# Bin Packing

## Worst Fit Algorithm

Despite its name, the Worst Fit Algorithm produces result that are consistently better than the First Fit Algorithm.  This does come with some extra processing though (on small data sets it doesn't really matter).  The only difference between the two algorithms is that Worst Fit picks the Bin with the most amount of free space (or creates a new Bin if no existing one can fit the Element) instead of just picking the first Bin available.

`   Private Sub WorstFit()      '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 WorstBin, WorstBinAmount 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)         WorstBin = -1         WorstBinAmount = Me.BinHeight + 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 least full Bin that can hold this Element            If WorstBinAmount > BinCount AndAlso BinCount + ElementsCopy(i) <= Me.BinHeight Then               WorstBinAmount = BinCount               WorstBin = j            End If         Next         If WorstBin = -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(WorstBin).GetUpperBound(0)            ReDim Preserve Bins(WorstBin)(BinElement + 1)            Bins(WorstBin)(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:

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