• i. Randomized Algorithms: Las Vegas vs Monte Carlo, error amplification, shuffling and anti-hack seeding, Chernoff and backwards analysis, derandomization.
• ii. Heuristic Optimization: hill climbing, simulated annealing, iterated local search, neighbourhoods and the contest checklist, 2-opt for TSP.
• iii. Randomized Hashing and Verification: set and Zobrist hashing, subarray multiset tests, Freivalds, Schwartz–Zippel, anti-hash attacks.
• iv. Sampling and Streaming: reservoir sampling (R, L, weighted), Floyd’s sampler, Misra–Gries, Count–Min, Bloom filters, HyperLogLog.
• v. Randomized Search: Color Coding and Random Walks: k-paths by color coding, random-walk 2-SAT and Schöning’s 3-SAT.