Random Golf of the Day #1: Shuffle an Array

Question

About the Series

I will be running a little series of code-golf challenges revolving around the theme of randomness. This will basically be a 9-Hole Golf Course, but spread out over several questions. You may participate in any challenge individually as if it was a normal question.

However, I will maintain a leaderboard across all challenges. The series will run over 9 challenges (for now), one posted every few days. Every user who participates in all 9 challenges is eligible for winning the entire series. Their overall score is the sum of their shortest submissions on each challenge (so if you answer a challenge twice, only the better answer one is counted towards the score). If anyone holds the top spot on this overall leaderboard for 28 days I will award them a bounty of 500 rep.

Although I have a bunch of ideas lined up for the series, the future challenges are not set in stone yet. If you have any suggestions, please let me know on the relevant sandbox post.

Hole 1: Shuffle an Array

The first task is pretty simple: given a non-empty array of integers, shuffle it randomly. There are a few rules though:

• Every possible permutation must be returned with the same probability (so the shuffle should have a uniform distribution). You can check if your algorithm is uniform/unbiased by implementing it in JavaScript on Will it Shuffle, which will produce a matrix of the biases - the result should look as uniform as their built-ins Fisher-Yates or sort (random order).
• You must not use any built-in or 3rd-party method to shuffle the array or generate a random permutation (or enumerate all permutations). In particular, the only built-in random function you may use is getting a single random number at a time. You may assume that any built-in random number method runs in O(1) and is perfectly uniform over the requested interval (in a mathematical sense - you may ignore details of floating-point representation here). If your language lets you obtain a list of m random numbers at once, you may use this facility, provided the m numbers are independent of each other, and you count it as O(m).
• Your implementation must not exceed a time complexity of O(N), where N is the size of the array to be shuffled. For instance, you cannot "sort by random numbers".
• You may either shuffle the array in place, or create a new array (in which case the old array may be modified however you like).

You may write a full program or a function and take input via STDIN, command-line argument, function argument or prompt and produce output via return value or by printing to STDOUT (or closest alternative). If you write a function that shuffles the array in place, you don't need to return it of course (provided your language lets you access the modified array after the function returns).

Input and output may be in any convenient list or string format, but must support arbitrary integers in the range -2³¹ ≤ x < 2³¹. In principle, your code should work for arrays up to length 2³¹, although this doesn't necessarily have to fit in your memory or complete within a reasonable amount of time. (I just don't want to see arbitrary size limits to hardcode loops or something.)

This is code golf, so the shortest submission (in bytes) wins.

Leaderboard

The following snippet will generate a leaderboard across all challenges of the series.

To make sure that your answers show up, please start every answer with a headline, using the following Markdown template:

# Language Name, N bytes

where N is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance:

# Ruby, <s>104</s> <s>101</s> 96 bytes

(The language is not currently shown, but the snippet does require and parse it, and I may add a by-language leaderboard in the future.)

/* Configuration */

var QUESTION_IDs = [45302, 45447, 46991, 49394, 51222, 66319, 89621, 120472]; // Obtain this from the url
// It will be like http://XYZ.stackexchange.com/questions/QUESTION_ID/... on any question page
var ANSWER_FILTER = "!.FjwQBrX2KXuFkv6p2lChi_RjzM19";

/* App */

var answers = [], page = 1, currentQ = -1;

function answersUrl(index) {
  return "https://api.stackexchange.com/2.2/questions/" +  QUESTION_IDs.join(";") + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER;
}


function getAnswers() {
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      if (data.has_more) getAnswers();
      else process();
    }
  });
}

getAnswers();

var SIZE_REG = /\d+(?=[^\d&]*(?:<(?:s>((?!>).)*<\/s>|((?!>).)+>)[^\d&]*)*$)/;
var NUMBER_REG = /\d+/;
var LANGUAGE_REG = /^#*\s*([^\n,]+)(?=,)/;//

function shouldHaveHeading(a) {
  var pass = false;
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    pass |= ["-", "="]
              .indexOf(lines[1][0]) > -1;
    pass &= LANGUAGE_REG.test(a.body_markdown);
  } catch (ex) {}
  return pass;
}

function shouldHaveScore(a) {
  var pass = false;
  try {
    pass |= SIZE_REG.test(a.body_markdown.split("\n")[0]);
  } catch (ex) {}
  if (!pass) console.log(a);
  return pass;
}

