Rules for Big O

There are several rules that make it easy to find the order of a given function:

• Any constant multipliers are dropped.
• The order of a sum is the maximum of the orders of its summands.
• A higher power of n beats a lower power of n.
• n beats log(n) (by a lot).
• log(n) beats 1 (just barely).
• 2ⁿ beats any power of n.

For example, in analyzing T(n) = 2 * n² + 5 * n + 100, we first drop all the constant multipliers to get n² + n + 1 and then drop the lower-order terms to get O(n²).