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# Asymptotic Notations – Data Structures

Asymptotic notations are mathematical tools that allow us to describe how the running time or space required by an algorithm grows as the size of the input grows. In other words, it helps us understand the performance of an algorithm in terms of how long it takes to run or how much memory it requires, as the input size increases. There are three main asymptotic notations that are commonly used:

1. Big O notation (O) describes the worst-case scenario for the running time of an algorithm. It represents an upper bound on the running time of the algorithm.
2. Big Ω notation (Ω) describes the best-case scenario for the running time of an algorithm. It represents a lower bound on the running time of the algorithm.
3. Big Θ notation (Θ) describes the average-case scenario for the running time of an algorithm. It represents a tight bound on the running time of the algorithm, meaning that it is both an upper and a lower bound on the running time of the algorithm.

For example, if an algorithm has a running time of O(n), it means that the running time of the algorithm grows linearly with the size of the input (n). On the other hand, if an algorithm has a running time of O(n^2), it means that the running time of the algorithm grows quadratically with the size of the input.

Asymptotic notations are important because they allow us to compare the performance of different algorithms, even if we don’t know the exact input sizes for which the algorithms will be used. By using asymptotic notations, we can get a sense of how the algorithms will scale as the input size increases, which can be very useful in practice.