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For example, at some point I'd like to change the current code so if we are given a hint and it is wrong, then we only search either [begin,hint) or (hint,end), depending on what the result of checking the hint was.
It seems to me that would result in 2x comparisons in common cases, even when the hint is "close". This is because you would likely need to walk up the tree and then back down.
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