Question

I have a parts list with 1000 rows. The two fields are “Part Number” and “Cost”. The costs range from $1 to $2000 (integers all).

• A034, 1
• A012, 5
• A084, 10
• B309, 13
• A094, 25
• A370, 50
• A233, 75
• A343, 75
• C124, 78
• …
• D239, 500
• …
• X998, 1980
• Z901, 2000

I want to create a list of all combinations of parts whose combined cost falls within a tight range (the gap of the range will never be more than $50). For example, given a range of $70-75, the returned list would be:

• A343 (total $75)
• A233 (total $75)
• A370, A094 (total $75)
• A370, B309, A084 (total $73)
• A370, B309, A084, A034 (total $74)

My first thoughts were to iterate through all possible combinations of parts that could meet the criteria (i.e. <= the upper number of the range) and report those combinations whose sums fell within the range. It quickly became obvious that would fail because the number of combinations becomes astronomical pretty quickly. But given that most combinations would not meet the criteria, is this problem reasonably solvable?

Given that the data is in a table in a MySQL database, my preferred solution would be some SQL or Stored Proc, next preferred PHP, finally Javascript.

(ETA: the missed hit discovered by @piotrm)

Answer 1

You have to limit maximum of total cost, or the number of combinations will go up to the sky no matter how you try to find them. In the following example it is limited to 75, but you may try other values to see it you can still find results in a reasonable time.

You can also adapt this solution to update combinations table on inserts or updates for your main table, letting you get results extremely quick for any range that doesnt exceed your set limit (but slowing inserts obviously as it’s where all the work is done).

Create tables and trigger:

CREATE TABLE `total_max75` (
 `id` int(11) NOT NULL AUTO_INCREMENT,
 `parts` varchar(255) NOT NULL,
 `num` int(11) NOT NULL,
 `total` int(11) NOT NULL,
 PRIMARY KEY (`id`),
 KEY `total` (`total`,`num`)
); 

CREATE TABLE `newparts` (
 `name` char(4) NOT NULL,
 `price` int(11) NOT NULL,
 PRIMARY KEY (`name`)
);

DELIMITER //
CREATE TRIGGER addtotal AFTER INSERT ON newparts
FOR EACH ROW
BEGIN
IF NEW.price <= 75 THEN
   INSERT INTO total_max75 ( parts, num, total )
     SELECT CONCAT( t.parts, ', ', NEW.name), 
       t.num+1, t.total+NEW.price 
   FROM total_max75 t
   WHERE t.total <= 75 - NEW.price AND num < 40;

   INSERT INTO total_max75( parts, num, total )
     VALUES( NEW.name, 1, NEW.price );
END IF;
END//
DELIMITER ;

Then populate using:

INSERT INTO newparts( name, price )
SELECT part_number, cost FROM yourtable
WHERE cost <= 75;

or (as test data)

INSERT INTO newparts( name, price ) VALUES
('A012', 5),('A034', 1),('A084', 10),('A094', 25),('A233', 75),
('A343', 75),('A370', 50),('B309', 13),('C124', 78);

And finally get your result using:

SELECT * FROM total_max75 WHERE total BETWEEN 70 AND 75;

You may put any range here with maximum less than 75 (or whatever you set as limit in the table creation part and trigger).

Results:

A084, A370, B309        73 (you missed this one in your question)
A034, A084, A370, B309  74
A233                    75
A343                    75
A094, A370              75