In my last post, I explained the notion of “chords.” English words analogize to “chords” of Latin letters. And as it turns out, thinking of English words as “chords” gives us a useful way to approach common problems involving English words.

Suppose you wanted to check if a “word” (sequence of Latin letters) exists in a dictionary. Naively, you could go through every entry in the dictionary. Clearly, this would take unpleasantly long for extremely large dictionaries.

If we think of words/entries in our dictionary as “chords” of Latin letters, we could represent each chord as a path in a graph of letters. For example:¹

After converting our dictionary into this form, to check if a “word” exists, we can try to follow the path. If we can follow the path to completion, the “word” exists. Otherwise, it doesn't exist in our dictionary (yet).

We call this data structure a “trie” or “prefix tree." As we alluded to in the beginning, it appears in efficient solutions to many common problems involving English words. Most notably, we use some version of a trie to efficiently implement autocorrect and string search (Aho-Corasick).

As I have framed, the trie generalizes beyond English words, to all populations representable as “chords.” We can swap out the graph of letters with a graph of whatever constituents make up the “chords” or interest.