Big O notation
Orders of common functions

Here is a list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. In each case, c is a positive constant and n increases without bound. The slower-growing functions are generally listed first.

The statement f (n) = O (n !) {\displaystyle f(n)=O(n!)} is sometimes weakened to f (n) = O (n n) {\displaystyle f(n)=O\left(n^{n}\right)} to derive simpler formulas for asymptotic complexity. For any k > 0 {\displaystyle k>0} and c > 0 {\displaystyle c>0}, O (n c (log n) k) {\displaystyle O(n^{c}(\log n)^{k})} is a subset of O (n c + ε) {\displaystyle O(n^{c+\varepsilon })} for any ε > 0 {\displaystyle \varepsilon >0}, so may be considered as a polynomial with some bigger order.
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