Question

I have a 2D array that holds unique integers – this represents a physical container with rows/columns – in each position there is a vial.

I know the integers that should be in the array and where they should be located.

My array however is shuffled with potentially many/all unique integers in the wrong positions.

I now need to sort the array – however this maps to a physical process and therefore I really want to reduce the number of sort steps involved due to potential human error.

Is this just a plain sort? or is there a more specific name for this scenario? Is there well known solutions?

My colleague has suggested just creating a list of swap [1][1] with [2][1] type instructions, which seems reasonable however I can’t quite get my head around if the order of swaps is important.

All assistance grateful.

Answer 1

If you really can tell, just by looking at the vial, where it belongs, the shortest way is to take the first vial that is in the wrong place out, then put it where it belongs, take whatever was there, put it to its proper place, etc., until you happen to get the vial that belongs where you originally made a “hole”. Then repeat.

Since you take out each vial at most once, and only if it is in the wrong place, I think that this is optimal with respect to physical motion.