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Big O notation is a mathematical term that describes how well algorithms work in computer science. It offers a technique to gauge how an algorithm's time or spatial complexity rises in proportion to the volume of input data.

Big O notation, in its simplest version, represents the worst-case behaviour of an algorithm when the input size increases indefinitely. It offers a technique to calculate the time and resources an algorithm will need to run on various input sizes.

Big O notation is expressed as `O(f(n))`

, where `f(n)`

stands for the function that characterises the algorithm's performance. The `O`

symbol, which is pronounced Big O, denotes the complexity of an algorithm's upper bound.

A Big O notation of `O(n)`

, for instance, indicates that an algorithm's performance increases linearly with the size of the input. The runtime of the algorithm will double as the input size does. The performance of an algorithm increases exponentially with the size of the input, on the other hand, if it has a Big O notation of `O(n2)`

. The algorithm will take four times longer to run if the input size doubles.

Big O notation is a crucial idea in computer science because it enables programmers and engineers to create effective algorithms and enhance the functionality of already-existing ones. We can decide how to scale our programmes and manage greater input sizes by knowing an algorithm's Big O notation.

As a result, Big O notation is an effective tool for evaluating algorithm performance and determining the best ways to optimise them. We can create scalable and more effective software systems by grasping this idea.

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