This is a Data structures & Algorithms question. For instance I have the following grades of functions: $O(1), O(2^n), O(n \log n), O(e^n), O(n^3), O(n^{1/3})$ and $O(\log \log n)$
I need to show and proof to which of these function grades does the function: $n^7$ belong to. I didn't get a chance to ask my professor on this topic so I'm not sure how to solve this problem.
The term of $O(...)$ means representation of the performance of a solution. It is not entirely clear what you see under the expression n ^ 7. And because it is a representation of the complexity of the algorithm is needed to know how this power will count. There can be several calculation algorithms, each of which will have a different expression of the complexity. If you used the algorithm to multiply numbers, then you can, for example, the multiplication using konvolučního algorithm for the discrete Fourier transform. Performance of such algorithm is the maximum $O(7\cdot n \cdot log\space n)$, where n is the number of components of the vector needed for representation of numbers using the discrete Fourier transform. Otherwise, if this is just a number, then I can also provide your own custom algorithm that takes advantage of the symmetry of the multiplication, exponentiation, and in case there is no need to perform a transformation for the convolution and there would be performance requirements could be smaller.
