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Can SCAN() and BYROW() be combined?
The support page for SCAN() contains the following example: =SCAN("",A1:C2,LAMBDA(a,b,a&b)) My general issue is combining BYROW() or BYCOLUMN() with ...
It looks like it should work and, indeed, a similar formula with REDUCE does work. Unfortunately SCAN produces an array on each row, leading to an array of arrays which hasn't been implemented within the calc engine. There are two distinct approaches to overcome the problem, neither of which is that attractive.
The first is to allow SCAN to run through the 6 values as a single sequence but to reset the resulting text to null whenever the scan returns to the first column. Rather than scanning the text array, I scanned the sequence {0,1,2;3,4,5} which can both be used to look up the text to concatenate and to identify the leading column.
= SCAN("", SEQUENCE(2,3,0), LAMBDA(str,k, LET( row, 1+QUOTIENT(k,3), column, 1+MOD(k,3), chr, INDEX(data, row, column), IF(column>1,str,"")&chr ) ) )The second approach follows your original formula more closely but, instead of allowing SCAN to build a text array, it builds a Thunk that contains the array. BYROW then creates an array of 2 thunks and if the result is passed to MAKEARRAY each thunk may be singled out by INDEX, then expanded by passing it a null parameter string and wrapped within a further INDEX, which will return a single value to be assembled into the solution array.
Thunkλ = LAMBDA(x,LAMBDA(x)) Forming a thunk: = LET( arrayϑ, Thunkλ(array), Returning its content: = arrayϑ()I will leave it to you to judge whether the most appropriate answer to your question is 'yes' or 'no'!
It looks like it should work and, indeed, a similar formula with REDUCE does work. Unfortunately SCAN produces an array on each row, leading to an array of arrays which hasn't been implemented within the calc engine. There are two distinct approaches to overcome the problem, neither of which is that attractive.
The first is to allow SCAN to run through the 6 values as a single sequence but to reset the resulting text to null whenever the scan returns to the first column. Rather than scanning the text array, I scanned the sequence {0,1,2;3,4,5} which can both be used to look up the text to concatenate and to identify the leading column.
= SCAN("", SEQUENCE(2,3,0),
LAMBDA(str,k,
LET(
row, 1+QUOTIENT(k,3),
column, 1+MOD(k,3),
chr, INDEX(data, row, column),
IF(column>1,str,"")&chr
)
)
)The second approach follows your original formula more closely but, instead of allowing SCAN to build a text array, it builds a Thunk that contains the array. BYROW then creates an array of 2 thunks and if the result is passed to MAKEARRAY each thunk may be singled out by INDEX, then expanded by passing it a null parameter string and wrapped within a further INDEX, which will return a single value to be assembled into the solution array.
Thunkλ
= LAMBDA(x,LAMBDA(x))
Forming a thunk:
= LET(
arrayϑ, Thunkλ(array),
Returning its content:
= arrayϑ()I will leave it to you to judge whether the most appropriate answer to your question is 'yes' or 'no'!
- First - and obviously - thanks for you thoughtful reply. I'll play with both options against other examples, but my gut feeling is that #2 will come up ahead.
Second - and this is sort of a general rant - having played around with many of the new shiny toys recently introduced to Excel, I must say the whole process feels strange, like "two steps forward - one step back". This one is a great example of Excel being inconsistent in applying its own logic: if something can be done by row (or by column) it should be always doable that way, instead of letting users find out (and memorizing) the circumstances where the logic works and where it doesn't. When you say, about the two approaches (in this case) to overcoming the problem, that "neither of which is that attractive" you are being, I feel, very polite. The near constant need to look for "alternatives", "workarounds", "hacks", etc. to resolve issues which should be straightforward is utterly exhausting....I see your point. The best I can say is that the pitfalls are relatively few.
A bit like traditional Excel where one tries to explain why
= COUNTIFS(MONTH(date),6))doesn't work. Because CONTIFS doesn't accept array parameters in place of a range reference always sounded a bit lame.
In the present case, I got to
= MAKEARRAY(2,3, Expandλ( BYROW(data, LAMBDA(row,Thunkλ(SCAN("", row, Concatλ)))) )) where Expandλ = LAMBDA(ϑ, LAMBDA(r,c, INDEX(INDEX(ϑ, r,1)(),,c) )); Concatλ = LAMBDA(array,cell, array&cell);It is heavy going but, once done, it can be reused. Hopefully, not too often!
As far as I can tell, I am not one of the 10,000 Excel users who rate as a developer by the ICAEW (referred to in your other answer), but I AM a long time, heavy user of Excel so I feel qualified to offer my two cents on this:
Having studied your approaches more closely, I have to say that I now tend to prefer your first approach (designated as "Single sequence" in your attachment). Still, the approach involves using 8 different functions (SCAN, SEQUENCE, LABMDA, LET, QUOTIENT, MOD, INDEX and IF)!
The solution proposed by mtarler - which also works - involves even more (LET, ROWS, COLUMNS, TEXT, SEQUENCE, SCAN, LAMBDA, IF, MOD, LEFT and MID) - 11 in total!
Just eyeballing these solutions (let alone parsing them) would give your run-of-the-mill non-developer user a headache...
What I imagine that type of user would do is just give up on spillable purity, use instead
=SCAN("",A1:C1,LAMBDA(a,b,a&b))and then drag it down one row - and be done with the whole thing.
