Question

I’ve read about Big O notation from many sources, including Skiena and the Wikipedia entry, the Example section of which states:

In typical usage, the formal definition of O notation is not used
directly; rather, the O notation for a function f(x) is derived by the
following simplification rules:

• If f(x) is a sum of several terms, the one with the largest growth rate is kept, and all others omitted.

• If f(x) is a product of several factors, any constants (terms in the product that do not depend on x) are omitted.

The solution to problem 2.2 is O((n^3)/3). Shouldn’t the “/3” be omitted, or am I missing something?

Answer 1

You are correct. 1/3 is a constant, and therefore should omitted.