Discover published sets by community

Average-case complexity is the expected time or space taken by an algorithm, averaged over all possible inputs. To calculate it, one must assume a probability distribution of all inputs and average out the complexities. However, this is often complex to compute and requires a good understanding of probabilistic analysis and the possible inputs to an algorithm.

Time complexity is a measure of the amount of time an algorithm takes to complete as a function of the length of the input. It is typically expressed using Big O notation, which provides an upper bound on the time requirements. To calculate it, identify the basic operations and their counts, and express as $O(f(n))$ where $f(n)$ represents the dominant growing part of the operations count.

Best-case complexity defines the minimum time or memory an algorithm requires and is typically denoted as big Omega ($\Omega$). It is the complexity in the most favorable scenario. To calculate it, consider the scenario where the algorithm performs the minimum number of operations.

Worst-case complexity describes the maximum amount of time or space that an algorithm could potentially take, and is often given by big O notation ($O$). This gives the upper limit of performance and is calculated by assuming the scenario that causes the algorithm to perform the maximum number of operations.