Is my triangle right?

Question

Given a, b, c the length of the three sides of a triangle, say if the triangle is right-angled (i.e. has one angle equal to 90 degrees) or not.

Input

Three positive integer values in any order

Output

Either a specific true output (true, 1, yes, ...) or a specific false output (false, 0, no, ...)

Example

5, 3, 4 --> yes
3, 5, 4 --> yes
12, 37, 35 --> yes
21, 38, 50 --> no
210, 308, 250 --> no

Rules

• The input and output can be given in any convenient format.
• In your submission, please state the true and the false values.
• No need to handle negative values or invalid edge triple
• Either a full program or a function are acceptable. If a function, you can return the output rather than printing it.
• If possible, please include a link to an online testing environment so other people can try out your code!
• Standard loopholes are forbidden.
• This is code-golf so all usual golfing rules apply, and the shortest code (in bytes) wins.

• user202729: Must we handle negative values or invalid edge triple?
• Digital Trauma: Very related. I'll leave it up to the rest of the community to decide if its a dup.
• Luis Mendo: I think that using coordinates instead of lengths changes the challenge significantly
• Kevin: There is no triangle with lengths 21, 38, 5, because 21 + 5 < 38. Is this an intentional pathological case that we have to handle?
• mdahmoune: @Kevin no you have not to handle this case. User202729 has already asked this question :)

Answer 1

Jelly, 5 bytes

2μSHe

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Technical note: Bytes are counted in Jelly codepage.

Explanation:

2μSHe Main link.
2 Square each number.
 μ With the new list,
 S calculate its sum,
 H and halve it.
 e Check if the result exists in the new list (squared input)

The problem is equivalent to being given three numbers a, b, c, and asking if there is a permutation such that a2 + b2 = c2. This is equivalent to whether (a2 + b2 + c2) ÷ 2 is one of a2, b2 or c2, so the program just checks that.

• Félix Gagnon-Grenier: well... I jelly.
• Charlie: Just a technical note: symbols ² and µ cost two bytes each in UTF-8, so your code has actually 7 bytes, not 5
• user202729: @Charlie Answer edited for clarification.

Answer 2

Python 2, 37 bytes

a,b,c=sorted(input())
1/(a*a+b*b-c*c)

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-2 thanks to FlipTack.
-1 thanks to Craig Gidney.

Outputs via exit code (0 = false, 1 = true).

• mbomb007: Bah. Came up with the exact same answer. You could modify the test suite to allow for any number of test cases: see here
• Erik the Outgolfer: @mbomb007 exec(code) hmmm, why exec (code) instead of exec code? :D ;-p
• FlipTack: Haha, how does this answer have double the upvotes of xnor's shorter one? Maybe people just like the sweet simpleness of it
• Erik the Outgolfer: @FlipTack ¯_(ツ)_/¯ (also xnor's isn't in Python 2)
• mbomb007: @EriktheOutgolfer Because the boilerplate isn't the part that is to be golfed. I made it so it'd work in either Python 2 or 3.

Answer 3

Java 8, 44 bytes

(a,b,c)->(a*=a)+(b*=b)==(c*=c)|a+c==b|b+c==a

Explanation:

Try it here.

(a,b,c)-> // Method with three integer parameters and boolean return-type
 (a*=a)+(b*=b)==(c*=c) // Return if `a*a + b*b == c*c`
 |a+c==b // or `a*a + c*c == b*b`
 |b+c==a // or `b*b + c*c == a*a`
 // End of method (implicit / single-line return-statement)

• corsiKa: Does it work without the parenthesis on the (c*=c)? The *= might have precidence over the == and you can save two bytes.
• Kevin Cruijssen: @corsiKa I'm afraid it's the other way around. == has precedence over *=. =, +=, *=, and similar assignments actually have the lowest precedence in Java operators.
• Olivier Grégoire: Can't find anything shorter... I tried to get the variables swapped to have the max value assigned to a (for instance), without any success. Well, I could do it, but around 65 characters...

Answer 4

Python 3, 37 bytes

lambda*l:sum(x*x/2for x in l)**.5in l

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Might run into float precision issues with large inputs.

