## A* Implementation in FB: Part 2

### Written by Torahteen

Well, I feel bad about making such a hard to understand and totally "unprofessional" looking tutorial last time. So, I'll try to be a bit better this time. Here goes for my second tutorial ever written.

So last time I left you off with some pseudo-code. Today, I'm gonna show you how to implement this into FB code. First things first. There are a few things that every A* program needs. These are your constants, your UDTs (User Defined Types), your open and closed lists, and your subs and functions. So to start, I'm gonna go ahead and throw some code at you.

DefInt A-Z '$Dynamic Declare Sub ClearScreen() Declare Sub DrawScreen() Declare Sub FindPath() Declare Sub AddToOpen(x As Integer, y As Integer) Declare Sub AddToClosed(x As Integer, y As Integer) Declare Sub AddToPath(x As Integer, y As Integer) Declare Function IsOnOpen(x As Integer, y As Integer) Declare Function IsOnClosed(x As Integer, y As Integer) const Ground = 0 const Water = 1 const Hill = 2 const Cliff = 3 const Wall = 4 const Start = 5 const Finish = 6 const False = 0 const True = Not False const GroundCost = 10 const HillCost = 25 const WaterCost = 50 const CliffCost = 100 Type SquareType fScore As Integer gScore As Integer hScore As Integer mType As Integer pX As Integer pY As Integer End Type Type PointType x As Integer y As Integer End Type

Ok, first of all notice that I use dynamic arrays in my program. What we have done here is declared the subs and functions that we are using in the program (you should think ahead so you can remember what subs and/or functions you need to implement), declared the constants (we'll get to these in a bit), and set up two UDTs.

Take a look at the constants. The first seven constants are used to make and read from a user-made map. Each square on the map has an mType, which says what kind of tile it is (ground, water, walls, etc.). The next two constants are my two boolean values (true and false). The last four are the most important. These are the G scores for each of the different passable squares (if you haven't allready, you should read my other tutorial, "Implementing A* in FB: Part One"). These values determine what path is the best. The higher the score, the less likely A* will choose that square for the path.

The two UDTs are SquareType and PointType. PointType is used for defining points on the map. SquareType is the type used for each tile on the map. SquareType has six variables. The f, g, and hScore variables are just that, the f, g, and h Scores for that square. The mType is one of the seven constants we defined ealier (Ground, Water, Cliff, etc.). pX and pY are the x and y values of this squares parent.

Ok, so now we open the "board.brd" file to get the height and width of the map. We'll then dimension all the global variables that we need to:

Open "board.brd" For Input As #1 Input #1, sWidth, sHeight Dim Shared Map(sWidth, sHeight) As SquareType Dim Shared OpenList() As PointType Dim Shared ClosedList() As PointType Dim Shared Path() As PointType Dim Shared mStart As PointType Dim Shared mFinish As PointType Dim Shared comp As PointType For y = 1 To sHeight For x = 1 To sWidth Input #1, Map(x,y).mType If Map(x,y).mType = Finish Then mFinish.x = x mFinish.y = y ElseIf Map(x,y).mType = Start Then mStart.x = x mStart.y = y End If Next x Next y Close #1

BTW, here is the example "board.brd" file from the last tutorial.

10,8 4,4,4,4,4,4,4,4,4,4 4,0,0,0,0,0,0,0,0,4 4,0,0,0,4,0,0,0,0,4 4,5,0,0,4,0,0,0,0,4 4,0,0,0,4,0,0,6,0,4 4,0,0,0,4,0,0,0,0,4 4,0,0,0,0,0,0,0,0,4 4,4,4,4,4,4,4,4,4,4

Notice I put a wall around the map. You should do this or it will screw A* up (well, my program anyway).

This get's the width and height from the "board.brd" file, dimensions a multi-dimensional array of SquareType variables, and dimensions all our other variables (they are all self-explanatory, except for comp, which is used later). The nested FOR loops at the end there input one square at a time into the Map array, each time checking to see if it inputed the start or finish square.

Now that we have our variables and our map, let's implement the Subs and Functions, starting with the helper subs.

