Math clear solution for The Angles of a Triangle by bryukh - python coding challenges

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Math solution in Clear category for The Angles of a Triangle by bryukh

from math import acos, degrees

def checkio(a, b, c):
    if a + b <= c or a + c <= b or b + c <= a:
        return [0, 0, 0]
    find_angle = lambda s1, s2, so: int(round(
        degrees(acos((s1 ** 2 + s2 ** 2 - so ** 2) / (2 * s1 * s2))), 0))
    return sorted([find_angle(a, b, c), find_angle(a, c, b), find_angle(b, c, a)])

#These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
    assert checkio(4, 4, 4) == [60, 60, 60], "All sides are equal"
    assert checkio(3, 4, 5) == [37, 53, 90], "Egyptian triangle"
    assert checkio(2, 2, 5) == [0, 0, 0], "It's can not be a triangle"

Aug. 20, 2013

Comments:

veky on Aug. 21, 2013, 5 p.m.
int(round(bla,0)) is just round(bla). Also, see "Always use a def statement instead of an assignment statement that binds a lambda expression directly to a name." (new version of PEP8). Otherwise, nice solution.

bryukh on Aug. 21, 2013, 9:12 p.m.
<blockquote> Also, see "Always use a def statement instead of an assignment statement that binds a lambda expression directly to a name." (new version of PEP8). </blockquote> Thanks. You are right. Lambda here is not good idea.

BornForDying on Sept. 4, 2013, 9:35 p.m.
round returns a float though? or is this a py3 thing?

veky on Sept. 5, 2013, 11:30 a.m.
It's a py3 thing. But he uses / for truediv (not floordiv), so I thought it's obvious he writes in py3. Anyway, even if it were float, [60] * 3 == [60.0] * 3, so there shouldn't be a problem.

BornForDying on Sept. 5, 2013, 4 p.m.
Ah cool - I didn't know this had changed in py3 is all, I was just curious. I guess it makes sense with the new division, as the rounded value would change back to a float if it needs to.

Cocoolanu on Feb. 10, 2018, 3:22 a.m.
I think this is the solution for python2, as round function will return an integer for python3 and return float for python2. If using Python3, there is no need to use int for converting round result.So here can directly use round(degrees(acos((s1 * 2 + s2 * 2 - so ** 2) / (2 * s1 * s2))))

veky on Feb. 11, 2018, 4:08 a.m.
Yes, Bryukh probably wrote a Py2 solution in his mind (with implicit `from future import division`:), then he gave it to a Py3 interpreter. Luckily, it worked. :-D

kvas on Nov. 13, 2013, 3:01 p.m.
<blockquote> Also, see "Always use a def statement instead of an assignment statement that binds a lambda expression directly to a name." (new version of PEP8). </blockquote> Of all people here, I least expected to hear this from you! :)

veky on Nov. 13, 2013, 4:10 p.m.
I don't know why. "Know the rules before you break them" is my motto. ;-)

hugoboss on Aug. 11, 2018, 1:34 p.m.
Lambda is not a straightforward thing, but it's pretty convenient as a 'key' argument in the some of the functions (max, ). imho. Not here, of course, it's obvious.

scottmiao on Nov. 23, 2013, 10:47 a.m.
<pre class='brush: python'> return [0, 0, 0] </pre> Why 'SORTED'?

bryukh on Nov. 24, 2013, 12:10 a.m.
Because <blockquote> The angles should be represented as a list of integers in ascending order. </blockquote>

gwie on Nov. 25, 2013, 8:56 p.m.
<pre class='brush: python'>if a + b <= c or a + c <= b or b + c <= a: </pre> Is not needed because a,b,c are in ascending order. You could just use: <pre class='brush: python'>if a + b <= c: </pre> But since it is not mentioned that a, b, c are in ascending order I guess you should check all cases. Maybe the task should mention that a, b, c are always in ascending order or test if the code works if it's not.

bryukh on Nov. 25, 2013, 9:22 p.m.
<blockquote> Is not needed because a,b,c are in ascending order. </blockquote> Where did you take it? We have the test like [15, 14, 19] for example or [50, 40, 30].

