Bin Packing

Best Fit Algorithm

   And now we come to our last algorithm, the Best Fit Algorithm.  The only difference between this and the Worst Fit Algorithm is that instead of picking a Bin with the most amount of free space, this algorithm picks the Bin with the least amount of free space in it that can still hold the current Element.  The results you obtain by using this algorithm are not always the same as the Worst Fit, sometimes it is slightly better, other times it is not.  It depends on the nature of the data supplied.

   Private Sub BestFit()
'Checks to make sure everything is initialized
If Elements Is Nothing Then Exit Sub

Dim ElementsCopy(Elements.GetUpperBound(0)) As Integer
ReDim Bins(0)
'Bin Number we are on, Bin Element we are on, Amount placed in the current Bin
Dim BinNumber, BinElement, BinCount As Integer
Dim BestBin, BestBinAmount As Integer
Dim i, j, k As Integer

'Make a copy of the array incase we need to sort it
DeepCopyArray(Elements, ElementsCopy)

'Sort in descending order if needed
If Me.Decreasing = True Then
End If

'Declare the first element in the first Bin
ReDim Bins(0)(0)

'Loop through each Element and place in a Bin
For i = 0 To ElementsCopy.GetUpperBound(0)
BestBin = -1
BestBinAmount = -1

For j = 0 To BinNumber
BinElement = Bins(j).GetUpperBound(0)

'Count the amount placed in this Bin
BinCount = 0
For k = 0 To BinElement
BinCount += Bins(j)(k)

'Find the most full Bin that can hold this Element
If BestBinAmount < BinCount AndAlso BinCount + ElementsCopy(i) <= Me.BinHeight Then
BestBinAmount = BinCount
BestBin = j
End If

If BestBin = -1 Then
'There wasn't room for the Element in any existing Bin
'Create a new Bin
ReDim Preserve Bins(BinNumber + 1)
BinNumber += 1

'Initialize first element of new bin
ReDim Bins(BinNumber)(1)
BinElement = 0

Bins(BinNumber)(BinElement) = ElementsCopy(i)
'There's room for this Element in an existing Bin
'Place Element in "Best Bin"
BinElement = Bins(BestBin).GetUpperBound(0)
ReDim Preserve Bins(BestBin)(BinElement + 1)
Bins(BestBin)(BinElement) = ElementsCopy(i)
End If

'All Elements have been place, now we go back and remove unused Elements
For i = 0 To BinNumber
For j = 0 To Bins(i).GetUpperBound(0)
If Bins(i)(j) = 0 Then
ReDim Preserve Bins(i)(j - 1)
End If

End Sub

With the same set of data as the last example, this algorithm will lay out something like this in memory:

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