Welcome to the Big O Analysis Tool (BOAT). BOAT lets you compare simple
math functions to see their big O properties.
### Features

### Example Expressions

- Analyze Big O / Big Theta of a single function
- Comparing the growth rate of two functions
- Solving recurrence relations with the master and muster theorems

**N * lg(N)**is N lg N**N**2**is N squared**factorial(N)**is N factorial

In competitive programming, the guideline is that an algorithm can do up
to ~3e8 operations and get accepted by the online judge. The following
table is from CP3 and gives an idea of
what complexity is necessary for different input sizes to achieve All
Correct (AC) without hitting Time Length Exceeded (TLE).

Reading the first line: if N=11, an algorithm of factorial complexity or N^6 (or better) is acceptable. If N=1e4, an algorithm using N^2 complexity is acceptable. At 1e5, N lg N or N sqrt N complexity is required and at 1e8, only O(N) algorithms will get accepted.

**NOTE:** The table is written for compiled code, if you are using an
interpreted language, you can add about 5 - 10x performance overhead to
get an idea of how long an algorithm will take to run.

Reading the first line: if N=11, an algorithm of factorial complexity or N^6 (or better) is acceptable. If N=1e4, an algorithm using N^2 complexity is acceptable. At 1e5, N lg N or N sqrt N complexity is required and at 1e8, only O(N) algorithms will get accepted.