Question

Of the following 10 functions, which are O(n)? Which are Ω(n)? Which are θ(n)?

Answer 1

Determining whether each function is
`\(O(n)\), \(\Omega(n)\), or \(\Theta(n)\)` requires specific function definitions. Without the functions provided, it is not possible to identify their complexity classes.

Step-by-step explanation:

To analyze the time complexity of a function in terms of
`\(O(n)\), \(\Omega(n)\), or \(\Theta(n)\),` we need the actual functions. These notations represent different growth rates in algorithmic complexity.

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`\(O(n)\)` (Big O) indicates an upper bound, representing the worst-case scenario for algorithmic efficiency.

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`\(\Omega(n)\)` (Big Omega) is a lower bound, signifying the best-case scenario.

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`\(\Theta(n)\)` (Big Theta) implies a tight bound, where the function's growth rate is sandwiched between upper and lower bounds.

Without the functions, it's impossible to precisely categorize them into these complexity classes. Each class has specific conditions and characteristics, and determining them relies on understanding the behavior of the functions as the input size (n) grows.

It's essential to have the functions in order to provide a meaningful analysis. If the specific functions are available, further calculations and evaluations would be necessary to determine their complexity classes accurately.