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Quoting a section from the article:
Big Greek Letters
Big O is often misused. Big O or Big Oh is actually short for Big Omicron. It represents the upper bound of asymptotic complexity. So if an algorithm is O(n log n) there exists a constant c such that the upper bound is cn log n.
Θ(n log n) (Big Theta) is more tightly bound than that. Such an algorithm means there exists two constants c1 and c2 such that c1n log n < f(n) < c2n log n.
Ω(n log n) (Big Omega) says that the algorithm has a lower bound of cn log n.
There are others but these are the most common and Big O is the most common of all. Such a distinction is typically unimportant but it is worth noting. The correct notation is the correct notation, after all.
What is Big O?
Big O notation seeks to describe the relative complexity of an algorithm by reducing the growth rate to the key factors when the key factor tends towards infinity. For this reason, you will often hear the phrase asymptotic complexity. In doing so, all other factors are ignored. It is a relative representation of complexity.
What Isn’t Big O?
Big O isn’t a performance test of an algorithm. It is also notional or abstract in that it tends to ignore other factors. Sorting algorithm complexity is typically reduced to the number of elements being sorted as being the key factor. This is fine but it doesn’t take into account issues such as:
Memory Usage: one algorithm might use much more memory than another. Depending on the situation this could be anything from completely irrelevant to critical; Cost of Comparison: It may be that comparing elements is really expensive, which will potentially change any real-world comparison between algorithms; Cost of Moving Elements: copying elements is typically cheap but this isn’t necessarily the case; etc.