Algorithm: time and space complexity

The trio of asymptotic complexity (O, Ω, θ):

1- The Big Oh “O”

f (n)=O(g(n))  reads as f on n is big oh of g of n

Eg- 5n+5=O (n) means 5n+5≤6n for all n≥5

O (1) that means a constant

O (n): linear

O (n²): quadratic

O (n³): cubic

O (2ⁿ): exponential

2- Omega “Ω”

f (n)= Ω(g(n)) reads as f of n is omega of g of n

         Eg- 4n+2= Ω means 4n+2≥4n for n≥1

In the case of Oh g(n) is an upper bound on the value of f(n) for all n, n ≥n_o  while statement f(n)= Ω (g(n)) states that g(n) only a lower bound on f(n)

3- Theta "θ"

f (n)= θ (g(n)) reads f of n is theta of g of n

Here f (n) = θ (g (n))

           G (n) is both upper and lower bound on f (n.)