This is a an interesting way of doing text search over a collection of documents, that I suppose makes sense if you only have a small number of documents to search.
Generally, an inverted index [1] is used rather than a trie, and collection-based term weights are calculated using something like IDF [2]. You could then use something like cosine to compute length normalised rankings for documents.
There are of course many different approaches to text search, but this is the first time I've personally come across this one.
If anyone is interested in an in depth look at how text search works, an Introduction to Information Retrieval [3] is available for free and is a fantastic book.
[1] https://en.wikipedia.org/wiki/Inverted_index