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While bored in high-school (when I was half my current age...), I found that f(x) = x(x-1) had some interesting properties, including e.g. that the maximum f for 0 ≤ x is f(e), and that the binding energy per nucleon of an isotope can be approximated as 6 × f(x ÷ 21)...

Anyway, write the shortest function or program that calculates the xth root of x for any number in your language's domain.

Examples cases

For all languages

     -1   >       -1
   ¯0.2   >    -3125
   ¯0.5   >        4
    0.5   >     0.25
      1   >        1
      2   >    1.414
      e   >    1.444 
      3   >    1.442
    100   >    1.047
  10000   >    1.001

For languages that handle complex numbers

   -2   >        -0.7071i
    i   >            4.81         
   2i   >    2.063-0.745i
 1+2i   >   1.820-0.1834i
 2+2i   >   1.575-0.1003i

For languages that handle infinities

-1/∞   >   0    (or ∞ or ̃∞)
   0   >   0    (or 1 or ∞)
 1/∞   >   0
   ∞   >   1
  -∞   >   1

For languages that handle both infinities and complex numbers

 -∞-2i   >   1      (or ̃∞)

̃∞ denotes directed infinity.

share|improve this question
1  
Here is a Wolfram Alpha plot for positive real x. If you omit the x limits in the query, Wolfram Alpha will include negative values of x where the function value depends on a choice of "branch" for the complex logarithm (or for a similar complex function). – Jeppe Stig Nielsen Feb 24 at 14:36
    
What about for languages that do not handle power of decimals? – Leaky Nun Mar 31 at 3:24
1  
@KennyLau Feel free to post with a note that says so, especially if the algorithm would work, had the language supported it. – Adám Mar 31 at 5:37

56 Answers 56

TI-BASIC, 3 bytes

Ans×√Ans

TI-BASIC uses tokens, so Ans and ×√ are both one byte.

Explanation

Ans is the easiest way to give input; it is the result of the last expression. ×√ is a function for the x'th root of x, so for example 5×√32 is 2.

share|improve this answer
7  
As far as I am aware ans would count as hardcoding inputs into variables and does not seem to be an accepted input method for code-golf. In that case, please make a full program or a function. – flawr Feb 24 at 9:14
3  
@flawr I can see what you're saying but it seems it's always been done like this. Maybe it warrants a meta post? – NinjaBearMonkey Feb 24 at 16:08
2  
Ans is STDIN/STDOUT for TI-Basic. – Timtech Feb 24 at 22:43
4  
stdin and stdout are text streams, usually for interactive text input and output. Ans is not interactive, unlike some other functions in TI-BASIC, which are interactive. – Olathe Feb 25 at 5:21
3  
@flawr The reason Ans is usually accepted is because its value is set by any expression (expressions are separated by :). Therefore something like 1337:prgmXTHROOT would input 1337, which looks a lot like input via CLAs in a normal language. – lirtosiast Mar 5 at 5:06

Jelly, 2 bytes

Try it online!

How it works

*İ    Main link. Input: n

 İ    Inverse; yield 1÷n.
*     Power (fork); compute n ** (1÷n).
share|improve this answer
    
Jelly doesn't have a stack. A dyad follow by a monad in a monadic chain behaves like APL's forks. – Dennis Feb 23 at 4:46
2  
No, J's ^% is a hook (which do not exist in Dyalog APL), not a fork. Jelly and APL code is difficult to compare since Jelly is left-to-right. The nearest equivalent would be ÷*⊢ (also a fork), which computes (1/x)**x because of the different direction. Since Jelly's atoms aren't overloaded (they are either monadic or dyadic, but never both), there can be monadic 1,2,1- and 2,1-forks. – Dennis Feb 23 at 4:58
    
Thanks for the clarification. Naturally, I'm quite intrigued by Jelly (which I still think should be named ȷ or something similar.) – Adám Feb 23 at 5:07

Javascript (ES2016), 11 bytes

x=>x**(1/x)

I rarely ever use ES7 over ES6.

share|improve this answer
2  
x=>x**x**-1 also works, again for 11 bytes. – Neil Feb 23 at 8:51
6  
All hail the new exponentiation operator! – mbomb007 Feb 23 at 21:33

Python 3, 17 bytes

lambda x:x**(1/x)

Self-explanatory

share|improve this answer
6  
I quite like lambda x:x**x**-1, but it's not shorter. – Seeq Feb 23 at 6:32
1  
@Seeq Your expression is the same length, but it has the advantage of working in both Python 2 and 3. – mathmandan Feb 23 at 17:54
1  
Python 2's shortest is lambda x:x**x**-1, so it is the same in 2 and 3. – mbomb007 Feb 23 at 21:31
    
Fails for integer input > 1. Example. – agtoever Feb 24 at 20:53
1  
@agtoever That's Python 2. This answer specifically states Python 3. – Mego Feb 24 at 21:01

J, 2 bytes

^%

Try it with J.js.

