Cup Stage
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Consider a world cup stage where players are competing in a knockout format: they face each other according to their positions in the bracket in a single-elimination match. The winners of each match advance to the next round until a champion is determined. Look at the example for 16 players.
Given two players' positions in the bracket and the total number of players, your program should determine what phase (final, 1/2, 1/4 etc.) they will face each other in, assuming they both win their matches until they meet.
Input: Three integers (int).
Output: String (str).
Examples:
assert cup_stage(10, 14, 16) == "1/2" assert cup_stage(5, 18, 32) == "final" assert cup_stage(5, 7, 8) == "1/2" assert cup_stage(1, 2, 2) == "final"
Preconditions:
- 1 <= pos1 < pos2 <= total;
- total = 2n, n = 1, 2,... .
