find the index of an array function in excel

Question

I have been working on a shortest path problem in excel (see image below) with dynamic programming. I got the numbers. However, I can't find a way to also find the index of the minimum number the path belongs to.

The formula loops over the row and column element-wise, and adds them together. Finally, it fins the minimum value.

For example: the highlighted cell (A15) has the answer 9 (minimum value = 5+4) Now I want to add the column name of this minimum value: C.

I am not an excel expert and have no idea how to do this. Any help is much appreciated!

Answer 1

It should be an index/match formula ie first find the position of the minimum value in the array using Match, then find the corresponding letter in the header row using Index:

=INDEX($B$11:$G$11,MATCH(MIN(TRANSPOSE(B$2:B$7)+$B14:$G14),TRANSPOSE(B$2:B$7)+$B14:$G14,0))

Note if ties are possible, this will find the first match.

In my version of Excel, this has to be entered as an array formula using Ctrl Shift Enter