# PureBasic Forum

 It is currently Fri Apr 20, 2018 4:17 am

 All times are UTC + 1 hour

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: A* Pathfinder using binary heapPosted: Sun Jun 17, 2007 6:41 pm
 Enthusiast

Joined: Fri Jun 30, 2006 4:30 pm
Posts: 578
Location: Middle East
Quote:
Serious A* programmers who want real speed use something called a binary heap. Using binary heap will be at least 2-3 times as fast and geometrically faster (10+ times as fast) on longer paths.

aStarLibrary.pbi

Code:
;A* Pathfinder (Version 1.82) by Patrick Lester. Used by permission.
;==================================================================

;An article describing A* and this code in particular can be found at:
;http://www.policyalmanac.org/games/aStarTutorial.htm

;Setup
;-----
;1. Include "aStarLibrary.pbi" at the top of your program.

;2. Create an array called walkability(x,y) that contains information
;  0 = walkable (the default value) and 1 = unwalkable. The array
;  should range from (0,0) in the upper left hand corner to
;  (mapWidth-1,mapHeight-1) in the bottom right hand corner.

;3. Adjust the following variables at the top of the .declareVariables
;  subroutine below. All three should be made global.
;  - tileSize = the width and height of your square tiles in pixels
;  - mapWidth = the width of your map in tiles = x value in
;    walkability array.
;  - mapHeight = the height of your map in tiles = y value in
;    walkability array.

;Calling the Procedures
;---------------------
;There are three main Procedures

;1.  FindPath(unit.unit,targetX,targetY)
;  - unit.unit = unit that is doing the pathfinding
;  - targetX,targetY = location of the target destination (pixel based coordinates)

;  The FindPath() Procedure returns whether a path could be found (1) or
;  if it's nonexistent (2). If there is a path, it stores it in a bank
;  called unit\pathBank.

;  This Procedure updates the current path.

;   This Procedure reads the path data generated by FindPath() and returns
;  the x and y coordinates of the next step on the path. They are stored
;  as xPath and yPath. These coordinates are pixel coordinates

;==========================================================
;DECLARE VARIABLES
Global tileSize = 1, mapWidth = 20, mapHeight = 20

;Create needed arrays
Global Dim walkability(mapWidth+1,mapHeight+1) ;array that holds wall/obstacle information
Global Dim openlist(mapWidth*mapHeight+2) ;1 dimensional array holding ID# of open list items
Global Dim whichList(mapWidth+1,mapHeight+1)  ;2 dimensional array used to record
;whether a cell is on the open list or on the closed list.
Global Dim openX(mapWidth*mapHeight+2) ;1d array stores the x location of an item on the open list
Global Dim openY(mapWidth*mapHeight+2) ;1d array stores the y location of an item on the open list
Global Dim parentX(mapWidth+1,mapHeight+1) ;2d array to store parent of each cell (x)
Global Dim parentY(mapWidth+1,mapHeight+1) ;2d array to store parent of each cell (y)
Global Dim Fcost(mapWidth*mapHeight+2)  ;1d array to store F cost of a cell on the open list
Global Dim Gcost(mapWidth+1,mapHeight+1)   ;2d array to store G cost for each cell.
Global Dim Hcost(mapWidth*mapHeight+2)  ;1d array to store H cost of a cell on the open list

;Declare constants
Global onClosedList = 10 ;openList variable
#notfinished = 0
#notStarted = 0
#found = 1
#nonexistent = 2; pathStatus constants
#walkable = 0
#unwalkable = 1; walkability array constants

Structure unit
xLoc.l
yLoc.l
targetX.l
targetY.l
pathLocation.l
pathLength.l
pathBank.l
xPath.l
yPath.l
pathStatus.l
EndStructure

;{ Declarations
Declare FindPath(*unit.unit,targetX,targetY)
;}

;==========================================================
;FIND PATH: This Procedure finds the path and saves it. Non-Blitz users please note,
;the first parameter is a pointer to a user-defined object called a unit, which contains all
;relevant info about the unit in question (its current location, speed, etc.). As an
;object-oriented data structure, types are similar to structs in C.
;  Please note that targetX and targetY are pixel-based coordinates relative to the
;upper left corner of the map, which is 0,0.
Procedure FindPath(*unit.unit,targetX,targetY)

;1.  Convert location data (in pixels) to coordinates in the walkability array.
startx = Round(*unit\xLoc/tileSize,0) : starty = Round(*unit\yLoc/tileSize,0)
targetX = Round(targetX/tileSize,0) : targetY = Round(targetY/tileSize,0)
;2.  Quick Path Checks: Under the some circumstances no path needs to
;be generated ...

