Help modifying recursive function - asp.net

Question

Given a canvas, let's say 10x10, and given 3 rectangles/squares.
Canvas = 10x10
Rectangle 1 = 2x2
Rectangle 2 = 3x3
Rectangle 3 = 2x4
I've created a recursive function that loops every position of every rectangle on the canvas, and it works fine. (I've included the function below incase anyone wants to see it but I don't think it's necessary).
We can see that rectangle 1 and 2 are non rotatable, IE, if you rotate either of them 90 degrees essentially they are the same shape. However rectangle 3 is rotatable.
How do I change/construct the loop/recurisve function so that it loops every position of every rectangle, along with every possible rotation?
The aim is to loop through every possible fitting of the shapes on the canvas.
Thanks for any help!
Sub recurse(ByVal startPoint As Integer)
Dim x As Integer
Dim y As Integer
Dim validSolution As Boolean = isSolutionValid()
Dim loopXTo As Integer
Dim loopYTo As Integer
Dim solutionRating As Integer
'If parent nodes create invalid solution, we can skip (375 iterations from 1,600 iterations saving)
If validSolution = True Then
If (startPoint = 0) Then
loopXTo = Math.Floor((canvasCols - squareObjects(startPoint).sqRows()) / 2) '576 iterations from 1,680 iterations
loopYTo = Math.Floor((canvasRows - squareObjects(startPoint).sqCols) / 2) '31,104 iterations from 90,720 iterations
Else
loopXTo = canvasCols - squareObjects(startPoint).sqRows
loopYTo = canvasRows - squareObjects(startPoint).sqCols
End If
'Loop all positions on canvas
For x = 0 To loopXTo
For y = 0 To loopYTo
'Set coords of square
squareObjects(startPoint).setSquareCords(x, y)
'Phyiscally place it in canvas
placeSquareOnCanvas(x, y, squareObjects(startPoint).sqRows, squareObjects(startPoint).sqCols)
'Recursive, get next square
If (startPoint + 1 < totalSquares) Then
recurse(startPoint + 1)
Else
validSolution = isSolutionValid()
'Is solution valud
If (validSolution = True) Then
solutions = solutions + 1
End If
iterations = iterations + 1
'Response.Write("<br /><b>Iteration " & iterations & "</b>")
If (validSolution) Then
'Rate solution, record if best
solutionRating = rateSolution()
If solutionRating > bestCellSaving Then
bestCellSaving = solutionRating
copySolution()
End If
'Response.Write(" <span style='color:green'> <B>VALID SOLUTION</B></span> (" & rateSolution() & ")")
End If
'printCanvas(canvas)
End If
squareObjects(startPoint).removeSquare(canvas)
Next
Next
End If
End Sub

Answer 1

If you extract the loops in a separate routine the solution emerges relatively easily.
I have changed the validSolution logic a bit to make the code shorter - now we don't call recurse if the solution is invalid and we don't need to check for isSolutionValid() at the beginning of recurse(). These changes make counting the iterations harder so I removed that code, but it should be possible to add it later.
The recurse() routine without the last "If" statement should behave exactly as your code. The last "If" statement essentially performs the loops for a rotated rectangle.
I am not sure how removeSquare() is implemented, but it may need to know the orientation to be able to work correctly.
Sub recurse(ByVal startPoint As Integer)
Dim loopXTo As Integer
Dim loopYTo As Integer
If (startPoint = 0) Then
loopXTo = Math.Floor((canvasCols - squareObjects(startPoint).sqRows) / 2)
loopYTo = Math.Floor((canvasRows - squareObjects(startPoint).sqCols) / 2)
Else
loopXTo = canvasCols - squareObjects(startPoint).sqRows
loopYTo = canvasRows - squareObjects(startPoint).sqCols
End If
fitSqare(loopXTo, loopYTo, False)
If (squareObjects(startPoint).sqCols <> squareObjects(startPoint).sqRows) Then
fitSqare(loopYTo, loopXTo, True)
End If
End Sub
Sub fitSquare(ByVal loopXTo As Integer, ByVal loopYTo As Integer, ByVal rotate As Boolean)
Dim x As Integer
Dim y As Integer
Dim solutionRating As Integer
Dim validSolution As Boolean
'Loop all positions on canvas
For x = 0 To loopXTo
For y = 0 To loopYTo
'Set coords of square
squareObjects(startPoint).setSquareCords(x, y)
'Phyiscally place it in canvas
If (rotate) Then
placeSquareOnCanvas(x, y, squareObjects(startPoint).sqCols, squareObjects(startPoint).sqRows)
Else
placeSquareOnCanvas(x, y, squareObjects(startPoint).sqRows, squareObjects(startPoint).sqCols)
End If
validSolution = isSolutionValid()
'Is solution valud
If (validSolution) Then
'Recursive, get next square
If (startPoint + 1 < totalSquares) Then
recurse(startPoint + 1)
Else
solutions = solutions + 1
'Rate solution, record if best
solutionRating = rateSolution()
If solutionRating > bestCellSaving Then
bestCellSaving = solutionRating
copySolution()
End If
End If
End If
squareObjects(startPoint).removeSquare(canvas) 'removeSquare may require additional work to handle rotated state
Next
Next
End Sub

Answer 2

If the canvas is always a square then you don't need to change much. The result for the rotated rectangle 3 is the same as for the unrotated, except the origin of the Canvas is different. Imagine leaving the Rectangle 3 unrotated and rotating the canvas 90 degrees in the other direction. This means that you should be able to use some maths on the same results to get your answer.

Answer 3

Put your (x,y) coordinate loop in its own function. Then call the (x,y) coordinate loop on a rectangle of WxH, and then call it again on the rotated rectangle HxW.
Alternatively you can put the branching on the two rotations of your rectangle inside the (x,y) loop, after both coordinates have been picked, but before you make the recursive call.
In both cases you will need to be careful about whether your rotation causes the rectangle to exceed the height or width of your bounding box.

Answer 4

Can't you simply scan the list of shapes and for those that are rectangles (SizeX != SizeY) add a cloned rectangle with { SizeX = source.SizeY, SizeY = source.SizeX } (eg.: rotated rectangle)?
That would of course mean to do the loops twice (one for the unrotated list of shapes and one for the rotated one).
=> doing something like
squareObjects(startPoint) = squareObjects(startPoint).Rotate();
recurse(startPoint);

Answer 5

Frankly I don't think your implementation is the best- but if you don't want to make big changes and make separate routines you can just put the code for the rectangles twice in the same function-iteration.
So after:
'Phyiscally place it in canvas
placeSquareOnCanvas(x, y, squareObjects(startPoint).sqRows, squareObjects(startPoint).sqCols)
[......]
End If
squareObjects(startPoint).removeSquare(canvas)
You can do a check
IF the square is rectangle (width <> height)
then copy the same code again (in Then code) changing sqRows with sqCols in placeSquareOnCanvas().
The recursion will not be anymore linear, as this will make 2 recursive branches for each rectangle. Maybe it is not very nice written copying the same code 2 times, but the result will be right, the code changing is minimal and this straight solution based on your code will have more performance than trying other tweaks.