Question

I have a list of numbers like

 $list = array(1,5,19,23,59,51,24) 

in actual code this is generated from database, so this array will hold up to 500 numbers that are different from each other.

each of these numbers in the database has a probability of occurring recorded. So i have a data from previous executions to generate random numbers from 1 to 500 and recorded the probabilities of each number generated for like 1000 times.

Now having list of numbers and probabilities for each number i want to write a function that will generate a random number from these 500 numbers based on their probabilities.

For example:

    number 1 has a chance of: 0.00123 //0.123%
    number 6 has a chance of: 0.0421 //4.21%
    number 11 has a chance of: 0.0133 //1.33%

so variable $finallist will look something like this:

   $finallist[1] = 0.00123;
   $finallist[6] = 0.0421;
   $finallist[11] = 0.0133;

Now if i run my function and pass in $finallist as a parameter i want to retrieve a random number between 1 and 6 but number 6 will have higher possibility of coming out than 1 and 11 will have higher possibility to come out than 1.

I have some functions written that deal with returning the random number based on its chance but it only takes 1 value as a parameter.

private function randomWithProbability($chance, $num, $range = false)
{
    /* first generate a number 0 and 1 and see if that number is in the range of chance */
    $rand = $this->getRandomFloatValue(0, 1);

    if ($rand <= $chance) 
    {
        /* the number should be returned */
        return $num;
    }
    else 
    {
        /* otherwise return a random number */
        if ($range !== false)
        {
            /* make sure that this number is not same as the number for which we specified the chance */
            $rand = mt_rand(1, $range);
            while ($rand == $num)
            {
                $rand = mt_rand(1, $range);
            }

            return $rand;
        }
    }
}

if anyone knows a solution/algorithm to do this or if there is anything built in to PHP would be a big help. Thank you so much.

Answer 1

The basic algorithm you’re looking for:

• add all the probabilities together and determine the maximum
• pick a random number between 0 and 1 and multiply it by the max
• find the entry that corresponds with that value

Example code:

<?php

// create some weighted sample data (id => weight)
$samples = array(
  'a' => 0.001,
  'b' => 0.004,
  'c' => 0.006,
  'd' => 0.05,
  'e' => 0.01,
  'f' => 0.015,
  'g' => 0.1
);

class Accumulator {
   function __construct($samples) {
      // accumulate all samples into a cumulative amount (a running total)
      $this->acc = array();
      $this->ids = array();
      $this->max = 0;
      foreach($samples as $k=>$v) {
         $this->max += $v;
         array_push($this->acc, $this->max);
         array_push($this->ids, $k);
      }
   }

   function pick() {
      // selects a random number between 0 and 1, increasing the multiple here increases the granularity
      // and randomness; it should probably at least match the precision of the sample data (in this case 3 decimal digits)
      $random = mt_rand(0,1000)/1000 * $this->max;
      for($i=0; $i < count($this->acc); $i++) {
         // looks through the values until we find our random number, this is our seletion
         if( $this->acc[$i] >= $random ) {
            return $this->ids[$i];
         }
      }
      throw new Exception('this is mathematically impossible?');
   }

   private $max; // the highest accumulated number
   private $acc; // the accumulated totals for random selection
   private $ids; // a list of the associated ids
}

$acc = new Accumulator($samples);

// create a results object to test our random generator
$results = array_fill_keys(array_keys($samples), 0);

// now select some data and test the results
print "picking 10000 random numbers...\n";
for($i=0; $i < 10000; $i++) {
   $results[ $acc->pick() ]++;
}

// now show what we found out
foreach($results as $k=>$v) {
   print "$k picked $v times\n";
}

The results:

> php.exe rand.php
picking 10000 random numbers...
a picked 52 times
b picked 198 times
c picked 378 times
d picked 2655 times
e picked 543 times
f picked 761 times
g picked 5413 times

Running the same code with this sample:

// samples with even weight
$samples = array(
   'a' => 0.1,
   'b' => 0.1,
   'c' => 0.1,
   'd' => 0.1
);

Produces these results:

> php.exe rand.php
picking 10000 random numbers...
a picked 2520 times
b picked 2585 times
c picked 2511 times
d picked 2384 times