Big Theta
Big Theta, denoted as Θ, is a notation used in computer science to describe the asymptotic behavior of functions. It provides a way to express the tight bounds of an algorithm's running time or space requirements. Specifically, Θ notation indicates that a function grows at the same rate as another function, both in upper and lower limits, making it a precise way to analyze performance.
In mathematical terms, if a function f(n) is Θ(g(n)), it means there are positive constants c₁, c₂, and n₀ such that for all n ≥ n₀, c₁ * g(n) ≤ f(n) ≤ c₂ * g(n). This helps in comparing algorithms, such as those used in sorting or searching, by providing a clear understanding of their efficiency.