Sub AddToOpen(x As Integer, y As Integer) Redim Preserve OpenList(uBound(OpenList) + 1) OpenList(uBound(OpenList)).x = x OpenList(uBound(OpenList)).y = y End Sub Sub AddToClosed(x As Integer, y As Integer) Redim Preserve ClosedList(uBound(ClosedList) + 1) ClosedList(uBound(ClosedList)).x = x ClosedList(uBound(ClosedList)).y = y End Sub Sub AddToPath(x As Integer, y As Integer) Redim Preserve Path(uBound(Path) + 1) Path(uBound(Path)).x = x Path(uBound(Path)).y = y End Sub Function IsOnOpen(x As Integer, y As Integer) For i = 1 to uBound(OpenList) If OpenList(i).x = x And OpenList(i).y = y Then 'It's on the open list IsOnOpen = True Exit For End If Next i End Function Function IsOnClosed(x As Integer, y As Integer) For i = 1 to uBound(ClosedList) If ClosedList(i).x = x And ClosedList(i).y = y Then 'It's on the closed list IsOnClosed = True Exit For End If Next i End Function

These are all fairly self-explanatory. The AddToXXXX subs simply REDIM the appropriate array, and then add the new value to them. The two IsOnXXXX functions loop through the appropriate array and checks if the square at x,y is on the list. If it is, it returns True. If not, it returns False.

Now for the center of the whole program, the FindPath subroutine.

Sub FindPath() 'A* pathfinding Algorithm Dim c As PointType 'Current Square Dim onFinish As Integer c.x = mStart.x 'Set the current square to c.y = mStart.y 'the start square coord. Do While onFinish = False 'Do this while we have not found the Finish square Print "."; AddToClosed c.x, c.y 'Add the current square to the Closed list For y = -1 to 1 For x = -1 to 1 If Not Map((c.x + x),(c.y+y)).mType = Wall Then 'If it is not a Wall square If (IsOnClosed((c.x + x),(c.y + y))) = False Then 'If it is not on the Closed List If (IsOnOpen((c.x + x),(c.y + y))) = False Then 'It is not on the Open list, add it 'Calculate F, G, and H scores 'G First If Map((c.x + x),(c.y + y)).mType = Ground Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + GroundCost ElseIF Map((c.x + x),(c.y + y)).mType = Hill Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + HillCost ElseIf Map((c.x + x),(c.y + y)).mType = Water Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + WaterCost ElseIF Map((c.x + x),(c.y + y)).mType = Cliff Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + CliffCost End If 'Now H score using Manhattan distance hx = 10 * (ABS(((c.x + x)-(mFinish.x)))) hy = 10 * (ABS(((c.y + y)-(mFinish.y)))) Map((c.x + x),(c.y + y)).hScore = hx + hy 'Finally, the F score Map((c.x + x),(c.y + y)).fScore = Map((c.x + x),(c.y + y)).gScore + Map((c.x + x),(c.y + y)).hScore 'Make the current square the parent of this square Map((c.x + x),(c.y + y)).pX = c.x Map((c.x + x),(c.y + y)).pY = c.y 'Then add this square to the Open List AddToOpen (c.x + x), (c.y + y) 'If it's the finish square, we've found the path! If (c.x + x) = mFinish.x And (c.y + y) = mFinish.y Then onFinish = True End If Else 'Then it is on the Open List. Check to see if this is the better route If Map((c.x + x),(c.y + y)).mType = Ground Then tempG = Map((c.x),(c.y)).gScore + GroundCost ElseIF Map((c.x + x),(c.y + y)).mType = Hill Then tempG = Map((c.x),(c.y)).gScore + HillCost ElseIf Map((c.x + x),(c.y + y)).mType = Water Then tempG = Map((c.x),(c.y)).gScore + WaterCost ElseIf Map((c.x + x),(c.y + y)).mType = Cliff Then tempG = Map((c.x),(c.y)).gScore + CliffCost End If If tempG < Map((c.x + x),(c.y + y)).gScore Then 'This is the better route 'Make the current square the parent of this square Map((c.x + x),(c.y + y)).pX = c.x Map((c.x + x),(c.y + y)).pY = c.y 'Recalculate G and F scores 'G Map((c.x + x),(c.y + y)).gScore = tempG 'F Map((c.x + x),(c.y + y)).fScore = Map((c.x + x),(c.y + y)).gScore + Map((c.x + x),(c.y + y)).hScore End If End If End If End If Next x Next y 'Go through the Open List to find the lowest F score curScore = 20000 'Set to a random number to start. For i = 1 to uBound(OpenList) If IsOnClosed((OpenList(i).x),(OpenList(i).y)) = False Then If Map((OpenList(i).x),(OpenList(i).y)).fScore <= curScore Then c.x = OpenList(i).x c.y = OpenList(i).y curScore = Map((OpenList(i).x),(OpenList(i).y)).fScore End If End If Next i Loop 'We've found the target square. Dim onStart As Integer c.x = mFinish.x c.y = mFinish.y i = 1 Do While onStart = False AddToPath c.x,c.y If c.x = mStart.x And c.y = mStart.y Then onStart = True End If x = c.x y = c.y c.x = Map(x,y).pX 'Make the Current Square the parent square c.y = Map(x,y).pY i = i + 1 'Increment i Loop End Sub

