Having every team grapple with every other team is like having guests exchange hugs at our dinner party: the dreaded O(n2), quadratic time. Ladder tournaments—popular in sports like badminton, squash, and racquetball—put players in a linear ranking, with each player allowed to issue a direct challenge to the player immediately above them, exchanging places if they prevail. Ladders are the Bubble Sorts of the athletic world and are thus also quadratic, requiring O(n2) games to reach a stable ranking. Perhaps the most prevalent tournament format, however, is a bracket tournament—as in the famous
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