Sagy wrote: ↑Wed Jul 24, 2024 19:16
I still believe that they will have a schedule of all the games with place holders (e.g. A1-C7 = first team from pot A hosting 7th team from Pot C) and draw the 36 balls one after the other starting with Pot A. The role that the computer will play is to alert with a team that in drawn in position x has to be placed in position y for its Pot to avoid an immediate issue or a deadlock.

Well, I have some concern about it.

It depends on the complexity of the algorithm to be used.

What you are suggesting would be the perfct solution, the "real draw", and requires the computer is alerting in advance that a certain move will cause a deadlocks some steps ahead.

This requires the most complex algorithm, the one which explores completely all the paths of the combinations tree to say if that step in the tree has still valid paths.

Many of us suggest this is too complex, there are a lot of possible paths to explore (I am not able to estimate the order of the number) and it requires too much time, memory and so it could be very hard to implement.

The Plan B could be some euristhic method which predetermines one or more possible fixtures.

Of course in this case it would not be a "real draw".

EDIT:

Just now I am thinking there could be a way in the middle, a plan C - thanks to Francisco post

Let us suppose Plan A is impossible because the possible combinations are something like 10^10 or 10^20, and so it is not possible to run live the algorithm during the draw.

0. The euristhic can predetermine an high number of fixtures, let me say 1,000 or 10,000 or as much as possible (PFS = predetermined fixtures set).

1. The first team X is selected.

2. Then you see which are the possible opponents Y1, ..., Yn in the fixtures in the PFS.

3. You draw Yk the first opponent of X only between Y1, ..., Yn.

4. Then you discard from the PFS all the fixtures where X and Yk does not match.

5. Go back to step 1. or 2. and go forward

until there is only one remaining fixture in the PFS.

When there is only one remaining fixtures in the PFS, you can complete the fixture.