Answer 5

JavaScript (ES6), (削除) 43 (削除ここまで) (削除) 41 (削除ここまで) 40 bytes

Saved 1 byte and fixed a bug thanks to @Neil

Takes input as an array of 3 integers. Returns true for right-angled and false otherwise.

a=>a.some(n=>Math.hypot(...a,...a)==n*2)

let f =
a=>a.some(n=>Math.hypot(...a,...a)==n*2)
console.log(f([5, 3, 4 ])) // --> yes
console.log(f([3, 5, 4 ])) // --> yes
console.log(f([12, 37, 35 ])) // --> yes
console.log(f([21, 38, 5 ])) // --> no
console.log(f([210, 308, 15])) // --> no

---

Original version, 44 bytes

Takes input as 3 integers. Returns 1 for right-angled and 0 otherwise.

(a,b,c)=>(a*=a)+(b*=b)==(c*=c)|a+c==b|b+c==a

Test cases

let f =
(a,b,c)=>(a*=a)+(b*=b)==(c*=c)|a+c==b|b+c==a
console.log(f(5, 3, 4 )) // --> yes
console.log(f(3, 5, 4 )) // --> yes
console.log(f(12, 37, 35 )) // --> yes
console.log(f(21, 38, 5 )) // --> no
console.log(f(210, 308, 15)) // --> no

• Kevin Cruijssen: Looks like we came up with the exact same answer (except for the => and -> difference between JavaScript and Java 8). ;) So obvious +1 from me.
• Neil: >>1 is unsafe, this returns true for [1, 1, 1].
• Neil: How about Math.hypot(...a,...a)==n*2?
• Arnauld: @Neil Very nice fix :)
• JollyJoker: @Neil There should be a ~= operator for "rougly equal" ;)

Answer 6

Triangular, 57 bytes

I haven't seen any in this language yet and it seemed appropriate to try and do one. It took a bit ... as I had to get my head around it first and I believe this could be golfed some more.

,$\:$:*/%*$"`=P:pp.0"*>/>-`:S!>/U+<U"g+..>p`S:U/U"p`!g<>/

Try it online!

This expands to the following triangle.

 ,
 $ \
 : $ :
 * / % *
 $ " ` = P
 : p p . 0 "
 * > / > - ` :
 S ! > / U + < U
 " g + . . > p ` S
 : U / U " p ` ! g <
> /

The path is quite convoluted, but I'll try and explain what I have done. I will skip the directional pointers. Most of the code is stack manipulation.

• $:* Square the first input.
• $:* Square the second input.
• S":Ug! Test if the second value is greater than the first.
  • true p" Swap with the first.
  • false p Do Nothing.
• $:* Square the third input.
• P":USg! Test if the third value is greater than the greatest of the previous.
  • true p+U- sum the current stack and take away stored third value
  • false p"U+- sum the least and stored third and subtract from greatest
• 0=% test equality to zero and output result.

Answer 7

Haskell ((削除) 33 (削除ここまで) (削除) 32 (削除ここまで) 31 bytes)

(\x->(sum x)/2`elem`x).map(^2)

Original version:

(\x->2*maximum x==sum x).map(^2)

Anonymous function. Takes a list in the form [a,b,c]. Outputs True or False.

First version checked if the sum of the squares was twice the square of the maximum.

Second, slightly better version checks if half the sum of squares is an element in the list of squares.

Edit: Accidentally counted a newline, thanks H.PWiz

• H.PWiz: Welcome to the site! This answer is only 32 bytes, maybe you counted an extra newline?
• H.PWiz: You can use the function Monad to save some more bytes here
• proud haskeller: also, the parentheses around sum can be thrown away. nice solution!

Answer 8

Perl 6, 24 bytes

{(*2+*2==*2)(|.sort)}

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*2+*2==*2 is an anonymous function that returns true if the sum of the squares of its first two arguments is equal to the square of its third argument. We pass the sorted input list to this function, flattening it into the argument list with |.

Answer 9

R, 31 (削除) 26 (削除ここまで) (削除) 30 (削除ここまで) bytes

cat(sum(a<-scan()^2)/max(a)==2)

I don't like this one as much, but it is shorter. Sums the squares and divides by the largest square. Truthy if 2.

Previous Version (modified with cat and with @Guiseppe's tip)

cat(!sort(scan())^2%*%c(1,1,-1))

Do a sum of the sorted input with the last item negated and return the ! not.

