triangle: Add JSON test data

[petertseng]

Pursuant to dicussion in #202, we won't have cases where a + b = c.
Examples are (2, 4, 2, Isosceles) and (1, 3, 4, Scalene).

As of this writing, 21 tracks implemented triangle:

• https://github.com/exercism/xcsharp/blob/master/exercises/triangle/TriangleTest.cs
• https://github.com/exercism/xcpp/blob/master/triangle/triangle_test.cpp
• https://github.com/exercism/xclojure/blob/master/exercises/triangle/test/triangle_test.clj
• https://github.com/exercism/xcoffeescript/blob/master/exercises/triangle/triangle_test.spec.coffee
• https://github.com/exercism/xlisp/blob/master/exercises/triangle/triangle-test.lisp
• https://github.com/exercism/xecmascript/blob/master/exercises/triangle/triangle.spec.js
• https://github.com/exercism/xelixir/blob/master/exercises/triangle/triangle_test.exs
• https://github.com/exercism/xelm/blob/master/exercises/triangle/TriangleTests.elm
• https://github.com/exercism/xerlang/blob/master/exercises/triangle/triangle_tests.erl
• https://github.com/exercism/xfsharp/blob/master/exercises/triangle/TriangleTest.fs
• https://github.com/exercism/xgo/blob/master/exercises/triangle/triangle_test.go
• https://github.com/exercism/xhaskell/blob/master/exercises/triangle/test/Tests.hs
• https://github.com/exercism/xjava/blob/master/exercises/triangle/src/test/java/TriangleTest.java
• https://github.com/exercism/xjavascript/blob/master/exercises/triangle/triangle.spec.js
• https://github.com/exercism/xlua/blob/master/exercises/triangle/triangle_spec.lua
• https://github.com/exercism/xnim/blob/master/triangle/triangle_test.nim
• https://github.com/exercism/xperl5/blob/master/triangle/cases.json
• https://github.com/exercism/xpython/blob/master/exercises/triangle/triangle_test.py
• https://github.com/exercism/xruby/blob/master/exercises/triangle/triangle_test.rb
• https://github.com/exercism/xscala/blob/master/exercises/triangle/src/test/scala/triangle_test.scala
• https://github.com/exercism/xswift/blob/master/exercises/triangle/TriangleTest.swift

This JSON file contains the combination of all their tests.
Most tracks have the same set of tests.

Haskell has a case specific to itself added in
exercism/haskell#142
This case is added to the common set.

The Go and Nim tracks have tests with +/- Infinity and NaN.
These cases are not added.

Closes #264
Closes exercism/todo#157

[petertseng]

could have sworn there was another, but now I can't find it

Found it. The other instance was sublist, not triangle. Commenting on new diff.

[kotp]

I just solved this in the Ruby track, and noticed that at first we test for 0's, then we test for "Triangle Equality" which provides the standard, simple, definition of a Triangle, mathematically. Once the tests for Triangle Equality happen, the tests for zero can go away.

As far as that goes, the Triangle Equality addresses the questions on negative numbers naturally as well, I think.

[rbasso]

I agree with @petertseng. The function should receive the side's lengths, so they have to be positive.

I don't understand what would be the interpretation of a negative size, because a vector length cannot be negative:

https://en.wikipedia.org/wiki/Triangle_inequality

In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):
∥ x + y ∥ ≤ ∥ x ∥ + ∥ y ∥

https://en.wikipedia.org/wiki/Norm_(mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

[kotp]

Those symbols (The double pipes) indicate absolute values, correct? This indicates that a "negative" distance is simply a distance with perspective (or direction), the "length" is absolute. The choice to normalize or not can be made in the method/function or required to be normalized outside of said function. Which suggests that the values for those vectors could have been negative, but are normalized in that function. Hence my view that taking a negative value may not be inappropriate. But we are free to choose.

The formula you link to using absolute function on the given lengths, suggests that we could go either way, enforcing that we are using "absolute" values.

Given the links you provide and that you understand the formulas, I would challenge your feign of non-mathyness... to use a technical term.

[rbasso]

The formula you link to using absolute function on the given lengths...

I think that this is where we disagree. I may be wrong but I think that - in that formula - x, y are vectors in a space.

... This indicates that a "negative" distance is simply a distance with perspective (or direction)...

Isn't signed real number just a 1-dimensional vector? If we treat the values in the exercise as 1-dimensional vectors, only degenerated triangles where a + b = c would be possible, right?

Given the links you provide and that you understand the formulas, I would challenge your feign of non-mathyness... to use a technical term.

I like math, but my knowledge is too shallow to allow me any confidence! 😄

[Insti]

The inspiration for this exercise is the triangle project from rubykoans.

The second part of that problem includes uses the following test cases:

assert_raise(TriangleError) do triangle(0, 0, 0) end
assert_raise(TriangleError) do triangle(3, 4, -5) end
assert_raise(TriangleError) do triangle(1, 1, 3) end
assert_raise(TriangleError) do triangle(2, 4, 2) end

I think, we should include degenerate triangles (above: 1, 3 & 4) in the test cases.
I think, we should not include triangles with negative edge lengths (above: 2).