function getAuthorName(a) {
  return a.owner.display_name;
}

function getAuthorId(a) {
  return a.owner.user_id;
}

function process() {
  answers = answers.filter(shouldHaveScore)
                   .filter(shouldHaveHeading);
  answers.sort(function (a, b) {
    var aB = +(a.body_markdown.split("\n")[0].match(SIZE_REG) || [Infinity])[0],
        bB = +(b.body_markdown.split("\n")[0].match(SIZE_REG) || [Infinity])[0];
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    var question = QUESTION_IDs.indexOf(a.question_id);
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    var language = headline.match(LANGUAGE_REG)[1];
    var user = getAuthorName(a);
    var userId = getAuthorId(a);
    if (!users[userId]) users[userId] = {name: user, nAnswer: 0, answers: []};
    if (!users[userId].answers[question]) {
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      users[userId].nAnswer++;
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  for (var userId in users)
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      user.score = 0;
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      sortedUsers.push(user);
    }  
  
  sortedUsers.sort(function (a, b) {
    if (a.nAnswer > b.nAnswer) return -1;
    if (b.nAnswer > a.nAnswer) return 1;
    return a.score - b.score;
  });
  
  var place = 1;
  for (var i = 0; i < sortedUsers.length; ++i) {
    var user = sortedUsers[i];
    var row = '<tr><td>'+ place++ +'.</td><td>'+user.name+'</td>';
    for (var j = 0; j < QUESTION_IDs.length; ++j) {
      var answer = user.answers[j];
      if (answer)
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      else
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body { text-align: left !important}

#leaderboard {
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#answer-list {
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  float: left;
}

#language-list {
  padding: 10px;
  width: 290px;
  float: left;
}

table thead {
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table td {
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td.total {
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}

td.missing {
  background: #bbbbbb;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b">
<div id="leaderboard">
  <h2>Leaderboard</h2>
  <p>
    Missing scores are shown as grey cells. A grey total indicates that the user has not participated in all challenges and is not eligible for the overall victory yet.
  </p>
  <table class="_user-list">
    <thead>
      <tr><td></td><td>User</td>
        <td><a href="https://codegolf.stackexchange.com/q/45302/8478">#1</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/45447/8478">#2</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/46991/8478">#3</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/49394/8478">#4</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/51222/8478">#5</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/66319/8478">#6</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/89621/8478">#7</a></td>
        <td><a href="https://codegolf.stackexchange.com/q/120472/8478">#8</a></td>
        <td></td><td>Total</td>
      </tr>
    </thead>
    <tbody id="users">

    </tbody>
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<table style="display: none">
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    <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr>
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Answer 1

Dyalog APL, 25 24 bytes

First for the 25-character solution: i{⊃a[⍺⍵]←a[⍵⍺]}¨?i←⌽⍳⍴a←⎕

                      a←⎕ ⍝ evaluated input, assign to "a"
                     ⍴a   ⍝ length
                    ⍳⍴a   ⍝ 1 2 .. length
                   ⌽⍳⍴a   ⍝ length .. 2 1
                 i←       ⍝ assign to "i"
                ?i        ⍝ random choices: (1..length)(1..length-1)..(1 2)(1)
i{            }¨?i        ⍝ for each index ⍺ and corresponding random choice ⍵
   a[⍺⍵]←a[⍵⍺]            ⍝ swap a[⍺] and a[⍵]
        ←                 ⍝ in Dyalog, assignment returns its right-hand side
  ⊃                       ⍝ first element, i.e. a[⍵]
                          ⍝ the result from {} is an array of all those a[⍵]

After some equivalence transformations on the above:

i {}¨ ?i  ←→  i {}¨∘? i   ⍝ because A f∘g B ←→ A f g B
          ←→  {}¨∘?⍨ i    ⍝ because f⍨ B ←→ B f B

we can get rid of the assignment i← and save a character:

{⊃a[⍺⍵]←a[⍵⍺]}¨∘?⍨⌽⍳⍴a←⎕

Answer 2

80386 machine code, 44 24 bytes

Hexdump of the code:

60 8b fa 0f c7 f0 33 d2 f7 f1 49 8b 04 8f 87 04
97 89 04 8f 75 ed 61 c3

Thanks to FUZxxl, who suggested using the rdrand instruction.

Here is the source code (can be compiled by Visual Studio):

__declspec(naked) void __fastcall shuffle(unsigned size, int array[])
{
    // fastcall convention:
    // ecx = size
    // edx = array
    _asm
    {
        pushad;             // save registers
        mov edi, edx;       // edi now points to the array

    myloop:
        rdrand eax;         // get a random number
        xor edx, edx;
        div ecx;            // edx = random index in the array

        dec ecx;            // count down
        mov eax, [edi + 4 * ecx];   // swap elements
        xchg eax, [edi + 4 * edx];  // swap elements
        mov [edi + 4 * ecx], eax;   // swap elements
        jnz myloop;

        popad;              // restore registers
        ret;
    }
}

Yet another Fisher-Yates implementation. Most of the golfing was achieved by passing parameters in registers.

