Write short notes: Tournament tree

Tournament Tree (Elimination Tree, Knockout Tournament)

A tournament tree is a tree data structure used to organize single-elimination tournaments. It is a special case of a binary tree, where all nodes have either 0, 1 or 2 children, and all leaves are at the same level.

Structure:

• Each node in the tree represents a match between two players or teams.
• The root node represents the final match of the tournament.
• The children of a node represent the two matches that must be played to determine the winner of the match represented by the parent node.
• The leaves of the tree represent the first round matches of the tournament.

Properties:

• The height of a tournament tree is equal to the number of rounds in the tournament.
• The number of nodes in a tournament tree is equal to (2^h - 1), where (h) is the height of the tree.
• The number of leaves in a tournament tree is equal to (2^h).

Applications:

• Tournament trees are used to organize single-elimination tournaments in a variety of sports, including tennis, basketball, and soccer.
• Tournament trees are also used in computer science to organize search algorithms and to solve optimization problems.

Example:

Consider a tournament tree for a single-elimination tennis tournament with 8 players. The tree is shown below:

         Player A
       /         \
     Player B     Player C
       /        \      /   \
    Player D    Player E Player F Player G
      /     \    /     \    /    \    /  \
   Player H Player I Player J Player K Player L Player M Player N Player O

The root node represents the final match between Players A and C. The children of the root node represent the two semi-final matches between Players B and C, and Players D and E. The leaves of the tree represent the first round matches between Players A and B, Players C and D, Players E and F, and Players G and H.

Advantages:

• Tournament trees are easy to understand and implement.
• Tournament trees are efficient for organizing single-elimination tournaments.
• Tournament trees can be used to solve a variety of problems in computer science.

Disadvantages:

• Tournament trees can be unbalanced, which can lead to unfair matchups.
• Tournament trees can be inefficient for organizing tournaments with a large number of participants.