Concepts3

Slope Trick

Slope Trick is a technique to maintain a convex piecewise-linear function implicitly using two heaps and a running constant.

#slope trick#convex dp#piecewise linear+11

⚙️AlgorithmAdvanced

Johnson's Algorithm

Johnson's Algorithm computes all-pairs shortest paths on sparse graphs by first removing negative edges via reweighting, then running Dijkstra from every vertex.

#johnson's algorithm#all pairs shortest paths#apsp+12

🗂️Data StructureAdvanced

Kinetic Tournament Tree

A kinetic tournament tree maintains the minimum (or maximum) of moving values whose pairwise order can change over time.

#kinetic data structure#tournament tree#certificate+12