Manhattan has 50,000 restaurants. Rural Wyoming has 3 per county. A fixed-size grid wastes cells on empty space and overloads dense areas. Quadtrees adapt.

User types three characters and expects instant suggestions. A hash map can’t do prefix lookups. A trie can, in O(k) time where k is the query length.

A normal index maps documents to words. An inverted index maps words to documents. That reversal is why search is fast.

Exact duplicates are easy. Near-duplicates are hard. SimHash turns documents into compact fingerprints where similar content produces similar hashes.

Counting unique items across billions of events. A HashSet needs gigabytes. HyperLogLog does it in 12KB. The trick is accepting a little error.

Bloom filters skip unnecessary disk reads in LSM trees by saying ‘definitely not here’ with zero false negatives. Learn how Cassandra and RocksDB use them.

LSM Trees vs B-Trees: the write-fast or read-fast tradeoff. Learn when to use B-trees (MySQL) vs LSM trees (Cassandra) based on your database workload.