pythagorean-triplet: implement canonical-data.json

[cmccandless]

Resolves #579

This data set was generated using this one-off script, for those who are curious about where the cases came from, with a runtime of ~21.5 seconds on my machine (primarily due to the test case for a large n).

I welcome additional test suggestions or suggestions for modification/removal of currently present cases or case format.

[petertseng]

I looked at descriptions and have no objections. I cannot think of any new cases to add, and I have no requests to remove any proposed case. For those who request to remove any cases I advise that at least one case of each of the following be kept:

• one triplet
• zero triplets
• > 1 triplets

Verifier says all proposed cases have the correct expectations.

require 'json'
require_relative '../../verify'

json = JSON.parse(File.read(File.join(__dir__, 'canonical-data.json')))

verify(json['cases'].map { |c| c.merge('expected' => c['expected'].sort) }, property: 'tripletsWithSum') { |i, _|
  n = i[?n]
  triplets = []
  (1...(n / 3)).each { |a|
    # c = n - a - b
    # a^2 + b^2 = c^2
    # a^2 + b^2 = n^2 - 2an - 2bn + a^2 + 2ab + b^2
    # 2bn - 2ab = n^2 - 2an
    # 2b(n - a) = n(n-2a)
    # b = n(n-2a) / 2(n-a)
    # b = (n(n-a) - an) / 2(n-a)
    b = n / 2 - a * n / (2 * (n - a))
    break if a >= b
    c = n - a - b
    triplets << [a, b, c] if a * a + b * b == c * c
  }
  triplets
}

Note the need to sort the expected output, simply because I understand the expected output has no ordering. It would be convenient for humans if the list presented in JSON were sorted, but I'm Approving (in the GitHub sense) as is anyway.

[rpottsoh]

👍

[sdublish]

I'm a bit unclear on how this resolves #1211 as it this does not modify description.md, but other than that, it looks fine to me.

[cmccandless]

As there are 3 approvals already, I will go ahead and squash-merge this. Thank you everyone for your input.

@petertseng, note that I have indeed sorted the expected output.

@sdublish You are right, I have removed the link from the PR description so #1211 will remain open.