Given a string s, count how many distinct (non-empty) substrings it has. Every substring is a prefix of some suffix — specifically, the suffix that starts at the same position. So building a trie out of every suffix of s, one after another, means every distinct substring gets a node somewhere in that trie, and the trie's own structure prevents any duplicate from getting a second node: two suffixes that happen to share a prefix walk through the exact same existing nodes for as long as they agree. Counting how many nodes actually get freshly created — rather than reused — across all n suffix insertions gives the number of distinct substrings directly, without ever having to build a substring string, hash it, or check a set for membership.