SQL query to find products matching a set of categories

Question

I have 3 tables: products, categories and pro_cat_link. A product can be linked to one or many categories through the table pro_cat_link.

My query must answer the fo

Answer 1

If you don't have too many categories, instead of keeping track of a column count, you can have a bitstring that represents the categories it is in (i.e., a 1 at position i means the product is in category i, and 0 means not in the category). Then, when searching for a group of categories, you generate a bitstring for that search, and AND all category strings with this string. The ones in the right category will produce the search string as the answer.

For example, let's say you have ten categories. Item1 is in categories 1, 3, 5, 6, 8, 10, so its category string is 1010110101. Item2 is in categories 1, 2, 4, 6, 8, 10, and so its category string is 1010101011. When searching for 3, 6, 8, and 10, you would generate the string s = 1010100100. Item1 & s = 1010100100 = s. Item2 & s = 1010100000 <> s.

Furthermore, you don't have to store it as a string, you could just store it as the actual base 10 equivalent. So Item1, Item2, and s are 693, 683, and 676 respectively. 693 & 676 = 676, but 683 & 676 = 672. Then, if you're adding a product to category i, just update it's category number by 2^(i - 1), and if you're removing from category i, just subtract 2^(i - 1).

Of course, if you have more categories than bits in a MySQL int, this won't work at all. Also, as FrustratedWithFormsDes points out in his answer, this then invokes all the problems of updating both pro_cat_link and this table (course, depending on what pro_cat_link is used for, this might eliminate it completely). Furthermore, if a category changes numbers, you have to update everything.