Answer 3

Java, 88 101

A basic Fisher-Yates shuffle does the trick. I get the feeling it'll be used pretty commonly here, since it's quick and easy to implement. There's some loop/assignment cramming here, but there's honestly not too much to golf; it's just short by nature.

void t(int[]s){for(int i=s.length,t,x;i>0;t=s[x*=Math.random()],s[x]=s[i],s[i]=t)x=i--;}

With some line breaks:

void t(int[]s){
    for(int i=s.length,t,x;
        i>0;
        t=s[x*=Math.random()],
        s[x]=s[i],
        s[i]=t
    )
        x=i--;
}

This shuffles in place, modifying the original array s[]. Test program:

public class Shuffle {
    public static void main(String[] args) {
        int[] a = {1,2,3,4,5,6,7,8,9};
        new Shuffle().t(a);
        for(int b:a)
            System.out.print(b+" ");
    }
    void t(int[]s){for(int i=s.length,t,x;i>0;t=s[x*=Math.random()],s[x]=s[i],s[i]=t)x=i--;}
}

Answer 4

Python 2, 86 bytes

from random import*
def S(L):i=len(L);exec"i-=1;j=randint(0,i);L[i],L[j]=L[j],L[i];"*i

This is a function which shuffles the array in place without returning it, using a straightforward implementation of the Fisher-Yates shuffle. Getting random numbers from Python is expensive...

Thanks to @xnor and @colevk for tips.

Answer 5

J, 45 44 characters

This was a tricky one.

<@({.,?@#@}.({,<^:3@[{])}.)&>/@(<"0@i.@#,<)

Here is an explanation:

1. # y: The tally of y, that is, the number of elements in y.
2. ?@# y: A random number uniformly distributed over the range from 1 to (#y)-1.
3. x { y: The item from y at index x.
4. (<<<x) { y: All items except the item at index x in y.
5. x , y: y appended to x.
6. x ({ , <^:3@[ { ]) y: The item at index x in y, then all the other items.
7. (?@# ({ , <^:3@[ { ]) ]) y A random it from y, then all the other items.
8. x {. y: The first x items taken from y.
9. x }. y: The first x items dropped from y.
10. x ({. , }.) y: The first x items taken from y, then the first x items dropped from y
11. x ({. , (?@# ({ , <^:3@[ { ]) ])@}.) y: The first x items taken from y, then the first x items from y processed as in number 7.
12. x ({. , ?@#@}. ({ , <^:3@[ { ]) }.) y: The same thing with the drop pulled in to save one character.
13. u/ y: u inserted between the items of y.
14. < y: y boxed.
15. <"0 y: Each item of y boxed.
16. i. y: integers from 0 to y - 1.
17. i.@# y: integers from 0 to (#y) - 1.
18. (<"0@i.@# , <) y: Integers from 0 to (#y) - 1 each boxed and then y in a single box. This is needed because arrays in J are uniform. A box hides the shape of its content.
19. x u&v y: like (v x) u (v y).
20. > y: y opened, that is, without its box.
21. x ({. , ?@#@}. ({ , <^:3@[ { ]) }.)&> y the phrase from number 12 applied to its unboxed arguments.
22. ({. , ?@#@}. ({ , <^:3@[ { ]) }.)&>/ y the phrase from number 21 inserted between items of y.
23. ({. , ?@#@}. ({ , <^:3@[ { ]) }.)&>/@(<"0@i.@# , <) y the phrase from number 22 applied to the the result of the phrase from number 18, or, a uniform permutation of the items of y.

Answer 6

Pyth, 25 bytes

Test it here.

Yet another Fisher-Yates implementation. Is essentially the same as @Sp3000 python solution, just in pyth.

FNrlQ1KONJ@QN XXQN@QKKJ)Q

Thanks to @Jakube for the swapping trick

<implicit>    Q=input()
FNrlQ1        For N in len(Q) to 1, only goes len Q-1 because how range implemented in pyth
 KON          K = random int 0-N
 J@QN         J=Q[N]
 <space>      Suppress print
 XXQN@QKKJ    Swap K and J
)             End for
Q             Print Q

Answer 7

Perl, 68 56 44

Like many other solutions, this uses the Fisher-Yates algorithm.

Using nutki's comment, 12 characters are saved by using $_ instead of $i and performing the operations in the array indices.

