Bin Packing

   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
         Array.Sort(ElementsCopy)
         Array.Reverse(ElementsCopy)
      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)
            Next

            '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
         Next


         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)
         Else
            '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
      Next

      '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
         Next
      Next

      GC.Collect()
   End Sub

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