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Using the formal definition of asymptotic notations, prove that: The running time of an algorithm t ( n ) is Theta ( g (
Using the formal definition of asymptotic notations, prove that:
"The running time of an algorithm tn is Theta gn if and only if its worstcase running time twn is
Ogn and its bestcase running time tbn is Omega gn
Notes:
There is no mention of the average case running time here:
tn is a function representing the running time of an algorithm in general, not for a specific
input class. It may have a different closed form for each input class, or no closed form at all.
twn is a function representing the running time of an algorithm for the specific class of
inputs designated as "worst case".
tbn is a function representing the running time of an algorithm for the specific class of
inputs designated as "best case".
This is an if and only if statement, so the proof usually involves two parts.
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