CombSort – A very efficient algorithm

' Comb Sort an array of any type'' CombSort is faster than all but QuickSort and close to it.' On the other hand, the code is much simpler than QuickSort' and can be easily customized for any array type' This routine is based on an article appeared on the Byte' magazine in about 1985.'' NUMELS is the index of the last item to be sorted, and is' useful if the array is only partially filled.'' Works with any kind of array, except UDTs and fixed-length' strings, and including objects if your are sorting on their' default property. String are sorted in case-sensitive mode.'' You can write faster procedures if you modify the first two lines' to account for a specific data type, eg.' Sub CombSortS(arr() As Single, Optional numEls As Variant,'  Optional descending As Boolean)'   Dim value As SingleSub CombSort(arr As Variant, Optional numEls As Variant, _    Optional Descending As Boolean)    Dim value As Variant    Dim index As Long    Dim firstItem As Long    Dim Gap As Long    Dim Swap As Boolean    ' account for optional arguments    If IsMissing(numEls) Then numEls = UBound(arr)    firstItem = LBound(arr)    Gap = numEls - firstItem + 1    Swap = False    Do While (Gap > 1 Or Swap)        ' divide Gap by 1.3 - the author says it's an empirical value        If Gap > 1 Then Gap = (10 * Gap)  13        ' another empirical value        If (Gap = 9 Or Gap = 10) Then Gap = 11        Swap = False        For index = firstItem To numEls - Gap            value = arr(index)            If (value > arr(index + Gap)) Xor Descending Then                ' if the items are not in order, swap them                arr(index) = arr(index + Gap)                arr(index + Gap) = value                Swap = True            End If        Next    LoopEnd Sub

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