What is the difference between O, Ω, and Θ?

Question

I am learning algorithm analysis. I am having trouble understanding the difference between O, Ω, and Θ.

The way they\'re defined is as follows:

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Answer 1

Big-O notation is often referred to as complexity of an algorithm because it assures us, that the algorithm will not perform substantially more worse for large n. However, as was rightly pointed out earlier, the Big-O gives us the asymptotic evaluation and our algorithm may behave differently when certain input is given. For example quick sort can be O(n^2), when the array is already sorted. OTOH, asymptotic situation may be improved in practice with neat implementation.