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Gray code code in the standings?

In the bottom-up standings, where there is a winner, I was told that it was somehow related to the gray code. I know that the gray code is an alternative code, it is recursive and useful for finding the best solution in various games, whitespace curves, error correction codes, hard drive positioning and is an abbreviation for a pianist, but how is this code related to the tournament chart?

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The following is developed from here :

A tournament is indeed a node in a binary tree. The value in each node contains the rating of the best rating team contained in the tournament tree. It turns out that the gray rating-1 code has a bit, which conveniently helps us to go down to the binary tree, a suitable place to place the team. When descending three, the bits in the gray rating code from least significant to most significant indicate which branch to take.

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