eli5: What does Big Oh, Big Omega, and Big Theta mean in algorithm?
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Big O, Big Omega, and Big Theta are ways of expressing the asymptotic complexity of algorithms, which refers to how the runtime of an algorithm scales as the input size increases. These notations provide a way to compare the efficiency of different algorithms and to understand how well an algorithm will perform as the input size grows.
Here is a brief overview of each notation:
Big O: Big O notation is used to describe an upper bound on the asymptotic complexity of an algorithm. It tells you the worst-case scenario for the runtime of an algorithm. For example, if an algorithm has a complexity of O(n), it means that the runtime will never exceed a certain multiple of n, where n is the size of the input.
Big Omega: Big Omega notation is used to describe a lower bound on the asymptotic complexity of an algorithm. It tells you the best-case scenario for the runtime of an algorithm. For example, if an algorithm has a complexity of Ω(n), it means that the runtime will always be at least a certain multiple of n, where n is the size of the input.
Big Theta: Big Theta notation is used to describe a tight bound on the asymptotic complexity of an algorithm. It tells you both an upper and lower bound on the runtime of an algorithm. For example, if an algorithm has a complexity of Θ(n), it means that the runtime will always be between a certain multiple of n and another multiple of n, where n is the size of the input.
In general, you want an algorithm to have a low asymptotic complexity, which means that it will scale well and be efficient even for large input sizes.
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