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• Giuseppe: For your previous version, !sort(scan())^2%*%c(1,1,-1) is 27 bytes. but I think you still need a cat.
• MickyT: Cheers @Guiseppe, forgot about the cat. The rules around REPL annoy me, but they are what they are.
• MickyT: @Giuseppe Also nice twist with the matrix multiplication. I would never have come up with that.

Answer 10

Brain-Flak, 68 bytes

({({({})({}[()])}{}<>)<>})<>({<(({}){}<>[({})])>(){[()](<{}>)}{}<>})

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Uses the observation in user202729's answer.

 { } for each input number
 {({})({}[()])}{} compute the square
 ( <>)<> push onto second stack
( ) push sum of squares onto first stack
 <> move to second stack
 { } for each square
 (({}){}<>[({})]) compute 2 * this square - sum of squares
 < >(){[()](<{}>)}{}<> evaluate loop iteration as 1 iff equal
( ) push 1 if any squares matched, 0 otherwise

Answer 11

Python 2, 43 bytes

lambda a,b,c:(a*a+b*b+c*c)/2in(a*a,b*b,c*c)

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Python 2, (削除) 79 (削除ここまで) (削除) 70 (削除ここまで) (削除) 68 (削除ここまで) 62 bytes

lambda*l:any(A*A+B*B==C*C for A,B,C in zip(l,l[1:]+l,l[2:]+l))

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• Martin Ender: The challenge was updated to limit inputs to integers.
• mdahmoune: 77 bytes tio.run/##hY/BCoMwDIbvPkVgF@ti0dayMXCgPsbYQZ0yL1U6d/…
• Socratic Phoenix: A*A is shorter...
• mdahmoune: 68 bytes tio.run/…
• Alex Varga: 41 bytes: lambda*x:sum(y*y for y in x)/2==max(x)**2

Answer 12

C (gcc), 49 bytes

n(a,b,c){return(a*=a)+(b*=b)-(c*=c)&a+c-b&b+c-a;}

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Improves on Kevin Cruijssens technique

Returns 0 for a valid triangle, and a non-zero value otherwise

• caird coinheringaahing: Welcome to PPCG!
• l4m2: Does it always work if you're using bitwise operations?

Answer 13

Triangularity, (削除) 49 (削除ここまで) 31 bytes

...)...
..IEO..
.M)2s^.
}Re+=..

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Explanation

Every Triangularity program must have a triangular padding (excuse the pun). That is, the ith line counting from the bottom of the program must be padded with i - 1 dots (.) on each side. In order to keep the dot-triangles symmetrical and aesthetically pleasant, each line must consist of 2L - 1 characters, where L is the number of lines in the program. Removing the characters that make up for the necessary padding, here is how the code works:

)IEOM)2s^}Re+= Full program. Input: STDIN, Output: STDOUT, either 1 or 0.
) Pushes a zero onto the stack.
 IE Evaluates the input at that index.
 O Sorts the ToS (Top of the Stack).
 M)2s^} Runs the block )2s^ on a separate stack, thus squaring each.
 R Reverse.
 e Dump the contents separately onto the stack.
 + Add the top two items.
 = Check if their sum is equal to the other entry on the stack (c^2).

Checking if a triangle is right-angled in Triangularity...

Answer 14

MATL, 7 bytes

SU&0)s=

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Explanation

Consider input [12, 37, 35].

S % Implicit input. Sort
 % [12, 35, 37]
U % Square each entry
 % [144, 1225, 1369]
&0) % Push last entry and remaining entries
 % STACK: 1369, [144, 1225]
s % Sum of array
 % STACK: 1369, 1369
= % Isequal? Implicit display
 % STACK: 1

Answer 15

C, (削除) 68 (削除ここまで) 54 bytes

Using user202729's solution.

f(a,b,c){return!((a*=a)+(b*=b)-(c*=c)&&a-b+c&&a-b-c);}

Thanks to @Christoph for golfing 14 bytes!

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C, 85 bytes

#define C(a,b,c)if(a*a+b*b==c*c)return 1;
f(a,b,c){C(a,b,c)C(b,c,a)C(c,a,b)return 0;}

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• Neil: Outputs 1 for parameters of 1, 1, 1 which is wrong...
• Steadybox: @Neil It's fixed now.
• corsiKa: Question was updated to use ints, might save some bytes.
• Christoph: f(a,b,c){a=!((a*=a)+(b*=b)-(c*=c)&&a-b+c&&a-b-c);}
• ceilingcat: 52 bytes

Answer 16

Julia 0.6, 16 bytes

!x=x⋅x∈2x.*x

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How it works

Let x = [a, b, c].

x⋅x is the dot product of x and itself, so it yields a2 + b2 + c2.

