PHP 上剩余分布的百分比限制

Question

有一个百分比列表。数字之和为 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];

我需要将最大数量限制为特定值，并将余数分配给其余数字。如果可能，保留剩余百分比的比例。

尝试了以下解决方案：

$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";

这段代码可以正常工作：

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

但是如果我将变量$limit更改为值6，由于余数相加而超出限制：

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

我找不到算法。

Answer 1

您可以尝试迭代方法。

1. 限制最大值
2. 当总和不是 100 时：
   1. 计算每一项低于限制的缺失值
   2. 将此值添加到限制下的项目，但不超过此限制

代码：(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));

输出：

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

7.4 之前的 PHP 版本请参见 this demo。