How it works

^%  Monadic verb. Argument: y

 %  Inverse; yield 1÷y.
^   Power (hook); compute y ** (1÷y).
share|improve this answer
    
How do you create the links to J.js? – Adám Feb 24 at 19:59
    
[text](link). Also, just writing the link will link to it. – VoteToSpam Feb 26 at 8:40
    
@VoteToSpam I meant how to create a "try it" link that executes a chosen expression. – Adám Apr 8 at 2:08
    
@Nᴮᶻ There's a last command permalink in the bottom right corner. – Dennis Apr 8 at 2:35

Haskell, 12 11 bytes

Thanks @LambdaFairy for doing some magic:

(**)<*>(1/) 

My old version:

\x->x**(1/x)
share|improve this answer
3  
(**)<*>(1/) is 11 bytes. – Lambda Fairy Feb 24 at 1:32
    
@LambdaFairy Thanks! Do you mind explaining? It looks like you are doing some magic with partially applied functions but as I am quite new to Haskell I do not really understand how this works=) – flawr Feb 24 at 9:02
    
This uses the fact that a 1-argument function can be considered an applicative functor (the "reader monad"). The <*> operator takes an applicative that produces a function, and an applicative that produces a value, and applies the function to the value. So in this case, a mind-bending way to apply a 2-argument function to a 1-argument function. – MathematicalOrchid Feb 24 at 16:43
2  
The function <*> takes 3 arguments, two functions f and g and an argument x. It is defined as (<*>) f g x = f x (g x), i.e. it applies f to x and g x. Here it's partially applied to f and g leaving out x, where f = (**) and g = (1/) (another partially applied function (a section) that calculates the reciprocal value of it's argument). So ( (**)<*>(1/) ) x is (**) x ((1/) x) or written in infix: x ** ((1/) x) and with the section resolved: x ** (1/x). -- Note: <*> is used in function context here and behaves differently in other contexts. – nimi Feb 24 at 16:52
    
@nimi So it's the equivalent of the S combinator i.e. S(**)(1/)? – Neil Mar 2 at 13:03

Pyth, 3 bytes

@QQ

Trivial challenge, trivial solution...

(noncompeting, 1 byte)

@

This uses the implicit input feature present in a version of Pyth that postdates this challenge.

share|improve this answer
    
Does this solution predate the feature of implicit input? – Leaky Nun Apr 7 at 23:39
    
@KennyLau Yes, by a long time. But I've edited the one-byte solution in anyway. – Doorknob Apr 8 at 4:40

JavaScript ES6, 18 bytes

n=>Math.pow(n,1/n)
share|improve this answer

Mathematica, 8 7 4 bytes

Surd

More builtin-only answers, and now even shorter! By definition, the next answer should be 13 bytes. (Fibonacci!) The pattern is broken. :(

share|improve this answer
1  
#^#^-1& saves 1 byte. – njpipeorgan Feb 23 at 15:16
    
NOW it is golfed. – Adám Feb 23 at 23:16
1  
NOW it is golfed. – CalculatorFeline Mar 10 at 2:43
1  
When Mthmtca is released, we are going to rule this board. – Michael Stern Mar 16 at 3:48
    
Hmm...time to look through my answers and make a compressed version of every builtin... – CalculatorFeline Mar 16 at 4:58

Java 8, 18 bytes

n->Math.pow(n,1/n)

Java isn't in last place?!?!