;If starting location and target are in the same location...
If startx = targetX And starty = targetY And *unit\pathLocation > 0
ProcedureReturn #found
EndIf
If startx = targetX And starty = targetY And *unit\pathLocation = 0
ProcedureReturn #nonexistent
EndIf
;If target square is unwalkable, return that it's a nonexistent path.
If walkability(targetX,targetY) = #unwalkable
Goto noPath
EndIf

;3.  Reset some variables that need to be cleared
If onClosedList > 1000000 ;occasionally redim whichList
Redim whichList(mapWidth,mapHeight)
onClosedList = 10
EndIf
onClosedList = onClosedList+2 ;changing the values of onOpenList and onClosed list is faster than redimming whichList() array
onOpenList = onClosedList-1
*unit\pathLength = #notStarted ;i.e, = 0
*unit\pathLocation = #notStarted ;i.e, = 0
Gcost(startx,starty) = 0 ;reset starting square's G value to 0

;4.  Add the starting location to the open list of squares to be checked.
numberOfOpenListItems = 1
openlist(1) = 1 ;assign it as the top (and currently only) item in the open list, which is maintained as a binary heap (explained below)
openX(1) = startx : openY(1) = starty

;5.  Do the following until a path is found or deemed nonexistent.
Repeat

;6.  If the open list is not empty, take the first cell off of the list.
;This is the lowest F cost cell on the open list.
If numberOfOpenListItems <> 0

;Pop the first item off the open list.
parentXval = openX(openlist(1)) : parentYVal = openY(openlist(1)) ;record cell coordinates of the item
whichList(parentXval,parentYVal) = onClosedList ;add the item to the closed list

;Open List = Binary Heap: Delete this item from the open list, which
;is maintained as a binary heap. For more information on binary heaps, see:
;http://www.policyalmanac.org/games/binaryHeaps.htm
numberOfOpenListItems = numberOfOpenListItems - 1 ;reduce number of open list items by 1
openlist(1) = openlist(numberOfOpenListItems+1) ;move the last item in the heap up to slot #1
v = 1
Repeat ;Repeat the following until the new item in slot #1 sinks to its proper spot in the heap.
u = v
If 2*u+1 <= numberOfOpenListItems ;if both children exist
;Check if the F cost of the parent is greater than each child.
;Select the lowest of the two children.
If Fcost(openlist(u)) >= Fcost(openlist(2*u))
v = 2*u
EndIf
If Fcost(openlist(v)) >= Fcost(openlist(2*u+1))
v = 2*u+1
EndIf
Else
If 2*u <= numberOfOpenListItems ;if only child #1 exists
;Check if the F cost of the parent is greater than child #1
If Fcost(openlist(u)) >= Fcost(openlist(2*u))
v = 2*u
EndIf
EndIf
EndIf
If u<>v ;if parent's F is > one of its children, swap them
temp = openlist(u)
openlist(u) = openlist(v)
openlist(v) = temp
Else
Break ;otherwise, exit loop
EndIf
ForEver

;7.  Check the adjacent squares. (Its "children" -- these path children
;are similar, conceptually, to the binary heap children mentioned
;above, but don't confuse them. They are different. Path children
;are portrayed in Demo 1 with grey pointers pointing toward
;for later consideration if appropriate (see various if statements
;below).
For b = parentYVal-1 To parentYVal+1
For a = parentXval-1 To parentXval+1

;If not off the map (do this first to avoid array out-of-bounds errors)
If a <> -1 And b <> -1 And a <> mapWidth And b <> mapHeight

;If not already on the closed list (items on the closed list have
;already been considered and can now be ignored).
If whichList(a,b) <> onClosedList