gwie on Nov. 26, 2013, 5:19 p.m.
Never mind, I'm an idiot. :D

bryukh on Nov. 26, 2013, 8:56 p.m.
No problem :)

Cjkjvfnby on Dec. 17, 2013, 10:05 p.m.
You can sort a,b,c at the begining. This will simplify check and you will not need sort at the end. <pre class='brush: python'>a, b, c = sorted((a, b, c)) </pre>

bryukh on Dec. 17, 2013, 10:17 p.m.
Thanks. This is a good idea.

ultras on Dec. 26, 2013, 9:33 a.m.
tiny remark: because you are checking for the valid triangle, the third angle can be calculated as (180 - alpha - beta) instead of acos.

bryukh on Dec. 27, 2013, 12:25 a.m.
Yes, you are right. Thanks.

veky on May 21, 2015, 9:44 p.m.
No it cannot. I tried to see why so many people make that mistake, now I see that's because of your comment. :-/ Suppose the true angles are 59.6, 59.7 and 60.7. Then you're supposed to return [60, 60, 61] and not [60]*3.

bryukh on May 25, 2015, 5:19 a.m.
A nice example. Thanks!

veky on May 25, 2015, 2:49 p.m.
Here is a concrete one, if you want to break half the solutions. :-] <pre class='brush: python'>checkio(59, 59, 60) should return [59, 59, 61], not [59, 59, 62] </pre>

bryukh on May 25, 2015, 3:31 p.m.
I'm too kind for this ;-)

Infini7y on Aug. 8, 2015, 10:51 a.m.
I would debate this, as returning ints is an approximation of the angles and should still obey the 180 rule, unless there is a specified assumption to overrule this.

veky on Aug. 8, 2015, 11:45 a.m.
I think the task text is perfectly clear. <blockquote> Each angle is [...] rounded to the nearest integer number. </blockquote> There is no mention of laws that hold for them together. You round each separately. <hr /> Your mistake is a very common one (and math teachers see it all the time), thinking that various operations (like rounding, or squaring, or ...) are distributive over addition. You certainly know that square(x) + square(y) is not the same as square(x+y), right? In completely the same way, there's no reason to expect round(alfa) + round(beta) + round(gamma) to be equal to round(alfa+beta+gamma) (=180°).

Infini7y on Aug. 9, 2015, 8:02 a.m.
I agree: "Each angle is measured in degrees and rounded". So calculation of the angle in degrees by round(180 - adeg - bdeg) is then perfectly legitimate to the request. If this is not valid, then a unit test should expose this. I don't think it is my mistake, but I will agree I have seen many instances of people calculating discrepancies in formula results by just adding them, and going way off base. And the angles returned are an approximation +/- 0.5 around the returned value, and preserving, by working backwards with the error range, will produce the given lengths within the error. So we may be splitting hairs here, but I think the '180 rule' should be preserved in the ints returned, or tests should enforce the tasks request. After all the test is the gate keeper of what is 'truth'.

veky on Aug. 9, 2015, 12:21 p.m.
<blockquote> the test is the gate keeper of what is 'truth’. </blockquote> If that was literally enforced, CiO would be a very strange place. :-/ Many tests here are extremely poor, and sometimes they don't even test the thing that was emphasised in the task text. I agree that it would be nicer if there was a test, but even if there isn't, still the task text can be read in only one way. <blockquote> "Each angle is measured in degrees and rounded". So calculation of the angle in degrees by round(180 - adeg - bdeg) is then perfectly legitimate to the request. </blockquote> I don't see how that follows. Look: I hope you agree with me that the triangle with sides a=2,b=2,c=3 exists, and is a valid example for this task. It has some angles. They are (in degrees) approximately 41.4, 41.4 and 97.2. In my world, [41,41,97] is the only correct answer. If I read you right, you insist that [41,41,98] must be accepted as a solution. But surely you then also think that [41,42,97] must be accepted, too - whatever the rounding is, if 97.2 can be rounded up to 98, surely 41.4 can be rounded up to 42. Now you see why your position is untenable? The triangle is isosceles. Its two angles are mathematically equal. If you're telling me that one number should be deterministically rounded both to 41 and to 42, I have no other option than to pronounce you crazy. :-/ The problem is even bigger if you have more angles; if you have a 70gon, you can have in it, for example, an exact angle of 50 which must be "rounded up" to 68 :-P to preserve the illusion of the same sum. No, you'll just have to give up the idea that rounded numbers sum to their rounded sum. It's mathematically impossible.