Test with the following:

import java.lang.Math;

public class Main {
  public static void main (String[] args) {
    Test test = n->Math.pow(n,1/n);
    System.out.println(test.xthRoot(6.0));
  }
}

interface Test {
  double xthRoot(double x);
}
share|improve this answer
    
It's the fact that it's a function – CalculatorFeline Feb 29 at 21:30

Java, 41 bytes

float f(float n){return Math.pow(n,1/n);}

Not exactly competitive because Java, but why not?

share|improve this answer
1  
Welcome to PPCG! I think you might be missing a return type on this function. – quartata Feb 23 at 18:28
    
Oops, got sloppy. A Java 8 answer already beat this one of course... – Darrel Hoffman Feb 23 at 23:18

Perl 5, 10 bytes

9 bytes plus 1 for -p

$_**=1/$_
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R, 19 17 bytes

function(x)x^x^-1

-2 bytes thanks to @Flounderer

share|improve this answer
    
Why not x^(1/x) ? Edit: x^x^-1 seems to work too. – Flounderer Feb 23 at 20:10
    
That's a snippet, and apparently people don't like snippets. – CalculatorFeline Feb 29 at 21:28
    
@CatsAreFluffy it is the definition of a function. – mnel Feb 29 at 21:30

NARS APL, 2 bytes

√⍨

NARS supports the function, which gives the ⍺-th root of ⍵. Applying commute (⍨) gives a function that, when used monadically, applies its argument to both sides of the given function. Therefore √⍨ xx √ x.

Other APLs, 3 bytes

⊢*÷

This is a function train, i.e. (F G H) x(F x) G H x. Monadic is identity, dyadic * is power, and monadic ÷ is inverse. Therefore, ⊢*÷ is x raised to 1/x.

share|improve this answer
    
@NBZ: I usually use Dyalog APL, but this should work with any recent APL that supports function trains. I went and tested it with NARS2000 and ngn/apl and they also worked. – marinus Feb 23 at 23:11
    
@NBZ: The obvious solution in NARS is √⍨, now that I'm looking at it, but that's a NARS-specific extension. Nevertheless, I'm going to submit that instead, as it's shorter. As for the others, my train gives consistent output (as it logically should) with {⍵*⍵*¯1}, except for 0, where my train behaves as the comments to the question want, but the naive implementation gives an error. – marinus Feb 23 at 23:26
    
@nbz: In ngn/apl, (+*÷) and {⍵*⍵*¯1} behave exactly equal, at least over the domain ⌈/⍬ ... 0 ... ⌊/⍬, as far as I can tell. (Perhaps there's some value somewhere for which they give slightly different answers because of floating point weirdness, but that's not really something I can see.) In Dyalog, it's going to depend on what ⎕div is. 0*0*¯1 is an error there in any case, (+*÷)0 only if ⎕div=0, otherwise it will be 1. (NARS gives 0 for 0√0, is that correct? If so, +*÷ is correct in ngn, but for Dyalog I think you'd have to resort to something like {⍵=0:0⋄⍵*÷⍵}.) 1/2 – marinus Feb 23 at 23:54
    
@NBZ: don't worry, I'm not offended, just trying to figure it out. – marinus Feb 23 at 23:57
1  
@nbz: ...shit. I forgot about complex numbers. – marinus Feb 24 at 0:02

Python 2 - 56 bytes

The first actual answer, if I'm correct. Uses Newton's method.

n=x=input();exec"x-=(x**n-n)/(1.*n*x**-~n);"*999;print x
share|improve this answer
    
Functions are okay. – CalculatorFeline Feb 24 at 1:18

CJam, 6 bytes

rd_W##

Try it online!

How it works

rd     e# Read a double D from STDIN and push it on the stack.
  _    e# Push a copy of D.
   W   e# Push -1.
    #  e# Compute D ** -1.
     # e# Compute D ** (D ** -1).
share|improve this answer

MATL, 5 bytes

t-1^^

Try it online!

t       % implicit input x, duplicate
 -1     % push -1
   ^    % power (raise x to -1): gives 1/x
    ^   % power (raise x to 1/x). Implicit display
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Seriously, 5 bytes

,;ì@^

Try it online!

Explanation:

,;ì@^
,;     input, dupe
  ì@   1/x, swap
    ^  pow
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Pylons, 5 bytes.

ideAe

How it works.

i # Get command line input.
d # Duplicate the top of the stack.
e # Raise the top of the stack to the power of the  second to the top element of the stack.
A # Push -1 to the stack (pre initialized variable).
e # Raise the top of the stack to the power of the second to the top element of the stack.
  # Implicitly print the stack.
share|improve this answer

Japt, 3 bytes

UqU

Test it online!