;If not a wall/obstacle square.
If walkability(a,b) <> #unwalkable

;Don't cut across corners (this is optional)
corner = #walkable
If a = parentXval-1
If b = parentYVal-1
If walkability(parentXval-1,parentYVal) = #unwalkable Or walkability(parentXval,parentYVal-1) = #unwalkable
corner = #unwalkable
EndIf
ElseIf b = parentYVal+1
If walkability(parentXval,parentYVal+1) = #unwalkable Or walkability(parentXval-1,parentYVal) = #unwalkable
corner = #unwalkable
EndIf
EndIf
ElseIf a = parentXval+1
If b = parentYVal-1
If walkability(parentXval,parentYVal-1) = #unwalkable Or walkability(parentXval+1,parentYVal) = #unwalkable
corner = #unwalkable
EndIf
ElseIf b = parentYVal+1
If walkability(parentXval+1,parentYVal) = #unwalkable Or walkability(parentXval,parentYVal+1) = #unwalkable
corner = #unwalkable
EndIf
EndIf
EndIf

If corner = #walkable
;If not already on the open list, add it to the open list.
If whichList(a,b) <> onOpenList

;Create a new open list item in the binary heap.
newOpenListItemID = newOpenListItemID + 1; each new item has a unique ID #
m = numberOfOpenListItems+1
openlist(m) = newOpenListItemID   ;place the new open list item (actually, its ID#) at the bottom of the heap
openX(newOpenListItemID) = a : openY(newOpenListItemID) = b ;record the x and y coordinates of the new item

;Figure out its G cost
If Abs(a-parentXval) = 1 And Abs(b-parentYVal) = 1
addedGCost = 14 ;cost of going to diagonal squares
Else
addedGCost = 10 ;cost of going to non-diagonal squares
EndIf

;Figure out its H and F costs and parent
Hcost(openlist(m)) = 10*(Abs(a - targetX) + Abs(b - targetY)) ; record the H cost of the new square
Fcost(openlist(m)) = Gcost(a,b) + Hcost(openlist(m)) ;record the F cost of the new square
parentX(a,b) = parentXval : parentY(a,b) = parentYVal  ;record the parent of the new square

;Move the new open list item to the proper place in the binary heap.
;Starting at the bottom, successively compare to parent items,
;swapping as needed until the item finds its place in the heap
;or bubbles all the way to the top (if it has the lowest F cost).
While m <> 1 ;While item hasn't bubbled to the top (m=1)
;Check if child's F cost is < parent's F cost. If so, swap them.
If Fcost(openlist(m)) <= Fcost(openlist(m/2))
temp = openlist(m/2)
openlist(m/2) = openlist(m)
openlist(m) = temp
m = m/2
Else
Break
EndIf
Wend
numberOfOpenListItems = numberOfOpenListItems+1 ;add one to the number of items in the heap

;Change whichList to show that the new item is on the open list.
whichList(a,b) = onOpenList

;8.  If adjacent cell is already on the open list, check to see if this
;path to that cell from the starting location is a better one.
;If so, change the parent of the cell and its G and F costs.
Else; If whichList(a,b) = onOpenList

;Figure out the G cost of this possible new path
If Abs(a-parentXval) = 1 And Abs(b-parentYVal) = 1
addedGCost = 14;cost of going to diagonal tiles
Else
addedGCost = 10 ;cost of going to non-diagonal tiles
EndIf

;If this path is shorter (G cost is lower) then change
;the parent cell, G cost and F cost.
If tempGcost < Gcost(a,b) ;if G cost is less,
parentX(a,b) = parentXval   ;change the square's parent
parentY(a,b) = parentYVal
Gcost(a,b) = tempGcost   ;change the G cost

;Because changing the G cost also changes the F cost, if
;the item is on the open list we need to change the item's
;recorded F cost and its position on the open list to make
;sure that we maintain a properly ordered open list.
For x = 1 To numberOfOpenListItems ;look for the item in the heap
If openX(openlist(x)) = a And openY(openlist(x)) = b ;item found
Fcost(openlist(x)) = Gcost(a,b) + Hcost(openlist(x)) ;change the F cost

