Subtracting ranges in VBA (Excel)

What I'm trying to do I'm trying to write a function to subtract Excel ranges. It should take two input parameters: range A and range B. It should return a range object consisting of cells that are part of range A and are not part of range B (as in set subtraction) What I've tried I've seen some examples on the web that use a temporary worksheet to do this (fast, but might introduce some issues with protected workbooks and such) and some other examples that go cell by cell through the first range checking for intersections with the second one (extremely slow). After some thinking I've come up with this code {1}, which works faster, but still is slow. Subtracting from a range representing the whole worksheet takes from 1 to 5 minutes depending on how complex the second range is. When I looked over that code trying to find ways to make it faster I saw a possibility for applying the divide-and-conquer paradigm, which I did {2}. But that had made my code slower instead. I'm not much of a CS guy, so I might have done something wrong or this algorithm simply is not the one the divide-and-conquer should be used on, I don't know. I have also tried rewriting it using mostly recursion, but that took forever to finish or (more often) had thrown Out of Stack Space errors. I didn't save the code. The only (marginally) successful improvement I've been able to do is adding a flip switch {3} and going first through rows, then (in the next call) through columns instead of going through both in the same call, but the effect was not as good as I've hoped. Now I see that even though we don't go through all rows in the first call, in the second call we still loop through the same amount of rows we would in the first one, only these rows are a little bit shorter :) I would appreciate any help in improving or rewriting this function, thank you! The solution, based on the accepted answer by Dick Kusleika Dick Kusleika, thank you very much for providing your answer! I think I'll use it with some modifications I've made: - Got rid of the global variable (mrBuild) - Fixed "some overlap" condition to exclude "no overlap" case - Added more complex conditions to choose whether to split the range top to bottom or left to right With these modifications the code runs very fast on the most of common cases. As it's been pointed out, it will still be slow with checkerboard-style huge range which I agree is unavoidable. I think this code still has a room for improvement and I'll update this post in case I modify it. Improvement possibilities: - Heuristics of choosing how to split the range (by columns or by rows) {0} Solution code BUGGY! See reply from SteveS below Update 2023-07-07 After posting this code to StackOverflow I started using it and hitting its limitations. Fixed version has become significantly more complex and yet it is not perfect, large merged cells may trip it up. Here is the code I've been using for the past 9 years: https://gist.github.com/sio/7423c651d7367de886bb256c4de5e45e Original buggy version below: ``` Public Function SubtractRanges(rFirst As Range, rSecond As Range) As Range ' ' Returns a range of cells that are part of rFirst, but not part of rSecond ' (as in set subtraction) ' ' This function handles big input ranges really well! ' ' The reason for having a separate recursive function is ' handling multi-area rFirst range ' Dim rInter As Range Dim rReturn As Range Dim rArea As Range Set rInter = Intersect(rFirst, rSecond) Set mrBuild = Nothing If rInter Is Nothing Then 'no overlap Set rReturn = rFirst ElseIf rInter.Address = rFirst.Address Then 'total overlap Set rReturn = Nothing Else 'partial overlap For Each rArea In rFirst.Areas Set mrBuild = BuildRange(rArea, rInter) 'recursive