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Generating random results by weight in PHP?

Posted by: admin November 19, 2017 Leave a comment

Questions:

I know how to generate a random number in PHP but lets say I want a random number between 1-10 but I want more 3,4,5’s then 8,9,10’s. How is this possible? I would post what I have tried but honestly, I don’t even know where to start.

Answers:

Based on @Allain’s answer/link, I worked up this quick function in PHP. You will have to modify it if you want to use non-integer weighting.

  /**
   * getRandomWeightedElement()
   * Utility function for getting random values with weighting.
   * Pass in an associative array, such as array('A'=>5, 'B'=>45, 'C'=>50)
   * An array like this means that "A" has a 5% chance of being selected, "B" 45%, and "C" 50%.
   * The return value is the array key, A, B, or C in this case.  Note that the values assigned
   * do not have to be percentages.  The values are simply relative to each other.  If one value
   * weight was 2, and the other weight of 1, the value with the weight of 2 has about a 66%
   * chance of being selected.  Also note that weights should be integers.
   * 
   * @param array $weightedValues
   */
  function getRandomWeightedElement(array $weightedValues) {
    $rand = mt_rand(1, (int) array_sum($weightedValues));

    foreach ($weightedValues as $key => $value) {
      $rand -= $value;
      if ($rand <= 0) {
        return $key;
      }
    }
  }

Questions:
Answers:

For an efficient random number skewed consistently towards one end of the scale:

  • Choose a continuous random number between 0..1
  • Raise to a power γ, to bias it. 1 is unweighted, lower gives more of the higher numbers and vice versa
  • Scale to desired range and round to integer

eg. in PHP (untested):

function weightedrand($min, $max, $gamma) {
    $offset= $max-$min+1;
    return floor($min+pow(lcg_value(), $gamma)*$offset);
}
echo(weightedrand(1, 10, 1.5));

Questions:
Answers:

There’s a pretty good tutorial for you.

Basically:

  1. Sum the weights of all the numbers.
  2. Pick a random number less than that
  3. subtract the weights in order until the result is negative and return that number if it is.
Questions:
Answers:

The naive hack for this would be to build a list or array like

1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10

And then select randomly from that.

Questions:
Answers:

This tutorial walks you through it, in PHP, with multiple cut and paste solutions. Note that this routine is slightly modified from what you’ll find on that page, as a result of the comment below.

A function taken from the post:

/**
 * weighted_random_simple()
 * Pick a random item based on weights.
 *
 * @param array $values Array of elements to choose from 
 * @param array $weights An array of weights. Weight must be a positive number.
 * @return mixed Selected element.
 */

function weighted_random_simple($values, $weights){ 
    $count = count($values); 
    $i = 0; 
    $n = 0; 
    $num = mt_rand(1, array_sum($weights)); 
    while($i < $count){
        $n += $weights[$i]; 
        if($n >= $num){
            break; 
        }
        $i++; 
    } 
    return $values[$i]; 
}

Questions:
Answers:

Plain and fair.
Just copy/paste and test it.

/**
 * Return weighted probability
 * @param (array) prob=>item 
 * @return key
 */
function weightedRand($stream) {
    $pos = mt_rand(1,array_sum(array_keys($stream)));           
    $em = 0;
    foreach ($stream as $k => $v) {
        $em += $k;
        if ($em >= $pos)
            return $v;
    }

}

$item['30'] = 'I have more chances than everybody :]';
$item['10'] = 'I have good chances';
$item['1'] = 'I\'m difficult to appear...';

for ($i = 1; $i <= 10; $i++) {
    echo weightedRand($item).'<br />';
}

Edit: Added missing bracket at the end.

Questions:
Answers:

You can use weightedChoice from Non-standard PHP library. It accepts a list of pairs (item, weight) to have the possibility to work with items that can’t be array keys. You can use pairs function to convert array(item => weight) to the needed format.

use function \nspl\a\pairs;
use function \nspl\rnd\weightedChoice;

$weights = pairs(array(
    1 => 10,
    2 => 15,
    3 => 15,
    4 => 15,
    5 => 15,
    6 => 10,
    7 => 5,
    8 => 5,
    9 => 5,
    10 => 5
));

$number = weightedChoice($weights);

In this example, 2-5 will appear 3 times more often than 7-10.