[petertseng]

I think, we should include degenerate triangles (above: 1, 3 & 4) in the test cases.

I do not care either way about (0, 0, 0) or the related case (10, 10, 0). I will gladly add (0, 0, 0) back in if all interested are agreed.

(1, 1, 3) is not a degenerate triangle; it is a violation of the triangle inequality. I say we have to include this one no matter what (and luckily it is already included).

I also do not care about (2, 4, 2), but many other people in #202 do. I only see myself as enacting the will of the people. I am happy to add it if that is what people want.
Corollary question: If we add (2, 4, 2), should we expect it to be illegal or isosceles? Note for historical context that we asked this question of all tracks in January and also recently merged #298.

[petertseng]

I think, we should not include triangles with negative edge lengths (above: 2).

My current inclination is to keep a case such as (3, 4, -5). If we do not, we may see submitted solutions that would say (3, 4, -100) is a valid scalene triangle, if they were posed such a question.

I can be persuaded that we should not include such cases. For example, in #287 (comment) there was a concern about tests having edge-itis. If we think that's what's happening here, very glad to drop the test instead.

[kotp]

If 2, 4, 2 is degenerative it should be illegal. (and it is degenerative). If the area of the triangle becomes 0, it should fail.

The question on 3, 4, -5, then is do we pass or fail it. We should include it, it clarifies, but do we clarify in the negative or the positive?

When given a negative number, I can only assume that the length from 0 is 5... to me, it is a relative position based on 0. The length is definitely 5, even though it is a negative sign.

[petertseng]

Here is my understanding of all test cases that require a decision, and what I have done with them in the current state of this PR.

• Exclude means a given case is not tested.
• Include, Illegal means a given case is tested, and the test expects that it is an illegal triangle.
• Include, Legal is the same as above, but s/illegal/legal/.

---

• (0, 0, 0): triangle: Add JSON test data #311 (comment) indicates support, and most tracks already have. Include, Illegal.
• (3, 4, -5): Exclude because triangle: Add JSON test data #311 (comment) shows two votes of support for Exclude. I will speak briefly about alternatives:
  • For Include, Illegal: I do think some tracks want to test this, for prevention of code that would declare (3, 4, -100) a legal scalene triangle, but I am happy to remove the test case to avoid edge-itis! If a subsequent PR causes the case to be included and illegal, I would suggest a change to the README accompany it.
  • For Include, Legal: If we make it a legal triangle in this JSON file as triangle: Add JSON test data #311 (comment) reasonably suggests, tracks will be in direct opposition to what the JSON file says until all tracks update. I will not be the person to submit the PR that puts the file into such a state. I leave that to an interested party, because I'm not interested one bit in making that change.
• (2, 4, 2), (1, 3, 4), etc.: Exclude. All right, I know that triangle: Add JSON test data #311 (comment) supports Include, Illegal and probably triangle: Add JSON test data #311 (comment) supports Include, Illegal as well, but I can't in good conscience include it in light of triangle: clarify confusion and adjust test suites #202. What's going on here? It's my perception that there are more votes in favor of Exclude among those interested in triangle: clarify confusion and adjust test suites #202 than the two for Include, Illegal here. Now, it's acknowledged by me that the Include, Illegal votes are more recent than the Exclude votes. It's possible that times have changed and we need to make a new decision. It would allay this concern if those involved in discussion at triangle: clarify confusion and adjust test suites #202 would update on their more recent thoughts. But ultimately, once again I think I have to leave it to an interested party.

However, one thing I will do is look through the existing tracks and see how they treat such cases.

• Exclude (6): C++ (via removed 242 case cpp#86), ECMAScript (via Remove test that allows degenerate triangles javascript#198), Javascript (via Remove test which allows degenerate (a+b=c) triangles DEPRECATED.javascript#164), Lua (via Removed gray area test in Triangle exercise lua#110), Scala (via Triangle scala#102), Swift (via Remove edge case 2-4-2 triangle swift#107)
• Include, Illegal (14): C#, Clojure, Coffeescript, Lisp, Elixir, Elm, Erlang, F#, Haskell, Java, Nim, Perl, Python, Ruby
• Include, Legal (1): Go (via triangle: Allow triangles where a+b == c go#232)

Guess Go's the outlier, and that's my doing too. Nevertheless, that's moot if the case is to be removed.

[kytrinyx]

(3, 4, -5): Exclude

I would vote to Exclude, and support the suggestion that if it gets included later we should update the README.

(2, 4, 2), (1, 3, 4), etc.: Exclude

I would also vote to Exclude here, with the reasoning being that the difference between "not a triangle" and "triangle but degenerate" is more about the math than about the interesting part of the programming challenge. I do tend to get pulled into "yes but it's WRONG" discussions, because I am a hopeless pedant (at least when I've had enough sleep to pay attention to the discussion), but I think that it is not helpful to the exercise itself to focus on this issue.

[petertseng]

Thanks, everyone.