Infini7y on Aug. 10, 2015, 6:49 a.m.
<blockquote> still the task text can be read in only one way. </blockquote> and yet, we're here. I think we have two paths here. One where you are saying the answer should be, exclusively for all the angles: angledegrees=round(cosinelawdeg(sidelengths)). And I'm voicing a preference for the returned angles satisfying the inner angles of a triangle in integer form. The pictographs and the text led me on this path, as the returned data is more usable, and inline with what the supposed requirement is, the angles of a triangle. I guess where I am debating from is when problems like these step out of toy problems, then what matters is what the returned data is used for, and thus the underlying rules/specs the data conforms to. Here it should conform to the angles of a triangle. And don't get me wrong, as an engineer, I am fully versed on rounding and error, so I wont belabour this further. And I am saying with the tests, more to the point, what consumes the output we produce, defines the requirements on the output.

veky on Aug. 10, 2015, 10:29 a.m.
Well, we're here precisely because you don't think there is only one reasonable interpretation of the task. (I presume that even you would agree that if there is only one true meaning, it must be what I'm saying. Your interpretation can only survive in a world where interpretation is fuzzy.) I'm trying to tell you your view is inconsistent. Yes, [a,b,180-a-b] are angles of a triangle (in degrees). But that triangle has almost nothing to do with the triangle we started with. I don't see what's accomplished by trying to stick to the notion of "angles of an abstract triangle" when the task is to measure a concrete triangle. Just one more example: imagine someone asks you what are the angles of a regular heptagon, rounded to integer degrees. In my world, the answer is clear: [129]*7. In your world, if I'm reading you right, you'd like to answer [129,129,129,129,129,129,126]. And I find that completely ridiculous. There is no rounding that will round 900/7 to an integer 126. Especially when six times you've already rounded that same number to 129.

Infini7y on Aug. 11, 2015, 7:05 a.m.
From Task: "Output: Angles of a triangle in degrees as sorted list of integers." I do agree there is a reasonable interpretation of the task. But our reasons are for a selected purpose. You seem very concerned with the rounding requirement over the triangle requirement. If the sum of your angles exceed 180 degrees, it is not a triangle. But if you want the return data to only approximate by closest integer, even if the sum of angles is greater than 180, I guess that is an allowed interpretation on this task. As far as not the triangle we started with, your assertion would fail this, depending on how much rounding (taking your returned data in reverse to get the side lengths). We are playing with geometry here, how is your abstract and concrete different. And as for order N-sided polygons, how did you arrive at your inside angle. My guess, is if equilateral and +symmetric (all inside angles equal) you used the geometric identity, in degrees, the angle is: 180 - (360/N) or 180(1 - 2/N). And the only answer your accepting is [round(180 - 360/N)]*N, even if the sum of angles is greater (violating the geometric requirement). Again two paths. My take is still the geometric requirement trumps the rounding, and how I apply it depends on the consumer of my output. So, from my view, this task specifies an output of a triangle using integer angles, which is a close (integer) approximation to the side length input. I have enjoyed haggling this, and think I know what you are after (minus your few almost derogatory re-phrasings). Back to the other puzzles, Cheers :).

veky on Aug. 11, 2015, 7:26 a.m.
I must say I don't get you. It seems you're focusing too much on "rounding to integers" as if it's something special. It's not. Even if they are floats, there is a pretty big chance they don't sum to exactly 180 degrees. And in that case you probably don't mind that, you just use rounded values without problems. <hr /> So, in your case, the answer to a question "what are the angles of a regular heptagon, rounded to integer number of degrees" can be "six of them are 129, and seventh is 126"? Then I suppose I have no further comment. And if you view it as derogatory, I'm afraid I can't help you. :-(