This code goes through the squares, adding them to the open or closed list, until it reaches the finishing square. At this point, it goes from the finishing square and, using the pX and pY of that square, adds each square's parent square to the path.

Ok, so we only have a two things left to do. Those are to implement the two remaining subs, DrawScreen and ClearScreen, and to make the code to show the path. The two subs are easy.

Sub ClearScreen() Line (0,0)-(639,479), 0, BF End Sub Sub DrawScreen() For y = 1 to uBound(Map, 2) For x = 1 to uBound(Map,1) Square = Map(x,y).mType Select Case Square Case Ground: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 2, BF Case Hill: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 21, BF Case Water: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 33, BF Case Wall: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 8, BF Case Cliff: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 7, BF Case Start: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 15, BF Case Finish: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 4, BF End Select Next x Next y Dim ox, oy As Integer ox = mFinish.x oy = mFinish.y For i = 1 To uBound(Path) x = Path(i).x y = Path(i).y Line (ox * 10 + 5,oy * 10 + 5)-(x * 10 + 5,y * 10 + 5), 14 ox = x oy = y Next i Circle (comp.x, comp.y), 3, 14 Locate 20,1 For i = 1 To uBound(Path) Print Path(i).x; Print ","; Print Path(i).y; Next i End Sub

The DrawScreen sub goes through the map, and depending on the mType, draws a colored square at that location. It then goes through the path, drawing a yellow line from square to square. Then it draws a circle at the comp's x and y position (which will be updated in the main part of the program). Finally, it prints out each coordinate for the path (I put that there before I used a yellow line). The ClearScreen sub just draws a black box over the screen (Faster than CLS).

Now, last but not least, we write out our main program which calls the FindPath sub, and shows the user our path.

CLS Screen 18 Print "Finding Path" FindPath Print "Path Found" sleep ClearScreen DrawScreen For i = 1 to uBound(Path) comp.x = (Path(i).x * 10 + 5) comp.y = (Path(i).y * 10 + 5) ClearScreen DrawScreen Sleep Next i Sleep End

That was the easiest part. Now, put it all together to get our final code!

