In competitive tournaments, it is common for all the players or teams to play in a series of matches in order to determine a single winner of the entire tournament. However, a number of different tournament formats exist. Here, we will concern ourselves with two tournament formats: elimination tournaments and round-robin tournaments.

In an elimination tournament, players (or teams) are grouped into pairs for their initial match. Players that lose their match are eliminated from the tournament; players that win their match proceed to the next round, whereupon they are again grouped into pairs. This process continues until only one player remains.

Answer the following questions in the context of elimination tournaments

1. How many total games must be played in an 8-player elimination tournament?

2. How many total games must be played in a 16-player elimination tournament?

3. Express the number of games that must be played in an N-player elimination tournament in big-O notation. (C++)

4. What is the maximum number of total games that must be played in a 16-player elimination tournament if each pairing is a best-of-seven match (e.g. a player must win 4 out of 7 against their opponent to proceed to the next round)?

5. What effect, if any, would a best-of-seven format have on the big-O complexity  from part 3 above? Explain your answer.

In a round-robin tournament, every player plays against every other player exactly once. The player who wins the most games wins the tournament (there are a number of more-or-less complicated tie-breaking rules that can be used in the case of a tie - we will ignore these).

In the same document as before, answer the following questions in the context of round-robin tournaments.

1. How many total games must be played in an 8-player round-robin tournament?

2. How many total games must be played in a 16-player round-robin tournament?

3. Express the number of games that must be played in an N-player round-robin tournament in big-O notation