You're correct.
It is their business to know your online footprint, your purchasing trends / history, your current search pattern, and your search history, and all kinds of other metrics.
The search engines and Microsoft and Apple (among others) sell this information to retailers and websites, and they use it themselves in the hopes you'll click on the adverts they place on the websites you're browsing. Google Analytics is one example of a data gathering service. They also know that Americans are impulse buyers with credit cards, if they can present adverts very quickly after your initial searches they stand a good chance of getting paid for that sale directly, or if you go to a brick-and-mortar they still get paid, indirectly but less $$.
Now think about the size and speed of the database they're using, and then think about the network size and speed, and the server farms size and speed of those servers because they're doing this to billions of people every second of single day. The algorithms are incredible.






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