2x.*x is the element-wise product of 2x and x, so it yields [2a2, 2b2, 2c2].

Finally, ∈ tests if the integer a2 + b2 + c2 belongs to the vector [2a2, 2b2, 2c2], which is true iff
a2 + b2 + c2 = 2a2 or a2 + b2 + c2 = 2b2 or a2 + b2 + c2 = 2c2, which itself is true iff
b2 + c2 = a2 or a2 + c2 = b2 or a2 + b2 = c2.

Answer 17

J, 10 bytes

-6 bytes thanks to FrownyFrog

=`+/@\:~*:

original answer

(+/@}:={:)@/:~*:

/: sort the squares *:, then check if the sum of the first two +/@}: equals the last {:

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• Jonah: that's awfully damn clever

Answer 18

Japt, 8 bytes

m2ø1⁄2*Ux2

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Japt -x¡, 7 bytes

Ë2ѶUx2

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• mdahmoune: I like the square symbols in your solution ;)

Answer 19

MS Excel, 48 Bytes

Anonymous worksheet function that takes input from the range [A1:C1] and outputs to the calling cell.

=Let(a,A1^2,b,B1^2,c,C1^2,Or(a+b=c,b+c=a,a+c=b))

Answer 20

PowerShell, 39 bytes

$a,$b,$c=$args|sort;$a*$a+$b*$b-eq$c*$c

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Sorts the input, stores that into $a,$b,$c variables. Then uses Pythagorean theorem to check whether a*a + b*b = c*c. Output is either Boolean True or False.

Answer 21

Gaia, 6 bytes

s¦ΣḥuĖ

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• s¦ - square each.

• Σ - sum.

• ḥ - ḥalve.

• u - square root.

• Ė - contains? Check if the square root is in the input.

• mdahmoune: Is it better than sorting version?
• Mr. Xcoder: @mdahmoune I believe it is better. I will try to solve it the other way around, but TBH I think that'd be longer.
• mdahmoune: Upvote any way :)

Answer 22

RProgN 2, 10 bytes

§22^r]‘\+e

Explained

§22^r]‘\+e
§ # Sort the input list
 22^r # Square each element in the list.
 ] # Duplicate it on the reg stack.
 ‘ # Pop the top (largest) element off it
 \+ # Swap it, sum the rest of the list.
 e # Are they equal?

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• mdahmoune: Why duplicate the list?
• ATaco: @mdahmoune RProgN2 doesn't keep the original list on the stack when popping an element off it, but stacks are by reference, so to keep the stack to do the sum part of it, it needs to be duplicated first.
• mdahmoune: Thanx upvote ;)

Answer 23

Racket, (削除) 64 (削除ここまで) 60 bytes

(λ(a b c)(=(+(* a a)(* b b)(* c c))(*(expt(max a b c)2)2)))

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How it works

Tests if a^2 + b^2 + c^2 is equal to twice the largest of a^2, b^2, and c^2.

Returns #t for right triangles and #f for all other inputs.

---

• -4 bytes thanks to @xnor's suggestion to use expt.

• mdahmoune: Awesome ;) but i think (define fun must be a part of the code...
• Misha Lavrov: Thank you! I think it's conventional to say that pure functions are allowed as answers. The (define fun ...) on TIO is just for convenience: we could equally well use this function as (... 3 4 5) where ... is the function. (So we could have a header of (print ( and a footer of 3 4 5)) if you prefer.)
• Misha Lavrov: (But this is one of my first Racket submissions, so I'm not too clear on what Racket-specific conventions there are, if any. Some past solutions using Racket have included #lang racket in the code; some haven't.)
• xnor: Racket is so wordy that it's shorter to repeat (max a b c) than to do a let binding, huh? I don't suppose it would be shorter to bind as an argument to a λ? Or, isn't there an exponentiation built-in?
• xnor: @MishaLavrov Then how about (*(expt(max a b c)2)2)?

