perfect-numbers: Implement canonical-data.json

[kytrinyx]

We want to have a standard set of test inputs and outputs for each exercise to
make it easier to port them to new languages, as well as to help keep the
exercises in sync.

The Perfect Numbers exercise can be found in the ./exercises/perfect-numbers/ directory.

The step-by-step instructions for how to compile a canonical-data.json file is
described in this section of the contributing guide.

See http://exercism.io/contribute/canonical-data/perfect-numbers for the up-to-date list of
language tracks that have an implementation of the Perfect Numbers exercise.

The tracking issue has more context.

[stkent]

I just built this for the Java track. For each classification (perfect, abundant, deficient) I included:

• A small test case to get started
• A medium test case that can still be computed by hand
• A very large test case that would be difficult to compute by hand

Actual test cases:

• Perfect: 6, 28, 33550336
• Abundant: 12, 24, 33550335
• Deficient: 8, 31, 33550337

These cases also cover all the examples given in the problem description (6, 28, 12, 24, 8). I'll review other tracks soon.

[stkent]

Existing implementations:

xcsharp: tests 3, 7, 13 (deficient), 6, 28, 496 (perfect), 12, 18, 20 (abundant)
xclojure: tests 13 (deficient), 28 (perfect), 12 (abundant), negative input not allowed
xdelphi: tests 3, 7, 13 (deficient), 6, 28, 496 (perfect), 12, 18, 20 (abundant)
xelisp: tests finding first n perfect numbers for n in 0, 1, 3, 4
xfsharp: tests 3, 7, 13 (deficient), 6, 28, 496 (perfect), 12, 18, 20 (abundant)
xgo: tests 1, 13 (deficient), 6, 28, 496, 8128 (perfect), 12 (abundant)
xjava: tests 8, 31, 33550337 (deficient), 6, 28, 33550336 (perfect), 12, 24, 33550335 (abundant)
xkotlin: tests 8, 31, 33550337 (deficient), 6, 28, 33550336 (perfect), 12, 24, 33550335 (abundant), negative input not allowed
xlua: tests 13 (deficient), 28 (perfect), 12 (abundant), calculating Aliquot sum for 0, 1, 15, 229
xobjective-c: tests 13 (deficient), 6, 28 (perfect), 12 (abundant)
xpython: tests 6, 28, 496, 8128, 33550336, 8589869056, 137438691328 (perfect), 8, 20, 42, 945 (not perfect)
xracket: tests finding first n perfect numbers for n in 0, 1, 3, 4
xruby: tests 13 (deficient), 28 (perfect), 12 (abundant)
xscala: tests 3, 7, 13, 33550337 (deficient), 6, 28, 496, 33550336 (perfect), 12, 18, 20, 33550335 (abundant)
xswift: tests 13 (deficient), 6, 28 (perfect), 12 (abundant)

[petertseng]

Nothing in this (my) comment is relevant to crafting a canonical-data.json, so those who are looking to craft one may ignore this comment. Read on for an interesting problem and experiment.

That's pretty nifty that among the three consecutive numbers one each of abundant, deficient, perfect were represented. I wonder for how many sequences of three consecutive 8-digit numbers this is true?

And how was this sequence of numbers found?!

Edit:

I took a look at it, and the problem becomes slightly less interesting once one sees how many 8-digit perfect numbers there are (rot13(gung bar vf gur bayl bar)). I suppose one could expand the problem to not restrict oneself to 8-digit perfect numbers though...

[stkent]

Observations:

• The vast majority of tracks require an implementation that identifies the classification (deficient/perfect/normal) of a number. Only a few tracks deviate from this (xelisp, xpython, xracket).
• Two tracks test for invalid input (xclojure, xkotlin).
• Many tracks do not test a non-prime deficient number.

Based on the range of values tested by existing implementations, I'm going to suggest the following tests in the following order for the canonical suite:

• Perfect: 6 (smallest), 28 (medium), 33550336 (large)
• Abundant: 12 (smallest), 30 (medium), 33550335 (large)
• Deficient: 2 (smallest prime), 4 (smallest non-prime), 32 (medium), 33550337 (large), 1 (edge case)
• Invalid (not whole numbers): 0 (non-negative integer), -1 (negative integer)

[stkent]

@petertseng exercise for the reader! 😉 Neat question though; feels very Project Euler-ish.