Bin Packing

First Fit Algorithm

  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
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)

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
'There's not room for this Element in this Bin
End If

'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

'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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