Asymptotic Notations - The Three
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Now, let’s formally learn the notations.
Asymptotic Notations are notations used to describe bounding behavior on the running time of an algorithm. There are three main notations, namely Big-O, Omega, and Theta.
Big-O notation or O(running time) represents the upper bound. Omega notation or Ω(running time) represents the lower bound. Theta notation or Θ(running time) represents the upper and lower bounds.
Suppose n is the input size(like a list of n numbers). Also, suppose c is some positive constant(like 1,24,4.5,8… so on). Then O(n) means that the algorithm you are analyzing takes no more than c*n operations, Ω(n) means that the algorithm you are analyzing takes at least c*n operations. Θ(n) means that the algorithm is both O(n) and Ω(n), meaning it is exactly c*n operations.
As you can see here, the constants are ignored in asymptotic notations. We will get to why in the next section.