How do dynamic filters work in online stores?

Question

Algorithms

Help me understand how filters work in online stores. It is interesting that the filter filters out products by very different types of characteristics and at the same time updates the filter itself, taking into account the already noted filtering parameters.

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Here's an example.

• When a filter is selected, it sends the filter data and returns the filtered products
  
• A new FILTER html-CODE is also sent. In which the number of products in different filter parameters was dynamically recalculated.
  

Questions:

1) How are the attributes of goods that are used in filtering stored? And how are they related to goods?
2) How is the number of products updated dynamically?

3) When choosing filters, the url changes. How does it work?
4) What can be sensible to read on this topic? I found only an article on Habré about a filter with radishes.

Answer 1

Do 1 big table or split into parts?

Answer 2

Briefly: "Waterfall slope" with COUNT priority from largest to smallest in 3NF database tables. => This is the fastest way without a "clean" "tree".