lily it may be nice to mention why practical implementations use ≤ for cutoffs rather than < typo i actually don’t know the reason for this (either the historical reason – why particular people chose to do it and how that influenced the implementations of others – or all the objective effects on typical search trees – although I can conjecture) lily The earliest easily accessible reference I know of is Moore and Knuth's 1975 paper which summarised the state of the art at the time; unfortunately it does not clarify why ≥ was chosen and merely show that historically it was; likely from their constraint that α < β, but that is an assumption <!-- i know that spending a lot of time on something doesn’t make it inherently good whatsoever but it’s still... discouraging, to be excited about something or slightly proud of an effort and then see it received unfavorably truthfully i can’t tell whether ×××××××’s comments are meant to be constructive or critical -->