Given a canvas, let’s say 10×10, and given 3 rectangles/squares.
Canvas = 10×10
Rectangle 1 = 2×2
Rectangle 2 = 3×3
Rectangle 3 = 2×4
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
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.