Transforming 404 pages into search pages

This has been originally posted on https://github.com/algolia/algoliasearch-jekyll-hyde/issues/4

> When a URL tries to reach a post that does not resolve to a real page, such as http://community.algolia.com/algoliasearch-jekyll-hyde/whatever currently the visitor is shown the 404.html page.
> But now that we have Search, how about having JavaScript take the "whatever" and put it in the search form, and automatically issue a search?

I don't think this is something that could be part of the plugin directly, but I'd be interested into adding this to themes.

Start by reviewing the theme's 404.html and the existing Jekyll search integration. Determine how an unresolved URL such as /whatever can supply its path to the search form and trigger a search; done means the missing-page visitor sees results for that term.

Written by the indexing model from the issue text.