Efficiently pick n random elements from PHP array (without shuffle)

Question

I have the following code to pick $n elements from an array $array in PHP:

shuffle($array);
$result = array_splice($array, 0, $n);

Given a large array but only a few elements (for example 5 out of 10000), this is relatively slow, so I would like to optimize it such that not all elements have to be shuffled. The values must be unique.

I'm looking fo the most performant alternative. We can assume that $array has no duplicates and is 0-indexed.

Answer 1

$randomArray = [];
while (count($randomArray) < 5) {
  $randomKey = mt_rand(0, count($array)-1);
  $randomArray[$randomKey] = $array[$randomKey];
}

This will provide exactly 5 elements with no duplicates and very quickly. The keys will be preserved.

Note: You'd have to make sure $array had 5 or more elements or add some sort of check to prevent an endless loop.

Answer 2

This function performs a shuffle on only $n elements where $n is the number of random elements you want to pick. It will also work on associative arrays and sparse arrays. $array is the array to work on and $n is the number of random elements to retrieve.

If we define the $max_index as count($array) - 1 - $iteration.

It works by generating a random number between 0 and $max_index. Picking the key at that index, and replacing its index with the value at $max_index so that it can never be picked again, as $max_index will be one less at the next iteration and unreachable.

In summary this is the Richard Durstenfeld's Fisher-Yates shuffle but operating only on $n elements instead of the entire array.

function rand_pluck($array, $n) {
    $array_keys = array_keys($array);
    $array_length = count($array_keys);
    $max_index = $array_length -1;
    $iterations = min($n, $array_length);
    $random_array = array();
    while($iterations--) {
        $index = mt_rand(0, $max_index);
        $value = $array_keys[$index];
        $array_keys[$index] = $array_keys[$max_index];
        array_push($random_array, $array[$value]);
        $max_index--;
    }
    return $random_array;
}

Answer 3

The trick is to use a variation of shuffle or in other words a partial shuffle.

performance is not the only criterion, statistical efficiency, i.e unbiased sampling is as important (as the original shuffle solution is)

function random_pick( $a, $n ) 
{
  $N = count($a);
  $n = min($n, $N);
  $picked = array_fill(0, $n, 0); $backup = array_fill(0, $n, 0);
  // partially shuffle the array, and generate unbiased selection simultaneously
  // this is a variation on fisher-yates-knuth shuffle
  for ($i=0; $i<$n; $i++) // O(n) times
  { 
    $selected = mt_rand( 0, --$N ); // unbiased sampling N * N-1 * N-2 * .. * N-n+1
    $value = $a[ $selected ];
    $a[ $selected ] = $a[ $N ];
    $a[ $N ] = $value;
    $backup[ $i ] = $selected;
    $picked[ $i ] = $value;
  }
  // restore partially shuffled input array from backup
  // optional step, if needed it can be ignored, e.g $a is passed by value, hence copied
  for ($i=$n-1; $i>=0; $i--) // O(n) times
  { 
    $selected = $backup[ $i ];
    $value = $a[ $N ];
    $a[ $N ] = $a[ $selected ];
    $a[ $selected ] = $value;
    $N++;
  }
  return $picked;
}

NOTE the algorithm is strictly O(n) in both time and space, produces unbiased selections (it is a partial unbiased shuffling) and produces output which is proper array with consecutive keys (not needing extra array_values etc..)

Use example:

$randomly_picked = random_pick($my_array, 5);
// or if an associative array is used
$randomly_picked_keys = random_pick(array_keys($my_array), 5);
$randomly_picked = array_intersect_key($my_array, array_flip($randomly_picked_keys));

For further variations and extensions of shuffling for PHP:

1. PHP - shuffle only part of an array
2. PHP shuffle with seed
3. How can I take n elements at random from a Perl array?

Answer 4

You could generate n-times a random number with mt_rand() and then fill these values in a new array. To go against the case where the same index gets returned twice we use the actual returned index to fill the new array and check always if the index exists in the new array, if so we use while to loop through it as long as we get a duplicate index. At the end we use array_values() to get a 0-indexed array.

$count = count($array) - 1;
$new_array = array();
for($i = 0; $i < $n; $i++) {
    $index = mt_rand(0, $count);
    while(isset($new_array[$index])) {
        $index = mt_rand(0, $count);
    }

    $new_array[$index] = $array[$index];
}
$new_array = array_values($new_array);

Answer 5

This will only show benifits for small n compared to an array shuffle, but you could

1. Choose a random index r n times, each time decreasing the limit by 1
2. Adjust for previously used indices
3. Take value
4. Store used index

Pseudocode

arr = []
used = []
for i = 0..n-1:
    r = rand 0..len-i
    d = 0
    for j = 0..used.length-1:
        if r >= used[j]:
            d += 1
    arr.append($array[r + d])
    used.append(r)
return arr

Answer 6

I wonder why everyone here make it so complicated?

Here's the fastest and simplest way:

$randomArray = array_rand(array_flip($array), $n);