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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. In computer science, it is commonly used to classify algorithms according to their worst-case or upper bound performance, giving an insight into the longest amount of time an algorithm can possibly take to complete or the most amount of space an algorithm can possibly require, as the size of the input data increases.
Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g., in memory or on disk) by an algorithm.
For example:
– If an algorithm is said to be O(n), it means that the time/space needed will increase linearly with the increase of the size (n) of the input data set.
– If an algorithm is described as O(1), it means it takes constant time/space regardless of the size of the input data set.
– Other common Big O notations include O(n^2), O(log n), and O(n log n), each representing different relationships between the size of the input and the time/space required.
Understanding Big O notation helps in comparing the efficiency of algorithms and in choosing the appropriate algorithm for solving a particular problem based on the expected size of the input data.