Algorithm analysis of progressive symbols (O, O, Θ, ω, ω) sums up __ algorithm

"Asymptotic notation" is used to express "asymptotically complex degree".

1. Asymptotic notation includes:

(1) Theta (theta): tight bounds. Equivalent to "="

(2)              O (Greater Europe): upper bound. The equivalent of "<="

(3) O (Theo): not tight upper bound. Equivalent to "<"

(4) Ω (large Omega): Lower bound. The equivalent of ">="

(5) Ω (small Omega): not a tight lower bound. Equivalent to ">"

Give the definition of these tokens:

Note: asymptotic nonnegative means "when n tends to infinity, f (n) and g (n) are nonnegative".

2. Use set theory to denote the relationship between these 5 symbols:

As you can see from the diagram above:

(1) if f (n) =θ (g (n)), then f (n) =o (g (n)) and f (n) =ω (g (n)).

(2) if f (n) = O (g (n)), then f (n) =o (g (n)).

(3) if f (n) =ω (g (n)), then f (n) =ω (g (n)).

Therefore, the most accurate use of these asymptotic notation should be "f (n) ∈o (g (n))", but it is generally written as "F (n) =o (g (n))".

Give some examples:

O (n^2) can be n,2n,1,2n^2 and so on.

Θ (n^2) can be n^2,3n^2 and so on.

Ω (n^2) can be n^3,n^10, but not n^2.

Ω (n^2) can be n^2,n^3,n^10 and so on.

O (n^2) can be n,1,3n, but not n^2.

3. To judge the asymptotic relationship of two functions

Here we have a very common method called "limit Method".

Seeing the above method, a lot of people will ask "why not O and ω." , because if f (n) =o (g (n)) is either f (n) = O (g (n)), or F (n) =θ (g (n)).

4. Relevant laws

5. Commonly used function order

The following is a list of functional classifications that are common when analyzing algorithms. All of these functions are on the verge of infinity, and the slower-growing functions are listed above. is an arbitrary constant.

Symbol	Name
	Constant (order, same below)
	Logarithmic
	Multiple logarithm
	Linear, sub Linear
	is the iterated logarithm
	Linear logarithm, or logarithmic linear, quasi-linear, hyper-linear
	Square
	Polynomial, sometimes called "algebra" (order)
	Exponent, sometimes called "geometry" (order)
	Factorial, sometimes called "combination" (order)