Big O notation for Ruby methods?

Question

How can I find the complexity of a Ruby method?

For example length? If I look at the source code, I see this:

               static VALUE
rb_ary_len         


        

Answer 1

You cannot get the relevant information from that. You have to look into the source of RARRAY_LEN and LONG2NUM.

A simple way to estimate the complexity of a method is to run benchmarks with arguments that differ along the dimension you are interested in, and plot that on a graph.

Answer 2

There is no maintained list of theoretical complexities of Ruby methods. Of interest to you is minitest/benchmark, which is used like this:

require 'minitest/autorun'
require 'minitest/benchmark'

class TestFoobar < Minitest::Benchmark
  def setup
    @foo_arrays = ( 1 .. 10_000 ).map { |n| [ 42 ] * n }
    # Because default benchmarking range is [1, 10, 100, 1_000, 10_000]
  end

  def bench_foo_size
    assert_performance_constant 0.99 do |n| @foo_arrays[ n ].size end
  end
end

If you run the above test, you can actually see that the performance of Array#size method is constant. If you change #bench_foo_size to:

def bench_foo_size
  assert_performance_linear 0.99 do |n| @foo_arrays[ n ].size end
end

The test will actually fail, because Array#size is not linear, but sublinear. minitest/benchmark is flexible and you can apply it to your own code as well as to built-in assets.

Answer 3

It is just O(1) for the length method. The length of an array is stored in a variable and can be returned without further calculations.

How to find out? By reading the source code and analysing the implementation and algorithms.