;See if changing the F score bubbles the item up from it's current location in the heap
m = x
While m <> 1 ;While item hasn't bubbled to the top (m=1)
;Check if child is < parent. If so, swap them.
If Fcost(openlist(m)) < Fcost(openlist(m/2))
temp = openlist(m/2)
openlist(m/2) = openlist(m)
openlist(m) = temp
m = m/2
Else
Break ;while/wend
EndIf
Wend
Break ;for x = loop
EndIf ;If openX(openList(x)) = a
Next ;For x = 1 To numberOfOpenListItems
EndIf ;If tempGcost < Gcost(a,b) Then
EndIf ;If not already on the open list
EndIf ;If corner = walkable
EndIf ;If not a wall/obstacle cell.
EndIf ;If not already on the closed list
EndIf ;If not off the map.
Next
Next

;9.  If open list is empty then there is no path.
Else
Path = #nonexistent
Break
EndIf

;If target is added to open list then path has been found.
If whichList(targetX,targetY) = onOpenList
Path = found
Break
EndIf

ForEver ;repeat until path is found or deemed nonexistent

;10.  Save the path if it exists. Copy it to a bank.
If Path = found

;a. Working backwards from the target to the starting location by checking
;each cell's parent, figure out the length of the path.
pathX = targetX : pathY = targetY
Repeat
tempx = parentX(pathX,pathY)
pathY = parentY(pathX,pathY)
pathX = tempx
*unit\pathLength = *unit\pathLength + 1
Until pathX = startx And pathY = starty

;b. Resize the data bank to the right size (leave room to store step 0,
;which requires storing one more step than the length)
ReAllocateMemory(*unit\pathBank, (*unit\pathLength+1)*4)

;c. Now copy the path information over to the databank. Since we are
;working backwards from the target to the start location, we copy
;the information to the data bank in reverse order. The result is
;a properly ordered set of path data, from the first step to the
;last.
pathX = targetX : pathY = targetY
cellPosition = *unit\pathLength*4 ;start at the end
While Not (pathX = startx And pathY = starty)
PokeW(*unit\pathBank+cellPosition,pathX) ;store x value
PokeW(*unit\pathBank+cellPosition+2,pathY) ;store y value
cellPosition = cellPosition - 4 ;work backwards
tempx = parentX(pathX,pathY)
pathY = parentY(pathX,pathY)
pathX = tempx
Wend
PokeW(*unit\pathBank,startx) ;store starting x value
PokeW(*unit\pathBank+2,starty) ;store starting y value

EndIf ;If path = found Then

;11. Return info on whether a path has been found.
ProcedureReturn Path; Returns 1 if a path has been found, 2 if no path exists.

;12.If there is no path to the selected target, set the pathfinder's
;xPath and yPath equal to its current location and return that the
;path is nonexistent.
noPath:
*unit\xPath = startingX
*unit\yPath = startingY
ProcedureReturn #nonexistent

EndProcedure

;==========================================================
;it to screen pixel coordinates.
EndProcedure

If pathLocation <= *unit\pathLength
x = PeekW(*unit\pathBank+(pathLocation*4))
ProcedureReturn tileSize * x + (1/2) * tileSize;align w/center of square
EndIf
EndProcedure

If pathLocation <= *unit\pathLength
y = PeekW(*unit\pathBank+(pathLocation*4+2))
ProcedureReturn tileSize*y + (1/2) * tileSize ;align w/center of square
EndIf
EndProcedure

;This Procedure checks whether the unit is close enough to the next
;path node to advance to the next one or, if it is the last path step,
;to stop.
If (*unit\xLoc = *unit\xPath And *unit\yLoc = *unit\yPath) Or *unit\pathLocation = 0
If *unit\pathLocation = *unit\pathLength
*unit\pathStatus = #notStarted
Else
*unit\pathLocation = *unit\pathLocation + 1
EndIf
EndIf
EndProcedure

example.pb - modified example of Heathen
Code:
InitSprite()
InitMouse()
InitKeyboard()

#width = 20
#height = 20

startx = 0
starty = 0
tox = 19
toy = 19

XIncludeFile "aStarLibrary.pbi"

Global unit.unit
unit\pathBank = AllocateMemory(1) ;data bank that unit's path data is stored   in
unit\xLoc = 5
unit\yLoc = 5

walkability(7,4) = 1
walkability(7,5) = 1
walkability(7,6) = 1
walkability(7,7) = 1

