Show HN: Boat – Big O analysis tool | Hacker News Reader

Show HN: Boat – Big O analysis tool

boat.algorithm.city

24 pointslogv9 comments

BOAT is a quick tool I made for analyzing and comparing the Big O growth rate of mathematical functions. I built it to help students get a sense of Big O notation, as its a common class exercise to have to rank several math functions in terms of their Big O. BOAT works by trying to find an upper and lower bound of a given math function by comparing the function against a set of known functions. If it can't find a tight bound, it tries to find an upper bound.

If it's given two functions, it will try to locate their crossover point (if any) using a binary search, as well as compare their growth rates to determine which will eventually grow faster. It might get some wrong (I'm curious which) as it only has a handful of function classes.

The last feature it has is an automated master/muster theorem solver. It's pretty simple - you give it the values of a recurrence relation and it tells you the big O.

Thanks for looking!

Doesn't appear to be very accurate.

https://boat.algorithm.city/analyzer/?&f=N*lg(N)*lg(lg(N))

"The Big Theta of N * lg(N) * lg(lg(N)) is O(n * lg(n))"

Thanks for the feedback and good catch!

The list of big O classes is the following:

   var classes = [
      define_func("0"),
      define_func("1"),
      define_func("lg(n)"),
      define_func("sqrt(n)"),
      define_func("n"),
      define_func("n * lg(lg((n)))"),
      define_func("n * lg(n)"),
      define_func("n * sqrt(n)"),
      define_func("n**2"),
      define_func("n**3"),
      define_func("n**4"),
      define_func("2**n"),
      define_func("n**n"),
      define_func("factorial(n)"),
      define_func("2**(2**n)"),
      define_func("n**(n**n)"),
    ];

lg(lg(N)) is very small, for 1e30, the value is approximately ~6 and at 1e60 it is ~7.6, at which point lg(lg(N)) is pretty much a constant value (or trivial), but yes - it is technically included in the growth rate, but for practical purposes can probably be ignored

Great name!

So it analyses math equations you input? I would call this a simulation, as my first impression was that it would analyse source code...

Yes, it analyzes a formula or recurrence relation - sorry to get your hopes up :-D I wish it could analyze source code, but the halting problem says that would be a bit difficult.

I think one could execute source code with varying size inputs to get an idea of a function's growth (assuming the function does halt), but I haven't thought about what that entails

PS: maybe I should have named it BOFAT (Big O Formula Analyzer Tool)

Surely the halting problem only applies in the general case, i.e. given a ideal enough language you could use heuristics or give results applicable only when in xyz conditions e.g. when these nested for loops are in action it's O(n^2)

Yes, this is likely true - I really need to think about it more, though. I don't know how to do static or runtime analysis, so I can't say much about it

The Big Theta of N^N^N^N is O(n * sqrt(n)) :)

wow, that's way off!

for n = 2, n^n^n^n returns 65536. for n = 3, javascript thinks its infinity.

i guess BOAT should start using decimal values for n so we can detect this problem.

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