State if each of the statements is true or false. Assume that n is a positive...

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Question

State if each of the statements is true or false. Assume that n is a positive...

State if each of the statements is true or false. Assume that n is a positive integer.

log(n!) always grows faster than n².
The greater the number of terms that are added in the expression for the running time of an algorithm, the higher the time complexity of the algorithm.
log(n) always grows faster than n.
log(log(n)) grows slower than log(n) when both log(log(n)) and log(n) are positive.
log(kⁿ) where k is a positive constant, is O(n).

engineering Computer-Science

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Answer 1

Answer #1

og(n!) always grows faster than n2.
False

The greater the number of terms that are added in the expression for the running time of an algorithm, the higher the time complexity of the algorithm.
False

log(n) always grows faster than n.
False

log(log(n)) grows slower than log(n) when both log(log(n)) and log(n) are positive.
True

log(kn) where k is a positive constant, is O(n).
True

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Answer 2

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