Is n or nlog(n) better than constant or logarithmic time?

Question

In the Princeton tutorial on Coursera the lecturer explains the common order-of-growth functions that are encountered. He says that linear and linearithmic running times are \"w

Answer 1

What we strive for is efficiency, in the sense of designing algorithms with a time (or space) complexity that does not exceed their theoretical lower bound.

For instance, using comparison-based algorithms, you can't find a value in a sorted array faster than Omega(Log(N)), and you cannot sort an array faster than Omega(N Log(N)) - in the worst case.

Thus, binary search O(Log(N)) and Heapsort O(N Log(N)) are efficient algorithms, while linear search O(N) and Bubblesort O(N²) are not.

The lower bound depends on the problem to be solved, not on the algorithm.