Asymptotic Notation 편집하기 (부분)

==Key Asymptotic Notations==
Asymptotic notation expresses how an algorithm's performance scales with input size. The most common types are:
===Big O Notation (O)===
*'''Definition:''' Represents an upper bound on an algorithm’s growth rate (worst-case complexity).
*'''Example:''' If an algorithm has O(n²) complexity, its runtime does not exceed a constant multiple of n² for large n.
*'''Usage:''' Ensures an algorithm will not perform worse than the given bound.
===Big Omega Notation (Ω)===
*'''Definition:''' Represents a lower bound on an algorithm’s growth rate (best-case complexity).
*'''Example:''' If an algorithm has Ω(n log n) complexity, its runtime is at least proportional to n log n.
*'''Usage:''' Guarantees that an algorithm will take at least the given time.
===Big Theta Notation (Θ)===
*'''Definition:''' Represents a tight bound (both upper and lower) on an algorithm’s growth rate.
*'''Example:''' If an algorithm has Θ(n log n) complexity, its runtime grows at exactly that rate.
*'''Usage:''' Defines an algorithm’s precise asymptotic behavior.
===Little o Notation (o)===
*'''Definition:''' Represents an upper bound that is not tight (strictly smaller growth rate).
*'''Example:''' If an algorithm has o(n²) complexity, its runtime grows slower than n² but not necessarily at a fixed rate.
===Little Omega Notation (ω)===
*'''Definition:''' Represents a lower bound that is not tight (strictly greater growth rate).
*'''Example:''' If an algorithm has ω(n log n) complexity, its runtime grows faster than n log n.