Next rArea Set rReturn = mrBuild End If Set SubtractRanges = rReturn End Function Private Function BuildRange(rArea As Range, rInter As Range, _ Optional mrBuild As Range = Nothing) As Range ' ' Recursive function for SubtractRanges() ' ' Subtracts rInter from rArea and adds the result to mrBuild ' Dim rLeft As Range, rRight As Range Dim rTop As Range, rBottom As Range Dim rInterSub As Range Dim GoByColumns As Boolean Set rInterSub = Intersect(rArea, rInter) If rInterSub Is Nothing Then 'no overlap If mrBuild Is Nothing Then Set mrBuild = rArea Else Set mrBuild = Union(mrBuild, rArea) End If ElseIf Not rInterSub.Address = rArea.Address Then 'some overlap If Not rArea.Cells.CountLarge = 1 Then 'just in case there is only one cell for some impossible reason ' Decide whether to go by columns or by rows ' (helps when subtracting whole rows/columns) If Not rInterSub.Columns.Count = rArea.Columns.Count And _ ((Not rInterSub.Cells.CountLarge = 1 And _ (rInterSub.Rows.Count > rInterSub.Columns.Count _ And rArea.Columns.Count > 1) Or (rInterSub.Rows.Count = 1 _ And Not rArea.Columns.Count = 1)) Or _ (rInterSub.Cells.CountLarge = 1 _ And rArea.Columns.Count > rArea.Rows.Count)) Then GoByColumns = True Else GoByColumns = False End If If Not GoByColumns Then Set rTop = rArea.Resize(rArea.Rows.Count \ 2) 'split the range top to bottom Set rBottom = rArea.Resize(rArea.Rows.Count - rTop.Rows.Count).Offset(rTop.Rows.Count) Set mrBuild = BuildRange(rTop, rInterSub, mrBuild) 'rerun it Set mrBuild = BuildRange(rBottom, rInterSub, mrBuild) Else Set rLeft = rArea.Resize(, rArea.Columns.Count \ 2) 'split the range left to right Set rRight = rArea.Resize(, rArea.Columns.Count - rLeft.Columns.Count).Offset(, rLeft.Columns.Count) Set mrBuild = BuildRange(rLeft, rInterSub, mrBuild) 'rerun it Set mrBuild = BuildRange(rRight, rInterSub, mrBuild) End If End If End If Set BuildRange = mrBuild End Function ``` Other code mentioned in the question {1} Initial code (go row by row, column by column) ``` Function SubtractRanges(RangeA, RangeB) As Range ' ' Returns a range of cells that are part of RangeA, but not part of RangeB ' ' This function handles big RangeA pretty well (took less than a minute ' on my computer with RangeA = ActiveSheet.Cells) ' Dim CommonArea As Range Dim Result As Range Set CommonArea = Intersect(RangeA, RangeB) If CommonArea Is Nothing Then Set Result = RangeA ElseIf CommonArea.Address = RangeA.Address Then Set Result = Nothing Else 'a routine to deal with A LOT of cells in RangeA 'go column by column, then row by row Dim GoodCells As Range Dim UnworkedCells As Range For Each Area In RangeA.Areas For Each Row In Area.Rows Set RowCommonArea = Intersect(Row, CommonArea) If Not RowCommonArea Is Nothing Then If Not RowCommonArea.Address = Row.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Row) End If Else Set GoodCells = AddRanges(GoodCells, Row) End If Next Row For Each Column In Area.Columns Set ColumnCommonArea = Intersect(Column, CommonArea) If Not ColumnCommonArea Is Nothing Then If Not ColumnCommonArea.Address = Column.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Column) End If Else Set GoodCells = AddRanges(GoodCells, Column) End If Next Column Next Area If Not UnworkedCells Is Nothing Then For Each Area In UnworkedCells Set GoodCells = AddRanges(GoodCells, SubtractRanges(Area, CommonArea)) Next Area End If Set Result = GoodCells End If Set SubtractRanges = Result End Function ``` {2} Divide and conquer ``` Function SubtractRanges(RangeA, RangeB) As Range ' ' Returns a range of cells that are part of RangeA, but not part of RangeB ' Dim CommonArea As Range Dim Result As Range Set CommonArea = Intersect(RangeA, RangeB) If CommonArea Is Nothing Then Set Result = RangeA ElseIf CommonArea.Address = RangeA.Address Then Set Result = Nothing Else 'a routine to deal with A LOT of cells in RangeA 'go column by column, then row by row Dim GoodCells As Range Dim UnworkedCells As Range For Each Area In RangeA.Areas RowsNumber = Area.Rows.Count If RowsNumber > 1 Then Set RowsLeft = Range(Area.Rows(1), Area.Rows(RowsNumber / 2)) Set RowsRight = Range(Area.Rows(RowsNumber / 2 + 1), Area.Rows(RowsNumber)) Else Set RowsLeft = Area Set RowsRight = CommonArea.Cells(1, 1) 'the next best thing to Nothing - will end its cycle rather fast and won't throw an error with For Each statement End If For Each Row In Array(RowsLeft, RowsRight) Set RowCommonArea = Intersect(Row, CommonArea) If Not RowCommonArea Is Nothing Then If Not RowCommonArea.Address = Row.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Row) End If Else Set GoodCells = AddRanges(GoodCells, Row) End If Next Row ColumnsNumber = Area.Columns.Count If ColumnsNumber > 1 Then Set ColumnsLeft = Range(Area.Columns(1), Area.Columns(ColumnsNumber / 2)) Set ColumnsRight = Range(Area.Columns(ColumnsNumber / 2 + 1), Area.Columns(ColumnsNumber)) Else Set ColumnsLeft = Area Set ColumnsRight = CommonArea.Cells(1, 1) End If For Each Column In Array(ColumnsLeft, ColumnsRight) Set ColumnCommonArea = Intersect(Column, CommonArea) If Not ColumnCommonArea Is Nothing Then If Not ColumnCommonArea.Address = Column.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Column) End If Else Set GoodCells = AddRanges(GoodCells, Column) End If Next Column Next Area If Not UnworkedCells Is Nothing Then For Each Area In UnworkedCells Set GoodCells = AddRanges(GoodCells, SubtractRanges(Area, CommonArea)) Next Area End If Set Result = GoodCells End If Set SubtractRanges = Result End Function ``` {3} Initial code + flip switch (row by row OR column by column in turns) ``` Function SubtractRanges(RangeA, RangeB, Optional Flip As Boolean = False) As Range ' ' Returns a range of cells that are part of RangeA, but not part of RangeB ' ' This function handles big RangeA pretty well (took less than a minute ' on my computer with RangeA = ActiveSheet.Cells) ' Dim CommonArea As Range Dim Result As Range Set CommonArea = Intersect(RangeA, RangeB) If CommonArea Is Nothing Then Set Result = RangeA ElseIf CommonArea.Address = RangeA.Address Then Set Result = Nothing Else 'a routine to deal with A LOT of cells in RangeA 'go column by column, then row by row Dim GoodCells As Range Dim UnworkedCells As Range For Each Area In RangeA.Areas If Flip Then For Each Row In Area.Rows Set RowCommonArea = Intersect(Row, CommonArea) If Not RowCommonArea Is Nothing Then If Not RowCommonArea.Address = Row.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Row) End If Else Set GoodCells = AddRanges(GoodCells, Row) End If Next Row Else For Each Column In Area.Columns Set ColumnCommonArea = Intersect(Column, CommonArea) If Not ColumnCommonArea Is Nothing Then If Not ColumnCommonArea.Address = Column.Address Then Set UnworkedCells = AddRanges(UnworkedCells, Column) End If Else Set GoodCells = AddRanges(GoodCells, Column) End If Next Column End If Next Area If Not UnworkedCells Is Nothing Then For Each Area In UnworkedCells Set GoodCells = AddRanges(GoodCells, SubtractRanges(Area, CommonArea, Not Flip)) Next Area End If Set Result = GoodCells End If Set SubtractRanges = Result End Function ``` A little helper function mentioned here and there: ``` Function AddRanges(RangeA, RangeB) ' ' The same as Union built-in but handles empty ranges fine. ' If Not RangeA Is Nothing And Not RangeB Is Nothing Then Set AddRanges = Union(RangeA, RangeB) ElseIf RangeA Is Nothing And RangeB Is Nothing Then Set AddRanges = Nothing Else If RangeA Is Nothing Then Set AddRanges = RangeB Else Set AddRanges = RangeA End If End If End Function ```