ ╵ ╶───┐ ╷ ╵ ╵ ├───────────────╴ │ ╷ └───╴ └───────┼───┬───────┤ ╵ ┌───┤ · ├───┘ · │ · │ · ╷ · ┌───┴───┐ · │ │ · │ ╵ ╴ ╴ │ ╶ ╶ ╵ │ │ ╶ ╶ ╶ ╶ ╶ ╶ ╶ ╶ ╷ │ · │ ╶ ╶ ╷ │ ╵ │ · │ · │ · · · │ · │ · │ · │ · · · │ · │ │ · └───┐ ╵ ├───────┴───────┐ ╶───────┴───────┬───────╴ ╷ │ · │ ╵ ╷ ╷ │ ╵ │ · │ · │ · ┌───┤ · │ · │ · │ · ╷ · ╵ · │ │ · · · │ ╵ │ ╷ ╴ ╴ ╴ ╴ ╴ ╴ │ │ ╷ ╴ ╴ ╴ ╴ │ · │ ╵ │ ╷ │ ╵ │ · │ · │ · │ · │ · │ · │ · │ · │ · · · │ ├───╴ · │ ╵ │ ╷ ╶───────┐ ╵ ├───────────────┐ │ ╷ ╶───┬───┘ · │ ╵ │ ╷ ╵ ╵ │ · ╵ · ╵ · │ · ╵ · └───┘ · │ · ├───────┤ │ · · · │ ╵ │ ╶ ╶ ╶ ╶ ╷ │ ╵ │ ╷ ╴ ╴ ╴ ╴ ╴ ╴ │ │ ╶ ╶ ╷ │ · · · │ ╵ │ ╶ ╶ ╵ │ · · · · · │ · · · · · · · │ · │ · · · │ │ · ┌───┤ ╵ └───────╴ ╷ │ ╵ ╵ ╷ ┌───────┐ ╵ │ └───┐ ╷ └───┐ · │ ╵ ├───────┼───────┬───┴───────┬───┬───┘ · ├───╴ · │ │ · │ · │ ╵ ╴ ╴ ╴ ╴ ╴ ╴ │ ╵ ╴ ╴ │ · · · │ ╵ │ │ ╶ ╶ ╷ │ · │ ╵ │ ╷ ╴ ╴ │ ╷ ╴ ╴ │ ╷ ╴ ╴ ╴ ╴ │ · │ · · · │ · · · │ │ · ╵ · ├───────────────┴───────┴───┐ · │ ╵ └───────┴───┐ ╷ │ · │ ╵ ╵ ╷ ╷ ╵ ╵ ╷ ╷ ╵ │ ╷ ┌───╴ ╵ │ · │ · ╶───┤ · ╶───┤ │ · · · │ · · · · · · · · · · · · · │ · │ ╵ ╴ ╴ ╴ ╴ · · │ ╷ │ · │ ╵ ╴ ╴ │ ╵ ╴ ╴ │ ╵ │ ╷ │ ╶ ╶ ╵ │ · │ · · · │ · · · │ ├───┐ · │ · ┌───────────╴ · ┌───┐ · │ · └───┬───╴ ╵ ┌───┘ ╷ │ · ├───────┴───────┤ ╵ ╵ ╷ │ ╵ ╶───┤ · └───┐ · │ · ╷ · │ │ · │ · │ · │ · · · · · · · │ · │ · │ · · · │ ╶ ╶ ╵ │ ╷ ╴ ╴ │ · │ · · · · · · · │ ╵ ╴ ╴ │ ╵ ╴ ╴ │ · · · │ · │ · │ · │ │ · │ · └───┘ · ┌───────────┘ · │ · ├───╴ · │ ╵ ┌───┘ ╷ ┌───┘ · │ · ╷ · ┌───╴ · └───────┴───┐ ╵ └───┐ · ╵ · ├───┘ · │ │ · │ · · · · · │ · · · · · · · │ · │ · · · │ ╵ │ ╷ ╴ ╴ │ · · · │ · │ · │ · · · · · · · · · │ ╵ ╴ ╴ │ · · · │ · · · │ │ · ├───────╴ · ├───┐ · ┌───┐ · ╵ · │ · ╶───┤ ╵ ╵ ╷ ┌───┘ · ╶───┤ · │ · └───┬───╴ · ┌───────┤ · ╷ ╵ │ · ╶───┘ · ╷ · │ │ · │ · · · · · │ │ · │ · │ · · · │ · · · │ ╵ ╴ ╴ │ · · · · · │ · │ · · · │ · · · │ ╶ ╶ ╷ │ · │ ╵ │ · · · · · │ · │ │ · ╵ · ┌───────┘ │ · ╵ · └───────┤ · ╷ · └───────┴───────┐ · ╵ · └───┐ · └───┐ · │ ╵ ╷ ╷ └───┘ ╵ ├───────────┤ · │ │ · · · │ │ · · · · · · · │ · │ · · · · · · · · · │ · · · · · │ · · · │ · │ ╵ │ ╶ ╶ ╶ ╶ ╵ │ ╷ ╴ ╴ ╴ ╴ │ · │ │ · ╶───┤ ╶───────┴───┬───────┐ · ├───┘ · ┌───────────┐ · ├───────────┴───╴ · │ · │ ╵ └───────┐ · │ ╷ ┌───╴ ╵ │ · │ │ · · · │ │ · · · │ · │ · · · │ · · · · · │ · │ · · · · · · · · · │ · │ ╵ ╴ ╴ ╴ ╴ │ · │ ╷ │ ╶ ╶ ╵ │ · │ ├───┐ · ├───────┬───╴ │ · ╷ · │ · │ · ┌───┤ · ╶───────┤ · │ · ╶───────┬───┐ · ├───┴───────┐ ╵ └───┘ ╷ │ ╵ ┌───┴───┤ │ · │ · │ │ │ · │ · │ · │ · │ · │ · · · · · │ · │ · · · · · │ · │ · │ │ ╵ ╴ ╴ ╴ ╴ │ ╵ │ ╷ ╴ ╴ │ │ · │ · │ ╷ ╵ ┌───┘ · │ · ╵ · ╵ · │ · ╵ · ┌───┐ · ╵ · └───────╴ · │ · ╵ · │ ┌───╴ └───────┐ · │ ╵ ╵ ╷ ╷ ╵ │ │ · │ · │ │ │ · · · │ · · · · · │ · · · │ · │ · · · · · · · · · │ · · · │ │ │ · │ ╵ ╴ ╴ │ ╵ │ │ · │ · │ └───┬───┴───────┴───┬───────┤ · ┌───┘ · ├───────────────────┴───────┤ └───────────┐ └───┴───────┤ ╵ │ │ · │ · │ │ │ │ · │ · · · │ │ │ │ ╵ │ │ · ╵ · ├───┐ │ ╶───────┐ ╵ ╷ │ · ╵ · ╷ · │ ╶───────────────────┐ └───┬───────┐ └───────┬───┐ │ ╵ │ │ · · · │ · │ │ │ │ │ · · · │ · │ │ │ │ │ │ │ ╵ │ │ · ╶───┤ · │ └───────┐ ├───────┤ └───┬───┴───┼───────────┬───────┐ ├───┐ ╵ ╷ ├───────┐ │ │ │ ╵ │ │ · · · │ · │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ╵ │ ├───╴ · ╵ · └───────┐ ╵ │ ╷ └───╴ ╵ ╷ ╵ ┌───╴ ╵ ╷ ╵ │ └───────┘ ╵ ╷ ╵ │ ╵ ╵ ╵ │ │ · · · · · · · · · │ │ │ │ │ │ │ │ │ ╵ │ └───────────────────┴───────┴───┴───────────────┴───────┴───────────┴───────┴───────────────────┴───────┴──────── │ ┘
Red
(imports maze generation code, see http://rosettacode.org/wiki/Maze_generation#Red) <lang 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</lang>
- Output:
Maze width: 15 Maze height: 15 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | | | | _ |_ | _ _ _| | _|_| |_ _| | | _| |_ | | | |_ _| _ _| | _ _ _|_ _| | |_ |_ | | _ _|_ _| _ | | | _| _| | | _ _ _|_ _|_| |_ _ _| _ _| |_| _ _ |_| | | _| _|_ _ _ | | _|_ _ _| | | | _| _ _ |_ |_ _ | | | | _| _| _|_ |_ _ _|_ _| | |_ | | _ | _| _ _ |_| | | |_ _| | |_ _ _| | | _| | | | _ _| |_ _ _ | |_ _|_ |_| | |_ | |_ |_ _ _|_ _ _ |_ | | _| | |_ | | | _| | |_ _ _ _|_ _|_ _|_ _|_ _ _ _|_| start: 2x4 end: 12x3 2x4 3x4 3x3 2x3 2x2 3x2 3x1 3x0 4x0 4x1 5x1 5x0 6x0 7x0 7x1 7x2 7x3 6x3 5x3 5x4 5x5 4x5 3x5 3x6 2x6 2x7 1x7 1x8 0x8 0x9 1x9 1x10 2x10 2x9 2x8 3x8 3x7 4x7 5x7 6x7 6x8 7x8 7x9 6x9 6x10 7x10 8x10 8x9 9x9 10x9 11x9 11x10 11x11 10x11 10x10 9x10 9x11 9x12 10x12 11x12 12x12 12x13 11x13 11x14 12x14 13x14 13x13 14x13 14x12 13x12 13x11 12x11 12x10 13x10 13x9 14x9 14x8 14x7 14x6 14x5 13x5 13x6 12x6 11x6 11x5 10x5 9x5 8x5 8x6 8x7 7x7 7x6 6x6 6x5 6x4 7x4 8x4 9x4 10x4 10x3 11x3 12x3
Ruby
This solution extends the maze generator script. To get a working script, copy & paste both parts into one file. <lang ruby>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</lang>
Example output:
