How to determinate round by element in tree (Tourn

问题:

Assume we have following tree:

1
    9
2
        13
3
    10
4 
            15
5
    11
6 
        14
7   
    12
8

Where elements(matches):
1-8 is round 1
9-12 is round 2
13-14 is round 3
15 is round 4

How I can determinate round of element "n" in shuch tree?

My current formulas are:

total_rounds = floor(log(totalTeams,2));

matches_per_round = (totalTeams / pow(2, current_round))

next_match_id = (totalTeams/2) + ceil(match_id/2)

total_matches = total_teams - 1

回答1:

Imagine the tree was numbered in reverse.

15
     7
14
         3
13 
     6
12 
             1
11
     5 
10 
         2
9   
     4
8

In that case, it'd simply be the logarithm of the number, rounded down. Now we simply subtract this number from the number of rounds, and we're done.

reverse_number = total_matches - match_number + 1;
reverse_match_round = floor(log(reverse_number, 2));
match_round = total_rounds - match_round;

(Note, reverse_match_round is actually 0-indexed, unlike match_round. However, since we subtract it from total_rounds, it's easier to keep it that way than to 1-index it. If you prefer it 1-indexed, simply add +1 to each of the last two lines.)