Percent limit with remainder distribution on PHP - php

Question

There is a list of percentages. The sum of the numbers is 100.
$percent = [20.88, 14.93, 14.14, 13.29, 5.06, 4.43, 4.24, 4.22, 2.57, 2.51, 2.38, 2.18, 1.94, 1.80, 1.34, 1.21, 0.81, 0.63, 0.50, 0.48, 0.30, 0.16];
I need to limit the maximum number to a specific value, and distribute the remainder over the rest of the numbers. If possible, keeping the proportions of the remaining percentages.
Tried the following solution:
$limit = 8;
// Calculating the remainder of numbers exceeding $limit.
$rest = array_reduce($percent, function ($a, $b) use ($limit) {
return $limit < $b ? $a += ($b - $limit) : $a;
});
// Number of numbers not exceeding $limit.
$small = array_reduce($percent, function ($a, $b) use ($limit) {
return $limit > $b ? ++$a : $a;
});
// Percent calc with limit up to $limit and addition of the remainder ($rest / $small).
array_walk($percent, function(&$value) use ($limit, $rest, $small) {
$value = $limit < $value ? min($value, $limit) : $value + ($rest / $small);
});
print_r($percent);
print(array_sum($percent)) . "\n";
This code works correctly:
Array
(
[0] => 8
[1] => 8
[2] => 8
[3] => 8
[4] => 6.7955555555556
[5] => 6.1655555555556
[6] => 5.9755555555556
[7] => 5.9555555555556
[8] => 4.3055555555556
[9] => 4.2455555555556
[10] => 4.1155555555556
[11] => 3.9155555555556
[12] => 3.6755555555556
[13] => 3.5355555555556
[14] => 3.0755555555556
[15] => 2.9455555555556
[16] => 2.5455555555556
[17] => 2.3655555555556
[18] => 2.2355555555556
[19] => 2.2155555555556
[20] => 2.0355555555556
[21] => 1.8955555555556
)
100
But if I change the variable $limit to the value 6, the limit is exceeded due to the addition of the remainder:
Array
(
[0] => 6
[1] => 6
[2] => 6
[3] => 6
[4] => 7.24
[5] => 6.61
[6] => 6.42
[7] => 6.4
[8] => 4.75
[9] => 4.69
[10] => 4.56
[11] => 4.36
[12] => 4.12
[13] => 3.98
[14] => 3.52
[15] => 3.39
[16] => 2.99
[17] => 2.81
[18] => 2.68
[19] => 2.66
[20] => 2.48
[21] => 2.34
)
100
I can't find an algorithm.

Answer 1

You can try an iterative approch.
limit the maximum value
while the sum is not 100:
compute the missing value for each item under the limit
add this value to item under the limit, without exceeding this limit
Code: (demo)
$percent = [20.88, 14.93, 14.14, 13.29, 5.06, 4.43, 4.24, 4.22, 2.57, 2.51, 2.38, 2.18, 1.94, 1.80, 1.34, 1.21, 0.81, 0.63, 0.50, 0.48, 0.30, 0.16];
$limit = 6;
// check if a solution is possible
if ($limit * count($percent) < 100) die("Not possible");
// 1. limit the maximum value
$limited = array_map(fn($value) => min($value, $limit), $percent);
// 2. while the sum is not 100
while (($remain = 100 - array_sum($limited)) > 0)
{
// get the "non-full" values
$filtered = array_filter($limited, fn($v) => $v < $limit);
// get the value to add for each items
$evenly = $remain / count($filtered);
// add the value (maximum as possible)
$limited = array_map(fn($value) => min($value + $evenly, $limit), $limited);
}
print_r($limited);
print_r(array_sum($limited));
Output:
Array
(
[0] => 6
[1] => 6
[2] => 6
[3] => 6
[4] => 6
[5] => 6
[6] => 6
[7] => 6
[8] => 4.9407142857143
[9] => 4.8807142857143
[10] => 4.7507142857143
[11] => 4.5507142857143
[12] => 4.3107142857143
[13] => 4.1707142857143
[14] => 3.7107142857143
[15] => 3.5807142857143
[16] => 3.1807142857143
[17] => 3.0007142857143
[18] => 2.8707142857143
[19] => 2.8507142857143
[20] => 2.6707142857143
[21] => 2.5307142857143
)
100
See this demo for PHP version prior to 7.4.