Generate a random number from a given set of numbers and chances - php

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