Finding the optimal draw of a balanced knockout tournament for a player
Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. Such tournaments can be represented by a balanced binary tree in which the leaves correspond to the players. A balanced knockout tournament is conducted in the following fashion. Players that correspond to sibling leaf nodes play a match against each other. The winner of the match proceeds up the tree to the next round. The winner of the balanced knockout tournaments is the player who reaches the root node. Example 1 : One of the balanced knockout tournament of which I have fond memories is the one on four teams that represents the semi finals and final of the 1992 cricket world cup. South Africa and New Zealand who lost their respective semi-finals were eliminated whereas Pakistan and England contested the final in Melbourne. It has long been observed that the draw (the way players/teams are paired up) of a balanced knockout tourna...