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order notation - ACCD - 09-05-2017

like question 32 33 34 35 36 true or false
 whats the different between "always" and "always" plus "all cases"? 
I think always means all cases.

RE: order notation - lusth - 09-05-2017

Without qualifiers, always means input size sufficiently large and worst case behavior. See the note at the start of that section:

Assume the worst case and sufficiently large input size unless otherwise indicated. The phrase the same time as means equal within a constant factor (or lower order term) unless otherwise indicated. The phrase by a stopwatch means the actual amount of time needed for the algorithm to run to completion, as measured by a stopwatch.