Infini7y on Aug. 11, 2015, 10:17 a.m.
I think to clarify for others, rephrasing the line, from 'and' to 'then': ""Each angle is measured in degrees and rounded to the nearest integer number"" --> ""Each angle is measured in degrees then rounded to the nearest integer number"". I am looking at the problem as returning a triangle, even if floats, and it will better approximate the input sides as greater precision is requested. And to your heptagon question, as last stated I would concede to [round(900/7)]*7. My point has been, and trying to portray, one of differing perspective, and that it is valid, on what is being asked, that of the original triangle question. As for almost derogatory, a analogous example is: ""I’m afraid I can’t help you. :-("" is edging on derogatory as I am not asking for help (in this instance), but debating your perspective, as an assumed peer. But hey my perspective may be fuzzy ;). Your points have been well taken, and I hope others will get some benefit to the counter perspective. Cheers =).

veky on Aug. 11, 2015, 10:29 a.m.
Maybe the problem is one of language. I meant "I am not going to apologize if you find this derogatory, since it honestly doesn't make sense to me. I am not trying to make it seem like I misunderstand you more than I actually do (which would 'derogatory' be), since I actually don't understand you at all." Having angles of regular Ngon be equal has completely the same importance as having them sum to (N-2)*pi. And since rounding to integer degrees can obviously preserve only one of these properties, I'd much rather that it be deterministic, and that means preserving equality. It's a pity that then you lose preserving sum, but that's just fact of life. And if you concede that (as it seems you do), I don't really see how you can still think what you do think in case of triangle. Where is the limit? N=4? 5? 6? Why? Only because 360 is nicely divisible by many small numbers? What if we used <a href="https://en.wikipedia.org/wiki/Gradian">gradians</a>, would your opinion be different even for triangles? <hr /> Only after I wrote previous reply I realized the first line of your preprevious comment, in which you emphasize that the task text also uses indefinite article: <blockquote> Angles of a triangle in degrees as sorted list of integers. </blockquote> You might have a point there. If it's so important that they be angles of some triangle, then of course [60,60,61] wouldn't qualify. But I think it's obvious, if you look at the line just above, that it's supposed to be the same triangle that "Input:" line is speaking about. Otherwise you might always return [60]*3. :-D

mombius on Dec. 30, 2013, 8:32 p.m.
Nice, I did the same but without the lambda function, I just copied the same three times...

CyroAvernus on Dec. 31, 2013, 7:13 p.m.
I used the same idea but without the lambda function ..... I used L.sort() instead of sorted

gp48maz1 on March 1, 2014, 10:14 p.m.
This is a really cool solution

boubisko on July 8, 2014, 6:53 p.m.
wow, I did it almost the same as you :)

ArchTauruS on Aug. 13, 2014, 3:50 a.m.
if sum((a,b,c)) <= max(a,b,c)*2 return [0,0,0]

ArchTauruS on Aug. 13, 2014, 3:54 a.m.
<pre class='brush: python'>import math def checkio(a, b, c): angle=lambda a,b,c:int(round((math.degrees(math.acos((b*b+c*c-a*a)/2./b/c))))) return [0,0,0] if sum((a,b,c)) <= max(a,b,c)*2 else sorted([angle(a,b,c),angle(b,a,c),angle(c,a,b)]) </pre>

bryukh on Aug. 13, 2014, 5:36 a.m.
And?

ArchTauruS on Aug. 13, 2014, 8:12 a.m.
No and. Just learn a lot from this site and you. And hard to discuss with my poor English.

Parzifal on Jan. 25, 2019, 10:39 a.m.
I am a bit confused about the import of type alias List in your(?) mission. For some time i tried to make good use of it, but finally dropped it. I cannot find it in your solution, too...

Marlen_Nurmakov on May 10, 2019, 5:30 a.m.
I wonder if there is a solution without importing math.

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