Popular Notations in Complexity Analysis of Algorithms
1. Big-O Notation
We define an algorithm’s worst-case time complexity by using the Big-O notation, which determines the set of functions grows slower than or at the same rate as the expression. Furthermore, it explains the maximum amount of time an algorithm requires to consider all input values.
2. Omega Notation
It defines the best case of an algorithm’s time complexity, the Omega notation defines whether the set of functions will grow faster or at the same rate as the expression. Furthermore, it explains the minimum amount of time an algorithm requires to consider all input values.
3. Theta Notation
It defines the average case of an algorithm’s time complexity, the Theta notation defines when the set of functions lies in both O(expression) and Omega(expression), then Theta notation is used. This is how we define a time complexity average case for an algorithm.
Worst, Average and Best Case Analysis of Algorithms
In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. But let’s take an overview of the asymptotic notation and learn about What is Worst, Average, and Best cases of an algorithm: