Θ, pronunciation: theta, theta; both upper and lower bounds (tight), meaning equal.
Ο, pronunciation: big-oh, Omi Kerong (uppercase); it means upper bound (tightness unknown), meaning less than or equal to.
ο, pronunciation: small-oh, Omi Kerong (lower case); it means not tight, meaning less than.
Ω, pronunciation: big omega, omega (uppercase); represents the lower bound (tightness unknown), meaning greater than or equal to.
ω, pronunciation: small omega, omega (lower case); it means not tight, greater than.
Big O notation (English: Big O notation) is a mathematical symbol used to describe the asymptotic behavior of a function. More precisely, it uses another (usually simpler) function to describe the asymptotic upper bound of the order of magnitude of a function.
The definition of the big Ω symbol is similar to that of the big O symbol, but the main difference is that the big O symbol indicates that the function is always smaller than a constant multiple of a specific function when it grows to a certain extent, and the big Ω symbol indicates that it is always greater than to describe a function. An asymptotic lower bound of orders of magnitude.
The big Θ symbol is a combination of the big O symbol and the big Ω symbol. The specific mathematical definition is given below:
The function f (n) represents the workload (efficiency) of a certain algorithm when the input size is n. When n tends to be very large, we will compare f (n) with another function g(n )Compare:
1) If 0, then f (n) is said to be strictly smaller than g(n) in the order of magnitude, which is recorded as f (n)=o(g(n)).
2) If, then f (n) is said to be strictly greater than g(n) in order of magnitude, and it is recorded as f (n)=w(g(n)).
3) If c, where c is a non-zero constant, then f (n) is said to be equal to g(n) in the order of magnitude, that is, f (n) and g(n) are functions of the same order of magnitude, denoted as: f (n )=Θ( g(n)).
4) If f (n) is less than or equal to g(n) in the order of magnitude, then it is recorded as f (n)=O(g(n)).
5) If f(n) is greater than or equal to g(n) in order of magnitude, then it is recorded as f(n)=Ω(g(n)).
Big O and big Ω all exist c, and small o and small w are for any c