Problem is as following:
We are 8 trumpet players in an orchestra.
There are for example 4 parts so there are always two players on the same part.
Now, there are not always the same two players playing the same part meaning the combination of players that play the same part change from piece to piece.
What is the cheapest way in terms of distance and/or the least amount of switches resulting that the players playing the same parts can sit next to each other on every piece?
Trumpet Players: a,b,c,d,e,f,g,h
Seats are arranged like that:
1st piece | a1 | b1 | c2 | d2 | | e3 | f3 | g4 | h4 | Next piece the players might play the following parts: | a2 | b1 | c3 | d1 | | e3 | f4 | g2 | h4 | and the next one againt different distribution of the parts: | a4 | b3 | c1 | d3 | | e2 | f4 | g2 | h1 |
how do we seat the players so that the least amount has to be traveled in order to reach the desired positions for the players playing the same parts to sit next to each other in the next piece?
additional notes: i dont care where the pairs are starting and if a1 sits left of b1 or the other way around.