Answer 24

05AB1E, 6 bytes

n{R`+Q

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• Nick Loughlin: The first example fails to detect [1,1,1] is not a valid input (common issue on some other attempts), but the second works fine.
• Okx: @NickLoughlin Oops, removed first example
• Emigna: You could do n{RÆ_ to save a byte.
• Makonede: @Emigna The _ could also be a >, since in this case they have the same effect - making a truthy output if the top of stack is 0 and falsy otherwise. Since 1 is the only truthy value in 05AB1E, > will increment 0 to 1 and output it; for other values, it will increment it and output it. Since any value other than 1 is falsy, it will be a falsy output.

Answer 25

Ruby, 31 bytes

->a{a,b,c=*a.sort;a*a+b*b==c*c}

Takes input as a list of 3 integers. Uses some ideas from other solutions.

• Reinstate Monica -- notmaynard: I just realized the answer I just posted is almost identical to yours. I promise I didn't copy yours (I actually had it sitting for a while in the "Post an answer" box), but since yours was submitted first, if you think mine is too close, I'll delete it.
• anna328p: @iamnotmaynard It's pretty much the same thing. this was a funny coincidence lol. Thanks for letting me know
• mdahmoune: If possible, please include a link to an online testing environment so other people can try out your code!

Answer 26

Java (OpenJDK 8), 68 bytes

a->{java.util.Arrays.sort(a);return a[0]*a[0]+a[1]*a[1]==a[2]*a[2];}

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• AdmBorkBork: Can you save some bytes using currying rather than an array?
• Olivier Grégoire: @AdmBorkBork Nope, because sort takes an array.
• ceilingcat: Suggest Math.hypot(a[0],a[1])==a[2] instead of a[0]*a[0]+a[1]*a[1]==a[2]*a[2]

Answer 27

TI-Basic, (削除) 13 (削除ここまで) (削除) 11 (削除ここまで) 10 bytes

max(Ans=R►Pr(min(Ans),median(Ans

Now works for inputs in any order and is shorter as well. Another -1 thanks to @MishaLavrov

• mdahmoune: If possible, please include a link to an online testing environment so other people can try out your code!
• Misha Lavrov: This only detects sorted right triangles: input of A=5, B=4, C=3 would not be correctly handled.
• Timtech: @MishaLavrov Thanks for pointing that out, it's actually shorter handling as a list. Now it works for inputs in any order.
• Misha Lavrov: If we leave off a single ), then max(Ans=R►Pr(min(Ans),median(Ans is also valid (though the computation we're doing here is different) and is one byte shorter.
• Timtech: @MishaLavrov That's interesting, I see what you mean. I think the expressions are equivalent for all non-negative inputs.

Answer 28

CJam, 9

q~$W%~mh=

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Explanation:

q~ read and evaluate the input (given as an array)
$W% sort and reverse the array
~ dump the array on the stack
mh get the hypotenuse of a right triangle with the given 2 short sides
= compare with the longer side

• mdahmoune: Some explanations ;) ?
• aditsu quit because SE is EVIL: @mdahmoune here you go
• kaine: Dang it. Didn't you write that language? Doesn't seem fair. (joke)

Answer 29

Pari/GP, (削除) 29 (削除ここまで) 24 bytes

f(v)=v~==2*vecmax(v)^2

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Saved five bytes by an obvious change from norml2(v) to v*v~.

Inspired by other answers.

Here v must be a row vector (削除) or a column vector (削除ここまで) with three coordinates.

Example of use: f([3,4,5])

Of course, you get rational side lengths for free, for example f([29/6, 10/3, 7/2]).

If I do not count the f(v)= part, that is 19 bytes. The first part can also be written v-> (total 22 bytes).

Explanation: If the three coordinates of v are x, y and z, then the product of v and its transpose v~ gives a scalar x^2+y^2+^z^2, and we need to check if that is equal to twice the square of the maximum of the coordinates x, y, z.

Extra: The same f tests for a Pythagorean quadruple if your input vector has four coordinates, and so on.

• mdahmoune: If possible, please include a link to an online testing environment so other people can try out your code!
• Jeppe Stig Nielsen: @mdahmoune You can use this tio.run link. However, it is much nicer to just install PARI/GP locally.

Answer 30

Ohm v2, (削除) 8 (削除ここまで) 6 bytes

2DS)Σε

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