Bin Packing

  Now let's talk about an algorithm with a little more "intelligence".  The First Fit Algorithm does exactly as its name implies.  It steps through the Elements sticking them into the first Bin it can, if there aren't any Bins that it will fit into, a new Bin is added.  You will get pretty efficient use of Bins with this algorithm.

   Private Sub FirstFit()
      '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 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)
         Dim bPlaced As Boolean = False

         'Loops through each Bin to find the first available spot
         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

            If BinCount + ElementsCopy(i) <= Me.BinHeight Then
               'There's room for this Element
               ReDim Preserve Bins(j)(BinElement + 1)
               Bins(j)(BinElement) = ElementsCopy(i)

               bPlaced = True
               Exit For
            Else
               'There's not room for this Element in this Bin
            End If
         Next


         'There wasn't room for the Element in any existing Bin
         'Create a new Bin
         If bPlaced = False Then
            'Add another 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)

         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: