Background A peaceful sports event of innocent cute little penguins...... mercilessly destroyed by Big Bad Monsters!
In short Single elimination tournament –Tree structure Taller penguin wins In case of a tie, compare index Must not let monsters win!
Direct simulation Stores the penguins in an array, and simulate the competition process After some tedious typing work, you get 50%
When there is no monsters The tallest penguin wins If tie, the lowest index Hurrah! 20%!
When monsters step in They may beat the potential winners Good news – monsters live in the same igloo. Their indexes are consecutive
Observation 1 When the monsters are not the tallest, we don’t have to be afraid of them Just ignore them
Observation 2 When the monsters on the left subtree, all normal penguins in that subtree will be beaten. Only consider the right subtree Similar holds for right subtree
Full Solution Call the penguins on the left(right) of the monsters “the left(right) band”. Find the largest subtree that is included in the bands –Lengths must be power of 2 Which subtree survives longer? –The taller (larger) one –Tie – the right one The tallest penguin in that subtree