DefInt A-Z '$Dynamic Declare Sub ClearScreen() Declare Sub DrawScreen() Declare Sub FindPath() Declare Sub AddToOpen(x As Integer, y As Integer) Declare Sub AddToClosed(x As Integer, y As Integer) Declare Sub AddToPath(x As Integer, y As Integer) Declare Function IsOnOpen(x As Integer, y As Integer) Declare Function IsOnClosed(x As Integer, y As Integer) const Ground = 0 const Hill = 2 const Water = 1 const Cliff = 3 const Wall = 4 const Start = 5 const Finish = 6 const False = 0 const True = Not False const GroundCost = 10 const HillCost = 25 const WaterCost = 50 const CliffCost = 100 Type SquareType fScore As Integer gScore As Integer hScore As Integer mType As Integer pX As Integer pY As Integer End Type Type PointType x As Integer y As Integer End Type Open "board.brd" For Input As #1 Input #1, sWidth, sHeight Dim Shared Map(sWidth, sHeight) As SquareType Dim Shared OpenList() As PointType Dim Shared ClosedList() As PointType Dim Shared Path() As PointType Dim Shared mStart As PointType Dim Shared mFinish As PointType Dim Shared comp As PointType For y = 1 To sHeight For x = 1 To sWidth Input #1, Map(x,y).mType If Map(x,y).mType = Finish Then mFinish.x = x mFinish.y = y ElseIf Map(x,y).mType = Start Then mStart.x = x mStart.y = y End If Next x Next y Close #1 CLS Screen 18 Print "Finding Path" FindPath Print "Path Found" sleep ClearScreen DrawScreen For i = 1 to uBound(Path) comp.x = (Path(i).x * 10 + 5) comp.y = (Path(i).y * 10 + 5) ClearScreen DrawScreen Sleep Next i Sleep End Sub FindPath() 'A* pathfinding Algorithm Dim c As PointType 'Current Square Dim onFinish As Integer c.x = mStart.x 'Set the current square to c.y = mStart.y 'the start square coord. Do While onFinish = False 'Do this while we have not found the Finish square Print "."; AddToClosed c.x, c.y 'Add the current square to the Closed list For y = -1 to 1 For x = -1 to 1 If Not Map((c.x + x),(c.y+y)).mType = Wall Then 'If it is not a Wall square If (IsOnClosed((c.x + x),(c.y + y))) = False Then 'If it is not on the Closed List If (IsOnOpen((c.x + x),(c.y + y))) = False Then 'It is not on the Open list, add it 'Calculate F, G, and H scores 'G First If Map((c.x + x),(c.y + y)).mType = Ground Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + GroundCost ElseIF Map((c.x + x),(c.y + y)).mType = Hill Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + HillCost ElseIf Map((c.x + x),(c.y + y)).mType = Water Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + WaterCost ElseIF Map((c.x + x),(c.y + y)).mType = Cliff Then Map((c.x + x),(c.y + y)).gScore = Map((c.x),(c.y)).gScore + CliffCost End If 'Now H score using Manhattan distance hx = 10 * (ABS(((c.x + x)-(mFinish.x)))) hy = 10 * (ABS(((c.y + y)-(mFinish.y)))) Map((c.x + x),(c.y + y)).hScore = hx + hy 'Finally, the F score Map((c.x + x),(c.y + y)).fScore = Map((c.x + x),(c.y + y)).gScore + Map((c.x + x),(c.y + y)).hScore 'Make the current square the parent of this square Map((c.x + x),(c.y + y)).pX = c.x Map((c.x + x),(c.y + y)).pY = c.y 'Then add this square to the Open List AddToOpen (c.x + x), (c.y + y) 'If it's the finish square, we've found the path! If (c.x + x) = mFinish.x And (c.y + y) = mFinish.y Then onFinish = True End If Else 'Then it is on the Open List. Check to see if this is the better route If Map((c.x + x),(c.y + y)).mType = Ground Then tempG = Map((c.x),(c.y)).gScore + GroundCost ElseIF Map((c.x + x),(c.y + y)).mType = Hill Then tempG = Map((c.x),(c.y)).gScore + HillCost ElseIf Map((c.x + x),(c.y + y)).mType = Water Then tempG = Map((c.x),(c.y)).gScore + WaterCost ElseIf Map((c.x + x),(c.y + y)).mType = Cliff Then tempG = Map((c.x),(c.y)).gScore + CliffCost End If If tempG < Map((c.x + x),(c.y + y)).gScore Then 'This is the better route 'Make the current square the parent of this square Map((c.x + x),(c.y + y)).pX = c.x Map((c.x + x),(c.y + y)).pY = c.y 'Recalculate G and F scores 'G Map((c.x + x),(c.y + y)).gScore = tempG 'F Map((c.x + x),(c.y + y)).fScore = Map((c.x + x),(c.y + y)).gScore + Map((c.x + x),(c.y + y)).hScore End If End If End If End If Next x Next y 'Go through the Open List to find the lowest F score curScore = 20000 'Set to a random number to start. For i = 1 to uBound(OpenList) If IsOnClosed((OpenList(i).x),(OpenList(i).y)) = False Then If Map((OpenList(i).x),(OpenList(i).y)).fScore <= curScore Then c.x = OpenList(i).x c.y = OpenList(i).y curScore = Map((OpenList(i).x),(OpenList(i).y)).fScore End If End If Next i Loop 'We've found the target square. Dim onStart As Integer c.x = mFinish.x c.y = mFinish.y i = 1 Do While onStart = False AddToPath c.x,c.y If c.x = mStart.x And c.y = mStart.y Then onStart = True End If x = c.x y = c.y c.x = Map(x,y).pX 'Make the Current Square the parent square c.y = Map(x,y).pY i = i + 1 'Increment i Loop End Sub Sub AddToOpen(x As Integer, y As Integer) Dim TempOpen(uBound(OpenList)) As PointType For i = 1 to uBound(OpenList) TempOpen(i).x = OpenList(i).x TempOpen(i).y = OpenList(i).y Next i size = uBound(OpenList) Redim OpenList(size+1) As PointType For i = 1 to uBound(TempOpen) OpenList(i).x = TempOpen(i).x OpenList(i).y = TempOpen(i).y Next i OpenList(uBound(OpenList)).x = x OpenList(uBound(OpenList)).y = y End Sub Sub AddToClosed(x As Integer, y As Integer) Dim TempClosed(uBound(ClosedList)) As PointType For i = 1 to uBound(ClosedList) TempClosed(i).x = ClosedList(i).x TempClosed(i).y = ClosedList(i).y Next i size = uBound(ClosedList) Redim ClosedList(size+1) As PointType For i = 1 to uBound(TempClosed) ClosedList(i).x = TempClosed(i).x ClosedList(i).y = TempClosed(i).y Next i ClosedList(uBound(ClosedList)).x = x ClosedList(uBound(ClosedList)).y = y End Sub Sub AddToPath(x As Integer, y As Integer) Dim TempPath(uBound(Path)) As PointType For i = 1 to uBound(Path) TempPath(i).x = Path(i).x TempPath(i).y = Path(i).y Next i size = uBound(Path) Redim Path(size+1) As PointType For i = 1 to uBound(TempPath) Path(i).x = TempPath(i).x Path(i).y = TempPath(i).y Next i Path(uBound(Path)).x = x Path(uBound(Path)).y = y End Sub Function IsOnOpen(x As Integer, y As Integer) For i = 1 to uBound(OpenList) If OpenList(i).x = x And OpenList(i).y = y Then 'It's on the open list IsOnOpen = True Exit For End If Next i End Function Function IsOnClosed(x As Integer, y As Integer) For i = 1 to uBound(ClosedList) If ClosedList(i).x = x And ClosedList(i).y = y Then 'It's on the closed list IsOnClosed = True Exit For End If Next i End Function Sub ClearScreen() Line (0,0)-(639,479), 0, BF End Sub Sub DrawScreen() For y = 1 to uBound(Map, 2) For x = 1 to uBound(Map,1) Square = Map(x,y).mType Select Case Square Case Ground: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 2, BF Case Hill: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 21, BF Case Water: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 33, BF Case Wall: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 8, BF Case Cliff: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 7, BF Case Start: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 15, BF Case Finish: Line(x * 10, y * 10)-(x * 10 + 10, y * 10 + 10), 4, BF End Select Next x Next y Dim ox, oy As Integer ox = mFinish.x oy = mFinish.y For i = 1 To uBound(Path) x = Path(i).x y = Path(i).y Line (ox * 10 + 5,oy * 10 + 5)-(x * 10 + 5,y * 10 + 5), 14 ox = x oy = y Next i Circle (comp.x, comp.y), 3, 14 Locate 20,1 For i = 1 To uBound(Path) Print Path(i).x; Print ","; Print Path(i).y; Next i End Sub

