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Here are some algorithms I like that can be explained in 15 minutes, aren't part of baseline CS knowledge, and do something surprising. What else should be on this list?
* Gosper's Hashlife * Pollard's lambda trick for hash collisions * The dense-sparse trick for clearable sets * Alpha-beta pruning * The Boyer-Moore majority algorithm * Floyd's algorithm for sampling without replacement * Escardó's "seemingly impossible" programs
Interpolation search - it can beat binary search and is actually useful! Format preserving encryption - a shuffle iterator / generate lots of random numbers without repeats Minimal perfect hashing - make a hash function that for known inputs gives 0 to N as output.