Macro draw()
StartDrawing(ImageOutput(0))
Box(0,0,640,640)
For x = 1 To 20
LineXY(x*32,0,x*32,640,#White)
Next x
For y = 1 To 20
LineXY(0,y*32,640,y*32,#White)
Next y
Box(starty*32,startx*32,32,32,#Yellow)
If unit > 0
For a = 0 To 100
If xx > -1 And yy > -1
Box(xx*32,yy*32,32,32,#Green)
EndIf
Next a
EndIf
Box(tox*32,toy*32,32,32,#Blue)
For x = 0 To 20
For y = 0 To 20
If walkability(x,y)=1
Box(x*32,y*32,32,32,#Red)
EndIf
Next y
Next x
StopDrawing()
EndMacro

unit\xLoc = startx
unit\yLoc = starty
FindPath(unit,tox,toy)

OpenWindowedScreen(WindowID(0),0,0,640,640,0,0,0)
CreateImage(0,640,640,#PB_Image_DisplayFormat)
draw()
Repeat
event = WaitWindowEvent()
FlipBuffers(2)
StartDrawing(ScreenOutput())
DrawImage(ImageID(0),0,0)
Circle(MouseX(),MouseY(),10,#White)
StopDrawing()
ExamineMouse()
ExamineKeyboard()
If MouseButton(#PB_MouseButton_Left) And walkability(MouseX()/32,MouseY()/32) = 0
walkability(MouseX()/32,MouseY()/32) = 1
t = GetTickCount_()
If *path > 0
FreeMemory(*path)
EndIf
unit\xLoc = startx
unit\yLoc = starty
FindPath(unit,tox,toy)
SetWindowTitle(0,Str(GetTickCount_()-t))
draw()
ElseIf MouseButton(#PB_MouseButton_Right) And walkability(MouseX()/32,MouseY()/32) = 1
walkability(MouseX()/32,MouseY()/32) = 0
t = GetTickCount_()
If *path > 0
FreeMemory(*path)
EndIf
;*path = get_path(startx,starty,tox,toy,#width,#height,allowdiag,blockdiag)
unit\xLoc = startx
unit\yLoc = starty
FindPath(unit,tox,toy)
SetWindowTitle(0,Str(GetTickCount_()-t))
draw()
EndIf
If KeyboardPushed(#PB_Key_Escape)
End
EndIf
Delay(1)
Until event = #PB_Event_CloseWindow

_________________

[Registered PB User since 2006]
[PureBasic 5.5] [Win 10 64bit]
[Intel i7 990x 3.47 Ghz] [18GB DDR3]

Last edited by JCV on Mon Jun 18, 2007 4:57 am, edited 1 time in total.

Top

 Post subject: Posted: Mon Jun 18, 2007 3:37 am
 PureBasic Expert

Joined: Fri Apr 25, 2003 4:34 pm
Posts: 827
You forgot to allow for this variable...
Code:
allowdiag = 0

_________________

Top

 Post subject: Posted: Mon Jun 18, 2007 5:19 am
 Enthusiast

Joined: Fri Jun 30, 2006 4:30 pm
Posts: 578
Location: Middle East
Variable is not used. Removed.
I'm using this method on my game and its fast on really huge maps.

I did some benchmark

Both 20x20 map

Using binary heap
0.062 seconds - 1k loops
Hearthen's example
0.781 seconds - 1k loops

Both 1000x1000 map

Using binary heap
0.078 seconds - 1k loops
Hearthen's example
1.312 seconds - 1k loops

_________________

[Registered PB User since 2006]
[PureBasic 5.5] [Win 10 64bit]
[Intel i7 990x 3.47 Ghz] [18GB DDR3]

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC + 1 hour

#### Who is online

Users browsing this forum: No registered users and 1 guest

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ PureBasic    Coding Questions    Game Programming    3D Programming    Assembly Programming    The PureBasic Editor    The PureBasic Form Designer    General Discussion    Feature Requests and Wishlists    Tricks 'n' Tips Bug Reports    Bugs - Windows    Bugs - Linux    Bugs - Mac OSX    Bugs - Documentation OS Specific    AmigaOS    Linux    Windows    Mac OSX Miscellaneous    Announcement    Off Topic Showcase    Applications - Feedback and Discussion    PureFORM & JaPBe    TailBite