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Hello , Do you know examples of functions belonging crowds O(sin (n)), Ω (sin (n)), Θ (sin (n)) ?
CRGreathouse said:it's easy to see that (among others) all positive functions are in Ω(sin n).
The "O(sin n)" complexity refers to the upper bound of the time or space required for an algorithm to run, as a function of the input size "n". In other words, it represents the maximum amount of resources that the algorithm will use to solve a problem of size "n".
The "Ω(sin n)" complexity represents the lower bound of the time or space required for an algorithm to run, as a function of the input size "n". It indicates the minimum amount of resources needed for the algorithm to solve a problem of size "n".
The main difference between these two complexities is that "O(sin n)" is an upper bound, while "Ω(sin n)" is a lower bound. This means that "O(sin n)" gives an upper limit on the resources used by the algorithm, while "Ω(sin n)" gives a lower limit. In simpler terms, "O(sin n)" represents the maximum efficiency of an algorithm, while "Ω(sin n)" represents the minimum efficiency.
The "Θ(sin n)" complexity is also known as the tight bound complexity. It represents the range of possible resource usage for an algorithm, as a function of the input size "n". In other words, it indicates the exact amount of resources an algorithm will use to solve a problem of size "n". This complexity is often used when analyzing the best and worst-case scenarios for an algorithm.
The "Θ(sin n)" complexity is determined by finding both the upper and lower bound complexities of an algorithm and then comparing them. If the upper and lower bounds are the same, then the "Θ(sin n)" complexity will also be the same. However, if they differ, then the "Θ(sin n)" complexity will be somewhere in between these two bounds.