A tournament tree is a complete binary tree reflecting results of a "knockout tournament": its leaves represent n players entering the tournament, and each internal node represents a winner of a match...

A tournament tree is a complete binary tree reflecting results of a "knockout tournament": its leaves represent n players entering the tournament, and each internal node represents a winner of a match played by the players represented by the node's children. Hence, the winner of the tournament is represented by the root of the tree.

a. What is the total number of games played in such a tournament?

b. How many rounds are there in such a tournament?

c. Design an efficient algorithm to determine the second-best player using the information produced by the tournament. How many extra games does your algorithm require?