Algorithm for generate single elimination round from previous groups phase in a tournament

[aprens]

An example tournament has two stages, groups play + bracket play. When the groups stage ends, the x top of each group go to bracket stage. In the brackets stage there are two basics rules:

• a winner of a group should not be matched against a winner of another group (only against 2nd or 3rd place)
• no two teams that played in the same group should be matched against each other.

For example, if we have 6 groups and top 2 each group advance to bracket, the bracket must be:



Another example with 4 groups of 8 teams and all teams advance to bracket:



I would appreciate any help. Thanks.

[PatrickStokes]

A group winner (1st place) should not face another group winner in the first round. → Only vs. 2nd or 3rd place teams.
Teams from the same group must not face each other in the first round. Optionally, you might want to keep the bracket “balanced” (e.g., 1A shouldn’t face 2B and 1B face 2A Geometry Dash if possible).
So total = 6 × 2 = 12 teams. We’ll need a 16-team bracket, meaning 4 byes