Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity
. It is used to describe the complexity of an algorithm, which is the number of iterations, calculations, or steps needed at most for the algorithm to reach its end-state
. In the context of algorithms, O(n) represents the number of operations required for an algorithm to run, where n is the input size
. For example, the Horner algorithm is an O(n) algorithm because it requires n iterations to calculate the polynomial
. In contrast, an O(n^2) algorithm requires a larger number of operations, and O(log n) algorithms have a runtime proportional to the logarithm of the input size
. The expression "2^O(n)" is shorthand for "2^f(n)" for some function f(n) with f(n) ≤ cn for large n
. This notation is used to describe algorithms with a runtime that grows extremely fast, and it is not simply equal to O(2^n) or any other constant