44:

sub f{@_[$_,$j]=@_[$j=rand$_,--$_]for 1..@_}

56:

sub f{$i=@_;$j=int(rand$i),@_[$i,$j]=@_[$j,$i]while$i--}

This is my first codegolf.

Answer 8

C, 63 61 60 bytes

i,t;s(a,m)int*a;{for(;m;a[m]=t)t=a[i=rand()%m--],a[i]=a[m];}

Just a straight implementation of Fischer-Yates that sorts the given array in place. Compiles and links perfectly fine with the visual studio compiler (vs2013, haven't tested the other versions) and the Intel Compiler. Nice looking function signature is s(int array[], int length). I'm legitimately impressed I beat Python and Ruby.

This does assume srand() is called and rand() is implemented properly, but I believe this rule allows for that:

You may assume that any built-in random number method runs in O(1) and is perfectly uniform over the requested interval

Nicely formatted version:

index, temp;
shuffle(array, length) int* array;  {
    for(;length; array[index] = temp)
        index = rand() % length--,
        temp = array[length],
        array[length] = array[index];
}

Answer 9

Octave, 88 77 bytes

function s=r(s)for(i=length(s):-1:1)t=s(x=randi(i));s(x)=s(i);s(i)=t;end;end

Yet another Fisher-Yates implementation... Should be fairly straightforward if I add the usual line returns and spacing:

function s=r(s)
  for(i=length(s):-1:1) # Counting down from i to 1
    t=s(x=randi(i));    # randi is builtin number generator for an int from 0 to i
    s(x)=s(i);
    s(i)=t;
  end
end

The "end" keywords really kill the golf score here, unfortunately. Hey, I can use "end" instead of "endfor" and "endfunction"!

Answer 10

Java 8, 77

(x)->{for(int i=x.length,j,t;;t=x[j*=Math.random()],x[j]=x[i],x[i]=t)j=i--;};

It's a lambda taking int[] and returning void. My first attempt seemed not very interesting, so I decided to have it exit by throwing an exception.

Test program:

interface shuff {
    void shuff(int[] x);
}
class Ideone
{
    public static void main (String[] args) throws java.lang.Exception
    {
        shuff s = (x)->{for(int i=x.length,j,t;;t=x[j*=Math.random()],x[j]=x[i],x[i]=t)j=i--;};
        int[] x = {3, 9, 2, 93, 32, 39, 4, 5, 5, 5, 6, 0};
        try {
            s.shuff(x);
        } catch(ArrayIndexOutOfBoundsException _) {}
        for(int a:x) System.out.println(a);
    }
}

Answer 11

Golflua, 37

How to run Golflua?

~@i=1,#X`r=M.r(i)X[i],X[r]=X[r],X[i]$

The input is provided as a table in the variable X. The table is shuffled in place.

Example usage:

> X={0,-45,8,11,2}
> ~@i=1,#X`r=M.r(i)X[i],X[r]=X[r],X[i]$
> w(T.u(X))
-45 0 8 11 2

Answer 12

R, 79 bytes

f=function(x){n=length(x);for(i in 1:n){j=sample(i:n,1);x[c(i,j)]=x[c(j,i)]};x}

This is a straightforward implementation of the Fisher-Yates shuffle. The R function sample draws a simple random sample of a given size from a given vector with equal probability. Here we're drawing a random sample of size 1 at each iteration from the integers i, ..., n. As stated in the question, this can be assumed to be O(1), so in all this implementation should be O(N).

Answer 13

Matlab, 67

Also implementing Fisher-Yates.

a=input('');n=numel(a);for i=1:n;k=randi(i);a([i,k])=a([k,i]);end;a

I thought it was too bad I could not use Matlab's randperm function. But after some fiddling around, I thought I may look at the source of randperm to see how it is done, and I was astonished to see that there was just one line: [~,p] = sort(rand(1,n)) =)

Answer 14

Perl, 44

sub f{($_[$x],$_)=($_,$_[$x=rand++$i])for@_}

Another perl in 44 characters. Example use:

@x=(1..9);f(@x);print@x

Answer 15

Mathematica, 82 90 83 93 bytes

Note: This variation the Fisher-Yates shuffle is actually Martin Büttner's solution, with some code paring by alephalpha. s is the input array. Nothing fancy-smancy, but sometimes the simple things are the most elusive.

f@s_:=(a=s;m=Length@a;Do[t=a[[r=RandomInteger@{1,m-1}]];a[[r]]=a[[m]]; a[[m]]=t,{n,1,m-1}];a)

Answer 16

Ruby, 57 bytes

->a{a.size.times{|i|j=rand(i+1);a[i],a[j]=a[j],a[i]};p a}

Input (as lambda function):

f.([1,2,3,4,5])

Output:

[2, 1, 4, 3, 5]

Answer 17

TI-BASIC, 46 bytes

For(X,dim(L1),2,-1:randInt(1,X→Y:L1(X→Z:L1(Y→L1(X:Z→L1(Y:L1

1   111   2  1111112       1111112 111112 1112 111112 1112

Source for byte count

Answer 18

K, 31 chars

f:{{l[i:x,1?x]:l@|i}'|!#l::x;l}

Not quite as short as the one I put up before (which got disqualified)...oh well.