Very simple: U is the input integer, and q is the root function on numbers.

share|improve this answer

Ruby, 15 Bytes

a=->n{n**n**-1}

Ungolfed:

-> is the stabby lambda operator where a=->n is equivalent to a = lambda {|n|}

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O, 6 bytes

j.1\/^

No online link because the online IDE doesn't work (specifically, exponentiation is broken)

Explanation:

j.1\/^
j.      push two copies of input
  1\/   push 1/input (always float division)
     ^  push pow(input, 1/input)
share|improve this answer
    
oh hey you did it yay – phase Mar 19 at 4:20

𝔼𝕊𝕄𝕚𝕟, 5 chars / 7 bytes

Мű⁽ïï

Try it here (Firefox only).

Trivial.

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Pyke (commit 29), 6 bytes

D1_R^^

Explanation:

D      - duplicate top
 1_    - load -1
   R   - rotate
    ^  - ^**^
     ^ - ^**^
share|improve this answer
    
Can haz link pls? – cat Feb 24 at 17:33
    
Oh, I thought you meant there's no implementation available. Yes, the interpreter doesn't have to be hosted, just a link to the repo / source (or docs) will suffice – cat Feb 24 at 17:36

C# - 18 43 41 bytes

float a(float x){return Math.Pow(x,1/x);}

-2 byes thanks to @VoteToClose

Try it out

Note:

First actual attempt at golfing - I know I could do this better.

share|improve this answer
    
Welcome to the crowd! It is exactly because of newcomers that I make trivial challenges like this. – Adám Feb 24 at 19:29
    
Fixed. Thanks for informing me about this – EnragedTanker Feb 25 at 15:40
    
@crayzeedude No problem at all. Nice job and again, welcome to PPCG! – Alex A. Feb 25 at 18:00
    
Does C# have float? – VTCAKAVSMoACE Feb 27 at 0:31
    
Indeed it does. – EnragedTanker Feb 27 at 18:29

Gogh, 2 bytes

This is the debut answer for Gogh!

Edited (2 bytes):

÷r

Original (5 bytes):

÷1¦/p

See the edit history for an explanation of this method.


Explanation

÷       “ Duplicate the TOS               ”
 r      “ Push the TOSth root of the STOS ”

x**(1/x)

Input is implicit and, with the o flag, output is implicit.


Usage

$ ./gogh <flags> <code-or-path> <input>

The flags used for this program should be io. The o flag signifies implicit output, and the i flag signifies input as an integer.

To add a trailing newline, add the n flag.

Working:User $ ./gogh nio '÷r' 9
1.276518
Working:User $ ./gogh nio '÷r' 100
1.047129

Or, without the n flag:

Working:User $ ./gogh nio '÷r' 9
1.276518Working:User $ ./gogh nio '÷r' 100
1.047129Working:User $
share|improve this answer
1  
Note: This answer is non-competing, as it was developed after the challenge was posted. – Zach Gates Mar 15 at 19:43
1  
@Nᴮᶻ: I wasn't insinuating I would win; just a fact. – Zach Gates Mar 15 at 20:18
1  
What is STOS and TOS? Also, don't flags count in th byte count? – Downgoat Mar 15 at 22:09
1  
using ndo seems to make this also work with floats – Downgoat Mar 15 at 23:41
1  
Also, generally interpreter flags count as extra bytes. – Eᴀsᴛᴇʀʟʏ Iʀᴋ Apr 5 at 21:39

C++, 48 bytes

#include<math.h>
[](auto x){return pow(x,1./x);}

The second line defines an anonymous lambda function. It can be used by assigning it to a function pointer and calling it, or just calling it directly.

Try it online

share|improve this answer
    
Does ^ not work in C++ as it does in C? – minerguy31 Feb 23 at 23:18
2  
@minerguy31: ^ is bitwise xor in C (and C++). – marinus Feb 23 at 23:19

PHP 5.6, 32 30 29 bytes

function($x){echo$x**(1/$x);}

or

function($x){echo$x**$x**-1;}

30->29, thank you Dennis!

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Milky Way 1.6.5, 5 bytes

'1'/h

Explanation

'      ` Push input
 1     ` Push the integer literal
  '    ` Push input
   /   ` Divide the STOS by the TOS
    h  ` Push the STOS to the power of the TOS

x**(1/x)


Usage

$ ./mw <path-to-code> -i <input-integer>
share|improve this answer

Awk, 8 bytes

$1^$1^-1

A shell command to check it

awk '{print $1^$1^-1}'

Longer version (+1) with

$1^(1/$1)
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