Return unique column headers matching criteria - excel

Question

Consider the following data below:
| 1st | 2nd | A | B | C | D | E | F | G | H |
|-----|-----|---|---|---|---|---|---|---|---|
| y | x | | | 1 | | | | | |
| y | x | | | 1 | | | | | |
| y | x | | | | 1 | | | | |
| | x | 1 | | | | | | | |
| y | | 1 | 1 | 1 | | | | | |
| y | x | | | | | | 1 | | |
| y | | | | | | | | 1 | |
| | x | | | | | 1 | | | |
| | x | | | | | | | | 1 |
| y | x | | | | | | | | 1 |
What I wish to do is to return all column headers (from A to H) that meets the following condition: it should have a value of 1 that is both aligned with a y and x value from the first two columns.
I already have a working array formula to do this, which is as follows:
{=INDEX($C$1:$J$1,SMALL(IF(($A$2:$A$11="y")*($B$2:$B$11="x")*($C$2:$J$11=1),COLUMN($C$1:$J$1)-COLUMN($B$1)),ROW(1:1)))}
However, while I drag this down, it returns two C values and one for D, F and H.
This is since there are two 1's under header C that meets the said condition. What I want is to return unique values, so C should only be returned once. I tried to make use of MATCH and additional COUNTIF instead of the SMALL function, but it is returning an error, and the 'Evaluate formula' feature of Excel isn't helping. Below if the erroneous formula I experimented with:
{=INDEX($C$1:$J$1,MATCH(0,IF(($A$2:$A$11="y")*($B$2:$B$11="x")*($C$2:$J$11=1),COUNTIF($N$1:N1,COLUMN($C$1:$J$1)-COLUMN($B$1))),0))}
A workaround I am currently doing is to make my first formula a "helper column" and then create another formula based from the first formula's result to return only the unique values. However, the double array formula is heavily affecting the efficiency of Excel's calculation due to the huge volume of data I'm dealing with.
Any help/suggestions will do please (no VBA please, since I believe it's not needed here). Thanks!

Answer 1

Insert a helper row. I did it just under your header row before your data. In this row you check to see if there is a 1 that lines up with an x and a y. I assumed this to be non blank, but if its specific values change the formula from <>"" to ="y" or =134 as the case may be. Place the following formula under your first column header you are interested in and copy right.
=--(0<SUMPRODUCT(($B$3:$B$12<>"")*($C$3:$C$12<>"")*(D3:D12=1)))
Then where you want to generate your list in a column without space and sorted in the order the appear in from left to right in the headings, use the following formula and copy down as required:
=IFERROR(INDEX($1:$1,AGGREGATE(15,6,COLUMN($D$2:$K$2)/$D$2:$K$2,ROW(A1))),"")
The above formula put in a blank value when no column heading applies are you have copied the formula down beyond the number of applicable columns.
The above formulas are based on the proof of concept image below. Adjust ranges to suit your needs.

Answer 2

Have you tried without the use of an array formula? I don't know how large the data actually is. But, this might be what you are looking for:
=IF(COUNTIFS($A:$A,"y",$B:$B,"x",C:C,1)>0,C1,"")
Assuming column A is "1st" and "H" is your last column at colunm J. Try pasting the formula at "K1" and drag it to your right until "S1".