Arrange in increasing order of asymptotic complexity I have the following functions that I need to rank in increasing order of Big-O complexity:
$$(\log n)^3, 10\sqrt n, n\log n, n\sqrt n, n^4 + n^3, (2.1)^n \cdot n^2, 3^n, 2^n \cdot n^3, n! + n, n^n. $$
My current ranking is as follows:
$$(\log n)^3 &lt; 10\sqrt n &lt; n\log n &lt; n\sqrt n &lt; n^4 + n^3 &lt; (2.1)^n \cdot n^2 &lt; 2^n \cdot n^3 &lt; 3^n &lt; n! + n &lt; n^n. $$
Is my ranking of the functions in increasing order of complexity correct?
You have mistake in $(2.1)^n \cdot n^2&lt;2^n \cdot n^3$, because it is equivalent $\left(\frac{2.1}{2}\right)^n&lt;n$