Recipe 2.7 Generating Biased Random Numbers
2.7.1 Problem
You want to generate random numbers,
but you want these numbers to be somewhat biased, so that numbers in
certain ranges appear more frequently than others. For example, you
want to spread out a series of banner ad impressions in proportion to
the number of impressions remaining for each ad campaign.
2.7.2 Solution
Use the pc_rand_weighted( ) function shown in
Example 2-1.
Example 2-1. pc_rand_weighted( ) // returns the weighted randomly selected key
function pc_rand_weighted($numbers) {
$total = 0;
foreach ($numbers as $number => $weight) {
$total += $weight;
$distribution[$number] = $total;
}
$rand = mt_rand(0, $total - 1);
foreach ($distribution as $number => $weights) {
if ($rand < $weights) { return $number; }
}
}
2.7.3 Discussion
Imagine if instead of an array in which the values are the number of
remaining impressions, you have an array of ads in which each ad
occurs exactly as many times as its remaining number of impressions.
You can simply pick an unweighted random place within the array, and
that'd be the ad that shows.
This technique can consume a lot of memory if you have millions of
impressions remaining. Instead, you can calculate how large that
array would be (by totalling the remaining impressions), pick a
random number within the size of the make-believe array, and then go
through the array figuring out which ad corresponds to the number you
picked. For instance:
$ads = array('ford' => 12234, // advertiser, remaining impressions
'att' => 33424,
'ibm' => 16823);
$ad = pc_rand_weighted($ads);
2.7.4 See Also
Recipe 2.6 for how to generate random
numbers within a range.
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