The mathematical foundation/framing of an algorithm's run time performance is defined by asymptotic analysis. We can easily determine the best case, average case, and worst-case scenarios of an algorithm using asymptotic analysis.
Best Case Scenario of an Algorithm : The best-case scenario for an algorithm is defined as the data arrangement in which the algorithm performs the best. Take a binary search, for example, where the best-case scenario is if the target value is in the very centre of the data we are looking for. The best-case scenario for binary search would have a time complexity of O(1) or constant time complexity.
Worst Case Scenario of an Algorithm : The worst collection of input for a given algorithm is referred to as the worst-case scenario of an Algorithm. For example, quicksort can perform poorly if the pivot value is set to the largest or smallest element of a sublist. Quicksort will degenerate into an algorithm with a time complexity of O(n^2), where n is the size of the list to be sorted.
Average Case Scenario of an Algorithm : The average-case complexity of an algorithm is the amount of some computational resource (usually time) used by the process, averaged over all possible inputs, according to computational complexity theory. For example, the average-case complexity of the randomised quicksort algorithm is O(n*log(n)), where n is the size of the list to be sorted.
