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Published byQuincy Hastey Modified over 3 years ago

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HKOI Senior Q2 - Igloo Ivan Li

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Background A peaceful sports event of innocent cute little penguins...... mercilessly destroyed by Big Bad Monsters!

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In short Single elimination tournament –Tree structure Taller penguin wins In case of a tie, compare index Must not let monsters win!

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Direct simulation Stores the penguins in an array, and simulate the competition process After some tedious typing work, you get 50%

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When there is no monsters The tallest penguin wins If tie, the lowest index Hurrah! 20%!

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When monsters step in They may beat the potential winners Good news – monsters live in the same igloo. Their indexes are consecutive

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Observation 1 When the monsters are not the tallest, we don’t have to be afraid of them Just ignore them

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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

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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

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Full Solution

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Alternative solution Maintain the start and end index of each igloo Simulate the rounds Calculate the boundaries –Match on the boundaries? –Who wins?

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Questions?

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