I came across places where floors and ceilings are neglected while solving recurrences.

Example from CLRS (chapter 4, pg.83) where floor is neglected:

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Here (pg.2, exercise 4.1–1) is an example where ceiling is ignored: (EDIT: I gather from public opinion that this is somewhat fishy.)

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In fact in CLRS (pg.88) its mentioned that:

"Floors and ceilings USUALLY do not matter when solving recurrences"

My questions:

  1. Here does "usually" means ALL cases ? If yes, i can just forget them all the time.
  2. If not, then when do floors and ceilings really count while solving recurrences ?

Note: This ain't a homework problem. I thought about it while I was refreshing my DS and algo concepts.

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