+---+---+---+---+---+ +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | * * | * | | * * | | | | + + +---+---+---+ + + +---+---+ + + + +---+ + +---+ +---+ | * | * * * * * | | * | * | | | | + +---+---+---+---+---+---+---+---+---+ + +---+---+ +---+---+---+---+ + | * | * * | * * * | * * | | | | + + +---+---+---+---+ + + +---+---+---+ + + + +---+---+---+ + | * | | * * | * * | * * * * | | | | + +---+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+---+ + + | * * * * | * * | | * | | | | | +---+---+---+ + +---+---+ +---+ + +---+---+---+ +---+---+ + + + | | * * | | * * | | | | | | | + + +---+---+---+ +---+---+ +---+ + +---+ + +---+---+---+ +---+ | | | * * | * * * | * * | | | | | | +---+ + + + +---+ + +---+ +---+---+ +---+ + +---+ +---+ + | | * | * * | * * | * * | | | | | | | | + + + +---+---+ +---+---+ +---+ + +---+---+ + + + + + + | | | * | | * | * * * | | | | | | | | + +---+ +---+ + + +---+---+ +---+---+---+ +---+ + +---+---+ + | * * | * * | | | +---+ +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Rust
This solution reuses the maze generator Rust code. The modified and new parts are marked with the label "MAZE SOLVING".Uses the rand library. <lang rust>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);
}</lang>
- Output:
The maze: +---+---+---+---+---+---+---+---+---+---+---+---+---+ +---+---+ | | | | | + +---+ + + +---+ + +---+---+---+---+---+ + + + | | | | | | | | | +---+---+---+---+ + +---+ + +---+---+ + +---+---+ + | | | | | | | | | + +---+---+ + +---+ + + + + + + +---+---+---+ | | | | | | | | | | + +---+ + + + +---+---+---+---+ + +---+---+---+ + | | | | | | | | | | | +---+ +---+ +---+---+ + +---+ + +---+---+ + + + | | | | | | | | | | | + +---+---+---+---+---+ + + + +---+ + + + + + | | | | | | | | | | + +---+ + +---+ +---+---+ + + +---+ + +---+---+ | | | | | | | | | | | | + + + + + + + +---+---+---+---+ + +---+ + + | | | | | | | | | | +---+ +---+---+ +---+---+ +---+---+ +---+---+ + + + | | | | | | | + + +---+---+---+ +---+ +---+---+---+ + +---+---+---+ | | | | | | | + +---+---+---+ +---+ +---+---+ + +---+---+ +---+ + | | | | | | | | + + + +---+---+ +---+---+ +---+---+---+---+---+ + + | | | | | | | | | + + +---+ +---+---+ +---+---+ + +---+---+ + +---+ | | | | | | | | | + +---+ +---+---+---+---+ +---+ +---+ + +---+---+ + | | | | | | | | +---+ + + + +---+ +---+ +---+ +---+---+---+---+ + | | | | | + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ The maze, solved: +---+---+---+---+---+---+---+---+---+---+---+---+---+ +---+---+ | | | * * * * * * * * | | + +---+ + + +---+ + +---+---+---+---+---+ + + + | | | * * | | | | | | +---+---+---+---+ + +---+ + +---+---+ + +---+---+ + | * * * * | | * * | | | | | | + +---+---+ + +---+ + + + + + + +---+---+---+ | * * * | * | | * * | | | | | | + +---+ + + + +---+---+---+---+ + +---+---+---+ + | | * * | * | | * * | | | | | | +---+ +---+ +---+---+ + +---+ + +---+---+ + + + | * * | * * * * | | | | | | | | | + +---+---+---+---+---+ + + + +---+ + + + + + | * | | | | | | | | | + +---+ + +---+ +---+---+ + + +---+ + +---+---+ | * | | | | | | | | | | | + + + + + + + +---+---+---+---+ + +---+ + + | * * | | | | | | | | | +---+ +---+---+ +---+---+ +---+---+ +---+---+ + + + | | * | | | | | + + +---+---+---+ +---+ +---+---+---+ + +---+---+---+ | | * * * * | | * * | | * * * | + +---+---+---+ +---+ +---+---+ + +---+---+ +---+ + | * * | * * | | * * | * * * * | | * | + + + +---+---+ +---+---+ +---+---+---+---+---+ + + | * | * | | * * * | * * * | | * * * * | * * | + + +---+ +---+---+ +---+---+ + +---+---+ + +---+ | * | * * | * * * * | | * * | | * * | | + +---+ +---+---+---+---+ +---+ +---+ + +---+---+ + | * * | * | * * | * * * | | * * | | +---+ + + + +---+ +---+ +---+ +---+---+---+---+ + | * * | * * | * * * | * * * | + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
Tcl
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).
<lang tcl>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]</lang> Example output:
+ +---+---+---+---+---+---+---+---+---+---+ | v | | + +---+ +---+---+---+---+---+---+---+ + | v | | > v | > v | | | + + +---+ + + + + + +---+ + | v | > ^ | v | ^ | v | | | | + +---+ +---+ + + + +---+ +---+ | v | > ^ | v < | ^ | v | | | | + + +---+ +---+ + + +---+ + + | > ^ | v < | > ^ | v | | | +---+---+ +---+ +---+ +---+ +---+---+ | v < < | > ^ | v < | > > > v | + +---+---+ +---+ +---+ +---+---+ + | > v | ^ < | > > ^ | | v | +---+ +---+---+ +---+---+---+ + + + | > > > ^ | | > +---+---+---+---+---+---+---+---+---+---+---+
zkl
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. <lang zkl>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()) }
}</lang>
- Output:
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | | * * | * * | * * * * * * | | +---+---+ + + +---+ + + + + +---+---+---+ + + | | * | * | | * | * * | | * * * | * | S | + +---+ + + +---+---+ +---+---+ + +---+ + + + | | | * | * | * * | * | | * | * * | * | * | + + +---+ + + + + +---+ +---+ + +---+ + + | | | * | * * | * * | | * * | * | * * | * | + + +---+ +---+---+---+---+ +---+ +---+ + +---+ + | | | * * | | | * * | | * * | * * | + +---+ +---+ + + + +---+ +---+ +---+---+ +---+ | E * * | | | | | | * | * * * * * | | + +---+---+---+---+ + + + + + +---+---+---+---+ + | | | | | | | * * | | | + + + + + + + + +---+---+---+ +---+---+ + + | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+