It's a basic Fisher-Yates shuffle. This was built with lots of help from the Kona mailing list.

Answer 19

JavaScript (ES6), 66

This function shuffles the array in place. It also returns a byproduct array that is NOT the shuffled output and must not be considered.

F=a=>a.map((v,i)=>a[a[i]=a[j=0|i+Math.random()*(a.length-i)],j]=v)

Answer 20

MATL, 16 bytes

XH`HnYr&)XHxvHHn

Try it online!

Fisher-Yates in MATL. Almost a third of this program is devoted to the letter H, which corresponds to the clipboard function in MATL.

Basically, H stores the unused items from the input, while the stack keeps track of the shuffled list.

Answer 21

Japt, 12

rÈiMqZÄ Y}[]

Try it!

-10 (about half ;) thanks to @Shaggy!

I have been wanting to try out a golfing language, and the Japt interpreter had good documentation and a way to try things out in the browser.

Below is the strategy I took:

• Reduce input seeding with an empty array
• At each step, find a random slot to insert the current element

Answer 22

Javascript ES6, 69

a=>{m=a.length;while(m)[a[m],a[i]]=[a[i=~~(Math.random()*m--)],a[m]]}

It's Fisher–Yates.

PS: Can be tested in Firefox

Answer 23

Pyth, 27 bytes

Test it here

FkQJOhlYaY?@YtJJkIJ XYtJk;Y

This is an implementation of the incremental Fisher-Yates shuffle, mentioned second here.

Answer 24

Haskell, 170

import System.Random
import Data.Array.IO
s a=do(_,n)<-getBounds a;sequence$map(\i->do j<-randomRIO(i,n);p<-a%i;q<-a%j;writeArray a j p;return q)[1..n]where(%)=readArray

Another Fisher-Yates solution inspired by the algorithm at https://wiki.haskell.org/Random_shuffle.

s is a function which has signature: IOArray Int a -> IO [a]

Answer 25

CJam - 30

q~_,,W%{_I=I)mr:J2$=@I@tJ@t}fI

Try it at http://cjam.aditsu.net/

Example input: [10 20 30 40 50]
Example output: 3020401050 (add a p at the end of the code for pretty printing)

If the code is allowed to take the input from the stack (like a function), then the first 2 characters can be removed, reducing the size to 28.

Explanation:

The code is longer than I hoped, due to the lack of a "swap" operator for arrays
(to be implemented later :p)

q~            read and evaluate the input (let's call the array "A")
_,,           make an array [0 1 2 ... N-1] where N is the size of A
W%            reverse the array, obtaining [N-1 ... 2 1 0]
{…}fI         for I in this array
    _I=       push A[I]
    I)mr:J    push a random number from 0 to I (inclusive) and store it in J
              stack: A, A[I], J
    2$=       get A[J]
    @I@t      set A[I] = A[J]
              stack: former A[I], A
    J@t       set A[J] = former A[I]

Answer 26

JavaScript (ES 6), 61

S=a=>(a.map((c,i)=>(a[i]=a[j=Math.random()*++i|0],a[j]=c)),a)

You can test it here by just adding a line that says shuffle = S (Firefox only).

Answer 27

STATA, 161

di _r(s)
set ob wordcount($s)
token $s
g a=0
foreach x in $s{
gl j=floor(runiform()*_n)+1
replace a=`$j' if word($s,_n)=`x'
replace a=`x' if word($s,_n)=`$j'
}
l

Expects input as space separated numbers. I can remove the headers and observation numbers from the output if you would like, but otherwise this is shorter.

Answer 28

Java, 93 bytes

a->{for(int b=0,c,d=0,e=a.length;b<e;c=a[b],a[b]=a[d],a[d]=c,b++,d=b)d+=Math.random()*(e-b);}

Example usage: http://ideone.com/RqSMnZ

Answer 29

SQF, 91 bytes

params["i"];{n=floor random count i;i set[_forEachIndex,i select n];i set[n,_x]}forEach i;i

Answer 30

Perl, 41 bytes

sub f{push@b,splice@_,rand@_,1while@_;@b}

Try it online!