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(2 pts) (a) What “better-known”/simpler complexity class is equivalent to O(N log N2); briefly explain why....

(2 pts) (a) What “better-known”/simpler complexity class is equivalent to O(N log N2); briefly explain why. (b) Explain under what conditions sorted(set(l)) runs faster than set(sorted(l)) for a list l (they both produce the same answer); state the worst-case complexity class of each.

(a)

(b)

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Answer #1

(a) The given complexity class is . We can compute that and . Thus the complexity class is equivalent to the complexity class .

(b) If the same elements appear more than once in l, then set(l) will eliminate the repeatations and then the number of elements will this get reduced. Running the sorted function will now take less time since the number of elements have decreased. On the other hand if we do the sorted function first, then it would operate on all the elements including the repetitions. Then when the set function is applied the repetitions will get deleted. This will take much longer time.

The worst case time complexity for both the classes is   since the sorting takes time in the worst case and the set formation takes time in the worst case.

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