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To answer your question about the bounds (Big-O, Big-Ω, and Big-Θ), I'll explain each of these notations and then apply them to a sample function. ### 1. Big-O Notation (O-notation): Big-O notation is used to describe an upper bound on the time complexity or space complexity of an algorithm. It represents the worst-case scenario, or the maximum amount of time an algorithm will take to complete, relative to the input size. Theorem: - If a function \( f(n) \) is O(g(n)), this means there exist positive constants \( c \) and \( n_0 \) such that for all \( n \geq n_0 _____ _________ _____ ________ _________ _______ ________ __________ _______.
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