Questions:
Answers:

Since I used IainMH’s solution, I may as well share my PHP code:

<pre><?php

// Set total number of iterations
$total = 1716;

// Set array of random number
$arr = array(1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5);
$arr2 = array(0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 5);

// Print out random numbers
for ($i=0; $i<$total; $i++){

    // Pick random array index
    $rand = array_rand($arr);
    $rand2 = array_rand($arr2);

    // Print array values
    print $arr[$rand] . "\t" . $arr2[$rand2] . "\r\n";

}

?></pre>

Questions:
Answers:
/**
 * @param array $weightedValues
 * @return string
 */
function getRandomWeightedElement(array $weightedValues)
{
    $array = array();

    foreach ($weightedValues as $key => $weight) {
        $array = array_merge(array_fill(0, $weight, $key), $array);
    }

    return $array[array_rand($array)];
}

getRandomWeightedElement(array('A'=>10, 'B'=>90));

This is very easy method. How get random weighted element. I fill array variable $key. I get $key to array $weight x. After that, use array_rand to array. And I have random value ;).

Questions:
Answers:

I just released a class to perform weighted sorting easily.

It’s based on the same algorithm mentioned in Brad’s and Allain’s answers, and is optimized for speed, unit-tested for uniform distribution, and supports elements of any PHP type.

Using it is simple. Instantiate it:

$picker = new Brick\Random\RandomPicker();

Then add elements as an array of weighted values (only if your elements are strings or integers):

$picker->addElements([
    'foo' => 25,
    'bar' => 50,
    'baz' => 100
]);

Or use individual calls to addElement(). This method supports any kind of PHP values as elements (strings, numbers, objects, …), as opposed to the array approach:

$picker->addElement($object1, $weight1);
$picker->addElement($object2, $weight2);

Then get a random element:

$element = $picker->getRandomElement();

The probability of getting one of the elements depends on its associated weight. The only restriction is that weights must be integers.

Questions:
Answers:

function getBucketFromWeights($values) {
$total = $currentTotal = $bucket = 0;

foreach ($values as $amount) {
    $total += $amount;
}

$rand = mt_rand(0, $total-1);

foreach ($values as $amount) {
    $currentTotal += $amount;

    if ($rand => $currentTotal) {
        $bucket++;
    }
    else {
        break;
    }
}

return $bucket;

}

I ugh modified this from an answer here Picking random element by user defined weights

After I wrote this I saw someone else had an even more elegant answer. He he he he.

Questions:
Answers:

Many of the answers on this page seem to use array bloating, excessive iteration, a library, or a hard-to-read process. Of course, everyone thinks their own baby is the cutest, but I honestly think my approach is lean, simple and easy to read/modify…

Per the OP, I will create an array of values (declared as keys) from 1 to 10, with 3, 4, and 5 having double the weight of the other values (declared as values).

$values_and_weights=array(
    1=>1,
    2=>1,
    3=>2,
    4=>2,
    5=>2,
    6=>1,
    7=>1,
    8=>1,
    9=>1,
    10=>1
);

If you are only going to make one random selection and/or your array is relatively small* (do your own benchmarking to be sure), this is probably your best bet:

$pick=mt_rand(1,array_sum($values_and_weights));
$x=0;
foreach($values_and_weights as $val=>$wgt){
    if(($x+=$wgt)>=$pick){
        echo "$val";
        break;
    }
}

This approach involves no array modification and probably won’t need to iterate the entire array (but may).


On the other hand, if you are going to make more than one random selection on the array and/or your array is sufficiently large* (do your own benchmarking to be sure), restructuring the array may be better.

The cost in memory for generating a new array will be increasingly justified as:

  1. array size increases and
  2. number of random selections increases.

The new array requires the replacement of “weight” with a “limit” for each value by adding the previous element’s weight to the current element’s weight.

Then flip the array so that the limits are the array keys and the values are the array values.
The logic is: the selected value will have the lowest limit that is >= $pick.

// Declare new array using array_walk one-liner:
array_walk($values_and_weights,function($v,$k)use(&$limits_and_values,&$x){$limits_and_values[$x+=$v]=$k;});

//Alternative declaration method - 4-liner, foreach() loop:
/*$x=0;
foreach($values_and_weights as $val=>$wgt){
    $limits_and_values[$x+=$wgt]=$val;
}*/
var_export($limits_and_values);

Creates this array:

array (
  1 => 1,
  2 => 2,
  4 => 3,
  6 => 4,
  8 => 5,
  9 => 6,
  10 => 7,
  11 => 8,
  12 => 9,
  13 => 10,
)

Now to generate the random $pick and select the value:

// $x (from walk/loop) is the same as writing: end($limits_and_values); $x=key($limits_and_values);
$pick=mt_rand(1,$x);  // pull random integer between 1 and highest limit/key
while(!isset($limits_and_values[$pick])){++$pick;}  // smallest possible loop to find key
echo $limits_and_values[$pick];  // this is your random (weighted) value

This approach is brilliant because isset() is very fast and the maximum number of isset() calls in the while loop can only be as many as the largest weight (not to be confused with limit) in the array. For this case, maximum iterations = 2!

THIS APPROACH NEVER NEEDS TO ITERATE THE ENTIRE ARRAY