# Triangle and/or Square? [duplicate]

This question already has an answer here:

# Explanation of the challenge

Given an input, return what shapes it could be. There are only a couple options.

1. Square
2. Triangle

Square

A square is in the following format:

XXXX
XXXX
XXXX
XXXX


So, in this example, the input would be:

16


And the output would be:

1 or "Square"


Triangle

We are only checking for equilateral triangles:

   X
X X
X X X
X X X X


So, in this example, the input would be:

10


And the output would be:

2 or "Triangle"


# Rules for input and output

Input must be a number.

Output can be an integer list or string list as long as you specify how your output works in your post. The output will be either a triangle, square, or both; never neither.

# Test Cases

36 ->  1,2 or 3 or ["Square","Triangle"] or "Both"

15 ->  2 or "Triangle"

4  ->  1 or "Square"


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## marked as duplicate by Peter Taylor code-golf StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 17 '17 at 10:50

• @ScottMilner In the post I specified you could use your own output method. – Neil May 4 '17 at 21:45
• The output needs to be ["Square"], as in a singleton list of the string Square? Or the string ["Square"]? Even just the string Square seems needlessly specific. – xnor May 4 '17 at 21:45
• Possibly a dupe of Polygonal Numbers!, which asks to list all k for a which a number is k-gonal. This restricts to k=3 and k=4. – xnor May 4 '17 at 21:56
• Is it acceptable to output a 1 or 0 to indicate whether it's a square, and another 1 or 0 to indicate if it's a triangle? – Maria May 4 '17 at 22:38
• Is [True, False] an OK output format (first one for triangle, second for square)? – xnor May 4 '17 at 23:10

# Jelly, 9 7 bytes

×8‘,µÆ²


Try it online!

Outputs [1,1] for both, [0,1] for square, [1,0] for triangle, [0,0] for neither.

Explanation

×8‘,µÆ² - main link, input a
,    - a list of the following two:
×8‘     - a×8+1 (which is square when a is triangle)
- (implicit) a
µÆ² - On the previous, check if each is a square


# Japt, 18 15 11 bytes

[U8*UÄ]®¬v1


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• You can save a few bytes with shortcuts: [U8*UÄ]®¬u1 ¥0 Also, u1 ¥0 can be reduced to v1 to save a couple bytes :-) – ETHproductions May 4 '17 at 23:18

# JavaScript (ES7), 40 32 bytes

Returns 1 for square, 2 for triangle, 3 for both or 0 for neither.

n=>!(n**.5%1)+2*!((8*n+1)**.5%1)


## Try It

Displays "Square/Triangle/Both/Neither" for clarity

f=
n=>!(n**.5%1)+2*!((8*n+1)**.5%1)
i.addEventListener("input",_=>o.innerText=["Neither","Square","Triangle","Both"][f(+i.value)])
<input id=i type=number><pre id=o>

• Nice one! I think you can remove both pairs of parentheses around exponentiations (that is, n=>(n**.5%1?0:1)+((8*n+1)**.5%1?0:2). You can save another couple bytes with !(n**.5%1) – ETHproductions May 4 '17 at 23:20
• In that case, 2*!((8*n+1)**.5%1) might save a byte too. – Neil May 4 '17 at 23:52

# Haskell, 4948 37 bytes

EDIT:

• -1 byte: @xnor suggested parametrizing on k.
• -11 bytes: And then turned it all inside out...

f takes an integer and returns a list: [3] for square, [2] for triangle, and [2,3] for both (or [] for neither.)

f n=[k|k<-[2,3],0<-scanl(-)n[1,k..n]]


Try it online!

This uses that triangular numbers are sums 1+2+3+4+...+i while square numbers are sums 1+3+5+7+...+i, thus by starting with n and using scanl(-) to subtract either the range [1,2..n] or the range [1,3..n] consecutively, each of those cases will eventually hit 0.

• Nice idea with the scan. I think it would help to write the two options as [1,k..n] for k<-[2,3]. – xnor May 4 '17 at 23:30
• One weird possibility is f n=[k|k<-[2,3],0<-scanl(-)n[1,k..n]]. – xnor May 4 '17 at 23:40
• @xnor That's starting to get pretty different, sure you don't want to post it yourself? – Ørjan Johansen May 4 '17 at 23:46
• @xnor Someone should do it, so I'm taking silence for a no ;) – Ørjan Johansen May 5 '17 at 12:01

# PHP, 67 bytes

Returns 2 for square, 1 for triangle, 3 for both and 0 for none

(^1|11\1)+$ Takes input in unary, outputs t and s on separate lines, where t and s are 0 or 1 indicating whether the shape is a triangle and/or square, respectively. Try it online! (Contains an additional \ to put both outputs on the same line to make the test cases more easily distinguishable.) ### Explanation Triangular numbers are the sums of consecutive integers starting from one. Square numbers are the ums of consecutive odd integers starting from one. Both of those are fairly easy to match with forward references. *M(^1|1\1)+$


This prints 0 or 1 depending on whether the given regex matches, but it doesn't actually modify the string (the * indicates a dry run). The regex either matches the initial one with ^1 or it matches exactly one more 1 than in the previous iteration with 1\1 (the \1 refers to what (^1|1\1) matched last time).

(^1|11\1)+\$


This is basically the same, except that we don't need a dry run and M is implicit. To go up by odd integers instead of all integers, we simply add two 1s on each iteration with 11\1.

# MATL, 11 10 bytes

t:UmGt:Ysm


Outputs two values 0 or 1 separated by newline. The first indicates if the input is square, and the second indicates if it is triangular.

Try it online!

### Explanation

Consider input 4 as an example.

t     % Implicit input. Duplicate
% STACK: 4, 4
:     % Range
% STACK: 4, [1 2 3 4]
U     % Square, elementwise. This gives square numbers
% STACK: 4, [1 4 9 16]
m     % Ismember
% STACK: 1
Gt    % Push input again. Duplicate
% STACK: 1, 4, 4
:     % Range
% STACK: 1, 4, [1 2 3 4]
Ys    % Cumulative sum. This gives triangular numbers
% STACK: 1, 4, [1 3 6 10]
m     % Ismember. Implicitly display
% STACK 1, 0


# Python 3, 72 67 bytes

x=input()
k=int((x*2)**.5)
print((x==int(x**.5)**2)+2*(2*x==k*k+k))


A bit longer than wanted. This is a full program that takes input from STDIN and outputs to STDOUT. STDERR should be empty as long as there isn't an I/O Exception and the input isn't invalid.

• Why len(input)? – Maria May 4 '17 at 22:24
• You can change this to Python 2 and remove the len (which I think should be int). – internet_user May 4 '17 at 22:40
• @Svetlana The specs were changed after I answered. Thanks for notifying me. – HyperNeutrino May 4 '17 at 23:38
• @pycoder ^ Thanks as well – HyperNeutrino May 4 '17 at 23:38
• Why is this getting downvotes? – HyperNeutrino May 5 '17 at 1:09

# Octave, 38 bytes

@(x)~mod(x^.5,1)+2*any(x==cumsum(1:x))


Outputs 1 for square, 2 for triangular, 3 for both, 0 for neither.

Try it online!