Skip List: Express Lanes and Coin Flips (AI Engineer Coding Interview)

The skip list, from first principles. You ride a train that stops at every station and your stop is far down the line. Plainly: keep numbers sorted, and find, add or remove any one of them fast. A sorted linked list inserts easily but searches one node at a time, and a sorted array searches fast but shifts on every insert. The skip list stacks sparse express lanes on a sorted linked list: search starts at the top left, moves right while the next key is not too big and drops a lane when it would overshoot, and a coin flip gives each new key its height so there is no rebalancing. We trace a search for fifty two in five steps against nine, an absent search in six steps against ten, and an insert of thirty five with a coin flip that splices a tower into two lanes. We see why it takes about two log n steps, break it with unlucky coins, duplicate keys, deletes that miss a lane and unbounded height, and state the honest cost: expected log n search, insert and delete, about two pointers per key, and for a million keys with seeded runs about twenty lanes, about thirty eight steps on average, worst seen seventy, against an average of five hundred thousand for a plain list. Trade-offs against balanced trees, sorted arrays and hash tables, uses in Redis sorted sets, RocksDB and LevelDB memtables, queues and rate limiters, ordered scans, randomness, cache behaviour, and the practice page. The third rung of the structures a database ships ladder. Built for the AI engineer coding round. Practice it yourself on the site (free, runs in your browser): https://vibeengines.com/algorithm/skip-list The page has a simulator, a coding task with hidden tests, hints and a full explainer. Chapters 0:00 The question: sorted, and fast to find, add, remove 0:50 Brute force: a linked list and a sorted array 1:19 The idea: express lanes, right then drop, coin flips 1:59 Tracing searches and an insert through ten keys 3:02 Why about log n steps and no rotations 3:34 Breaking it: unlucky coins, deletes, height cap 4:21 The code, with live state 4:48 Time and space in detail, with a million keys 5:53 Trade-offs: balanced tree, sorted array, hash table 6:35 Where it lives in AI systems 7:06 Edge cases: scans, randomness, cache, empty list 7:45 Practice it on Vibe Engines Third rung of the structures a database ships ladder on the site: the B-tree, the LSM tree, the skip list, the piece table and consistent hashing. #skiplist #datastructures #algorithms #redis #aiengineer #systemdesigninterview #codinginterview