算法:最便宜的产品包装组合

在数据库中，我有一个不同包装的价目表，每个包装至少包含以下产品之一：照片，平面图，EPC。示例 （ID |标题 |价格）：

12 Photo    10.00   
13 EPC  20.00   
14 Floor Plan   20.00   
15 4 Photos 40.00   
16 4 Photos + EPC   55.00   
17 4 Photos + Floor Plan    55.00   
18 4 Photos + Floor Plan + EPC  75.00   
etc...

现在我无法弄清楚如何始终确定最便宜的套餐组合。例如，如果我想要 5 张照片和一个平面图，则项目 17 + 12 的组合会比组合 5x12 和 14 （70.00） 便宜 （65.00）。我已将价目表转换为以下数组并将其传递给我的算法尝试，但它失败了......谁能把我推向正确的方向？

Array
(
    [12] => Array
       (
           [price] => 10.00
           [items] => Array
              (
                 [0] => 1 // photo
                 [1] => 0 // floor plan
                 [2] => 0 // epc
              )
       )
    [13] => Array
       (
           [price] => 20.00
           [items] => Array
              (
                 [0] => 0 // photo
                 [1] => 0 // floor plan
                 [2] => 1 // epc
              )
       )
    [14] => Array
       (
           [price] => 20.00
           [items] => Array
              (
                 [0] => 0 // photo
                 [1] => 1 // floor plan
                 [2] => 0 // epc
              )
       )
    [15] => Array
       (
           [price] => 40.00
           [items] => Array
              (
                 [0] => 4 // photo
                 [1] => 0 // floor plan
                 [2] => 0 // epc
              )
       )
    [16] => Array
       (
           [price] => 60.00
           [items] => Array
              (
                 [0] => 4 // photo
                 [1] => 0 // floor plan
                 [2] => 1 // epc
              )
       )
       etc...
)

发现者：

class CombinationFinder {
    private $products = array();
    public function __construct($products) {
        $this->products = $products;
        // sort by overall amount of items
        uasort($this->products, function ($a, $b) {
            $sum_a = array_sum($a['items']);
            $sum_b = array_sum($b['items']);
            if ($sum_a == $sum_b) {
                return 0;
            }
            return $sum_a < $sum_b ? -1 : 1;
        });
    }
    private function intersect($combo, $purchased) {
        return array_map(function ($a, $b) {
            $result = $b-$a;
            return $result < 0 ? 0 : $result;
        }, $combo, $purchased);
    }
    private function possibility($purchased, $limit) {
        $price = 0;
        $combination = array();
        foreach($this->products as $pid => $combo) {
            // if adding this combo exceeds limit, try next combo
            if($price + $combo['price'] >= $limit) {
                continue;
            }
            // see if combo helps
            $test = $this->intersect($combo['items'], $purchased);
            if(array_sum($test) === array_sum($purchased)) {
                continue;
            }
            // add combo and deduct combo items
            $combination[] = $pid;
            $price += $combo['price'];
            $purchased = $test;
            // if purchased items are covered, break
            if(array_sum($purchased) === 0) {
                return array('price' => $price, 'combination' => $combination);
            }
        }
        return false;
    }
    public function getCheapest($photos, $floorplans, $epc) {
        $purchased = array((int)$photos, (int)$floorplans, (int)$epc);
        $limit = 9999;
        while($test = $this->possibility($purchased, $limit)) {
            $limit = $test['price'];
            $possibility = $test;
        }
        sort($possibility['combination'], SORT_NUMERIC);
        echo 'Cheapest Combination: '.implode(', ', $possibility['combination']);exit;
    }
}