Advanced Data Structures and Techniques

These are the structures that appear when a problem needs repeated range queries, repeated prefix lookups, or repeated connectivity checks, and a linear scan per query is too slow. They come up in the harder end of interviews and constantly in competitive programming.

The material assumes the earlier topics are solid — segment trees make sense once binary trees do, and disjoint sets are much clearer after graph connectivity. Each lesson visualises the operation that gives the structure its advantage: the range decomposition in a segment tree, the path compression in a disjoint set, the shared prefixes in a trie.