It depends if you employ neural networks using Tensorflow and find some good user experience designer you should be able to acomplish it low cost

In order to use search results from

other search engines you need permission

from the company maintaining it. Automated

searches burden their webservers

and makes it more difficult to enrich the

search results with ads.

Often there is a specialized API available

that makes it easy to send queries and

get results in a machine-readable format

like XML or JSON.

https://de.wikipedia.org/wiki/OpenSearch

http://www.opensearch.org/Documentation/Frequently_asked_questions

http://www.data2type.de/xml-xslt-xslfo/newsfeeds-rss-atom/rss-2-0-und-vorgaengerversionen/erweiterungsmodule/opensearch-modul-von-amazon/

Regards,

Joachim

But tecnically those website do not perform a search in their own site, but perform searhes somewhere else to show them on their website.

If you want to implement a search engine in your own website you can use Google Custom Search Engine.

You can also add whatever domain or domains you want to get information from and ban sites you dont want  to ever show results.

https://cse.google.com/