Big O

The notation Ο(n) is the formal way to express the upper bound of an algorithm's running time. It measures the worst case time complexity or the longest amount of time an algorithm can possibly take to complete.

If, $$f(n) <= C.g(n)$$ for $$n >= n0, c>0 , n0 >= 1$$ then

$$ f(n) = O(g(n))

$$

Example

Let us consider a given function,f(n)=4.n3+10.n2+5.n+1

Considering g(n)=n3,

f(n)⩽5.g(n) for all the values of n>2

Hence, the complexity of f(n) can be represented asO(g(n)), i.e.O(n3)