And there you have it! It really isn't too difficult. Here are a few more tips:

### Preventing the "Go Through Walls" problem

You may notice that in a game, this would generate paths that cut through the corner of the wall. To prevent this, you need to keep A* from checking diagonal squares that are next to a wall. I haven't tried this but have been told it isn't too hard. Go ahead and give it a shot.

### Turn it into a function

One of the greatest things about any algorithm is the ablility to make it into a function. Make the FindPath sub in this code into a function that asks for:

- An array such as the Map array in this example.
- A starting square.
- A Finishing square.

All it would take is a little bit of messing around with the code. Try it out!

### There is more than the Manhattan Method

There is more than one method of calculating the H score. Here are a couple:

**Euclidean Distance**

The Euclidean Distance is the exact distance in a straight line to the finishing square. It is really only feasible if your units can move at any angle rather than in grid directions (north, southwest, etc.). The formula is:

**H = D * SQR((TargetX - SquareX)^2 + (TargetY - SquareY)^2)**

Where D is the is the minimum cost to move from one square to another (The lowest G cost).**Diagonal Distance**

The Diagonal Distance is perhaps a slightly better formula for diagonally moving units (such as in the example). It simply accounts for the ability to move diagonally across squares.

**H = D * max(ABS(TargetX - SquareX) + ABS(TargetY - SquareY))**

### So in Conclusion

Thanks for taking the time to read this tutorial. I hope I did better this time. This program can be downloaded on my site in the "Programming" section. If there are any questions or comments, you can PM Torahteen on the QBN message boards, or you can post a message on my site's forum. Until next time!

Torahteen