Algorithms Analysis Practice Test

In asymptotic analysis, Big-O notation is utilized to describe the upper bound of an algorithm's growth rate. This means that Big-O provides a way to express the maximum limit on how an algorithm's runtime or space requirement can grow concerning the input size. For instance, when we say an algorithm is O(n²), it indicates that, in the worst case, the algorithm will not exceed a quadratic growth relative to the size of the input.

This is particularly useful for evaluating the efficiency of algorithms since it allows developers and computer scientists to understand how an algorithm will perform as the input size increases and to compare the efficiency of different algorithms in a rigorous way.

Other notations have different purposes: Big-Theta provides a tight bound, describing both upper and lower bounds, while Big-Omega describes a lower bound. Small-o is used to indicate that a function grows strictly slower than another function, but does not serve the purpose of defining an upper bound in the same way Big-O does.