Data-Structures

You can project n points into O(log n / eps^2) dimensions and keep every distance. The theorem underneath every vector database.

O(log n) proof that one item belongs to a huge set. Git, certificate transparency, and every blockchain are the same data structure.

Constant space, no false negatives, a tunable false-positive rate, and the exact formula for the tradeoff.

Adding a node should move 1/n of the keys, not all of them. One idea, and virtual nodes to fix its variance (Balls into bins and the power of two choices).

Exact distinct-count needs linear space; approximate needs almost none. HyperLogLog and Count-Min as the constructive half.

What a hash function actually guarantees, as opposed to what it seems to do.

Why a dynamic array's O(n) resize is still O(1) per push, and how to prove it rather than hand-wave it.

Collisions arrive at sqrt(N), not N. Sets every hash length, UUID size, and nonce width you will ever choose.