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Category:Non-Apple hardwareQ:
Is the Big O notation in general applicable to non-polynomial functions?
I'm learning about Big O notation and I was told that Big O notation is applicable only to polynomial functions. What if I want to compute, for example, the time complexity of the expression:
f(n) = n * f(n-1) + n*f(n-1) + n*f(n-1) +... + n*f(n-1)
and I want to make the big O complexity estimations, but what if there is no relation between the n's and the f's? What if there are more than one function involved, say f(n) = n * f(n-1) + n*f(n-2) + n*f(n-3) and so on. Will the Big O notation still apply?
A:
Yes it is, for example if f(x) is a polynomial.
For example f(n) = n*f(n-1) + n*f(n-2) + n*f(n-3) +... + n*f(n-k)
Then it is O(f(n) = n^k)
A:
I will start my answer with the following formal definitions (I don't know how other researchers or teachers call them, I just call it "definition of the big O notation")
Definition of big O notation
A function f(n) is said to be O(g(n)) if and only if there exist constants c and N such that
f(n) N
Definition of the big O notation
I say f ac619d1d87
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