Asymptotic Notation Asymptotic Notation Asymptotic notation is a mathematical notation used to describe the limiting behavior of a function as its input approaches infinity. It is commonly employed in computer science and mathematics to analyze the efficiency and performance of algorithms. Big O Notation (\(O\)): Definition: \(f(n)\) is \(O(g(n))\) if there exist positive constants \(c\) and \(n_0\) such that \(0 \leq f(n) \leq c \cdot g(n)\) for all \(n \geq n_0\). Explanation: Big O notation provides an upper bound on the growth rate of a function. It represents the worst-case scenario in terms of time or space complexity. Example: \(f(n) = 2n^2 + 3n + 1\) is \(O(n^2)\) because \(2n^2 + 3n + 1 \leq c \cdot n^2\) for some constant \(c\) when \(n\) is sufficiently large. Omega Notation (\(\Omega\)): Definition: \(f(n)\) is \(\Omega(g(n))\) if there exist positive constants \(c\) and \(n_0\) such that \(0 \leq c \cdot...