PHP - 在数组中查找最小值并组合所有可能的数字以达到给定的总和

Question

Not sure following scenario is belong to Knapsack Problem or Coin Change Approach. Would like to seek solution of this problem in PHP language. Require simple solution because not understand some algorithms (text theory) provided from Internet.

Given a Table (A) as following:

TABLE (A)
---------
Item    |    Name    |    Price ($)
-------- ------------ --------------
1       |   Adidas   |      35
2       |   Nike Run |      70
3       |   Puma     |     100
4       |   Nike     |      85
5       |   NB       |      65

1. Combine any of 3 items in the table (A), sum up more than or equal to $200.
   • First, sorting the table (A).
   • Second, get the minimum/smallest amount (Price). In this case is $35.
   • Third, check one by one from the others amount.
   • Fourth, Sum up 3 possibilities of combination that more than or equal to $200.

Result:

Item    |    Name    |    Price ($)
-------- ------------ --------------
1       |   Adidas   |      35
5       |   NB       |      65
3       |   Puma     |     100

Given another sample Table (B) as following:

TABLE (B)
---------
Item    |    Name    |    Price ($)
-------- ------------ --------------
1       |   Adidas   |       5
2       |   Nike Run |      35
3       |   Puma     |     110
4       |   Nike     |      65
5       |   NB       |      15

1. Combine any of 3 items in the table (B), sum up more than or equal to $200.
   • First, sorting the table (B).
   • Second, get the minimum/smallest amount (Price). In this case is $5.
   • Third, check one by one from the others amount.
   • Fourth, Sum up 3 possibilities of combination that more than or equal to $200.
   • Fifth, if the smallest combine with others and failed to sum up total of $200, get second smallest and repeat first step to fourth step.
   • Sixth, the best minimal/smallest value is $35 in this case.

Result:

Item    |    Name    |    Price ($)
-------- ------------ --------------
2       |   Nike Run |      35
4       |   Nike     |      65
3       |   Puma     |     110

Answer 1

Say table A is an associative array, let's call it $a. To find the first combination that will be >= 200 do this:

$rowsWithValueOver200 = array();
foreach($a as $value) {
    foreach($a as $value2) {
        // Make sure to ignore the value selected in the first loop.
        if ($value2 == $value)
            continue;

        foreach($a as $value3) {
            // Make sure to ignore the value selected in the first and second loop.
            if ($value3 == $value)
                continue;
            if ($value3 == $value2)
                continue;

            $total = $value3['Price'] + $value2['Price'] + $value['Price'];

            if ($total >= 200) {
                // Store all of the rows in the new array.
                $rowsWithValueOver200[] = $value;
                $rowsWithValueOver200[] = $value2;
                $rowsWithValueOver200[] = $value3;
                break;
            }
        }
    }
}

So we iterate through the array 3 times. Check the sum once we're looking at 3 unique values. All the time making sure that we don't include the previously selected array element ($value or $value2). This could certainly be cleaned up a little and made more universal, but it'll work for 3 elements. A refactor of this into a more universal function would make recursive calls to itself, allow for a start position (then use a for loop instead of foreach).

To find the minimum value is pretty simple.

$minVal = PHP_INT_MAX; // Initially something high, here it is the maximum integer value.
$minRow;
foreach($rowsWithValueOver200 as $value) {
    if ($value['Price'] < $minVal){
        $minVal = $value['Price'];
        $minRow = $value;
    }
}

Set your minimum value (minVal) to check against to something really high. Iterate through the array values and if the $value['Price'] is less than the current minVal, then it is now the minVal and store the array element in $minRow for later reference.

3 and 4 I'm not sure what you're asking. It's not clear. If you want to find the sum of the three rows in $rowsWithValueOver200 then you could just use what I had in the first answer. If you want to do it with just the 3 final elements then do this:

$total = 0;
foreach($rowsWithValueOver200 as $value) {
    $total += $value['Price'];
}

If you're looking for other possibilities that sum up to 200 or more then just use the first example, but instead of a foreach at the first loop use a for loop with an index. Start at each index.

Good luck!

Answer 2

MySQL is properly equip to accomplish this all on its own. You could pull your entire table for PHP to figure out, but this can get expensive on resources, and it most definitely will produce slower results, especially with larger databases. PHP usually needs to loop through the data several times to do enough array manipulation which MySQL can accomplish very easily.

Assuming your database looks like this:

CREATE TABLE IF NOT EXISTS `A` (
  `Item` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `Name` varchar(10) NOT NULL,
  `Price` decimal(10,2) NOT NULL,
  PRIMARY KEY (`Item`),
  UNIQUE KEY `Name` (`Name`)
) ENGINE=InnoDB  DEFAULT CHARSET=latin1 AUTO_INCREMENT=6 ;

INSERT INTO `A` (`Item`, `Name`, `Price`) VALUES
(1, 'Adidas', '35.00'),
(2, 'Nike Run', '70.00'),
(3, 'Puma', '100.00'),
(4, 'Nike', '85.00'),
(5, 'NB', '65.00');

You can query it like so:

SELECT @leastprice := min(`Price`) FROM `A`;
SELECT t1.Name AS Name1, t2.Name AS Name2, t3.Name AS Name3,
       t1.Price AS Price1, t2.Price AS Price2, t3.Price AS Price3,
       (t1.Price+t2.Price+t3.Price) AS `Total`
    FROM `A` t1
    LEFT JOIN `A` t2 ON t1.Item != t2.Item
    LEFT JOIN `A` t3 ON t1.Item != t2.Item AND t2.Item != t3.Item
    WHERE t1.price = @leastprice
      AND t2.price<=t3.price
      AND t1.price+t2.price+t3.price >= 200;

Result:

---

Edit:
For your second case, assuming your database looks like this:

 CREATE TABLE IF NOT EXISTS `B` ( `Item` int(10) unsigned NOT NULL AUTO_INCREMENT, `Name` varchar(10) NOT NULL, `Price` decimal(10,2) NOT NULL, PRIMARY KEY (`Item`), UNIQUE KEY `Name` (`Name`) ) ENGINE=InnoDB DEFAULT CHARSET=latin1 AUTO_INCREMENT=6 ; INSERT INTO `B` (`Item`, `Name`, `Price`) VALUES (1, 'Adidas', '5.00'), (2, 'Nike Run', '35.00'), (3, 'Puma', '110.00'), (4, 'Nike', '65.00'), (5, 'NB', '15.00'); 

You can query it like so:

 SELECT @leastTalliablePrice := min(t1.Price) FROM `B` t1 LEFT JOIN `B` t2 ON t1.Item != t2.Item LEFT JOIN `B` t3 ON t1.Item != t2.Item AND t2.Item != t3.Item WHERE t2.price<=t3.price AND t1.price+t2.price+t3.price >= 200; SELECT t1.Name AS Name1, t2.Name AS Name2, t3.Name AS Name3, t1.Price AS Price1, t2.Price AS Price2, t3.Price AS Price3, (t1.Price+t2.Price+t3.Price) AS `Total` FROM `B` t1 LEFT JOIN `B` t2 ON t1.Item != t2.Item LEFT JOIN `B` t3 ON t1.Item != t2.Item AND t2.Item != t3.Item WHERE t1.price = @leastTalliablePrice AND t2.price <= t3.price AND t1.price+t2.price+t3.price >= 200; 

Result:

If for some reason your database doesn't have 3 or more distinct items, or their prices aren't enough to reach your desired total, the query would simply return 0 rows in the same manner that a SELECT results 0 rows if it can't find any rows to select. But if there were more than one match in the above case, it would result multiple rows like as the case in my first screenshot.