Defining Big-O Notation

Question

I really want to know the real definition. I tried to read the book, but could not understand it.

O: Worst case of Big-O notation.
Θ: average theta designation.
Ω: best omega notation.

Why does Wikipedia represent the speed of algorithms only in Big-O, including its average, best, and worst cases? Why didn’t they replace these formal keywords?

Answer 1

O, Θ, and Ω do not represent the worst, middle, and best case; although they have a similar meaning.

The designation Big-O f (n) = O (g (n)) means that f grows slower than g for large values ​​of n ("n> n ₀" " n" ). , g - : g (, - O (n!)). Big-O : Big-O.

Ω (f , g), , , ( , , Ω (1)).

, g , O (g), Ω (g). , O- (O, n²) Big-O ( , n²) Ω Ω (n).

: sort merge - O (n log n) Ω (n log n). , Θ (n log n), , Θ- (, , ).

, , - "f" "f _avg", . , f = O (n²) - , , f _avg= O (n log n).

Answer 2

, , .

, - .

Big-O, Theta Omega , .

Big-O, Theta Omega. .

. : O Ω ?

: big-O (, ) ( Theta).

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.

, , , f(n) = k1n k1.

k1n - O (n), Θ (n), Ω (n). , O (n ²), O (n ³),... Ω (1), Ω (log n), Ω (log log n),..., , .

: g(n) = k2n2 h(n) = k3n2, O (n ²), Θ (n ²), Ω (n ²).

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: , , ? Theta ?

, - ( , ).

, , / . - (0 ⁿ) Ω (1.5 ⁿ), ~ θ (1.6 ⁿ) .