Setup This week I learned about the "Quick Find" or "Quick Union" algorithm. Imagine an NxN grid of nodes, some of which are connected by lines. A connection can be interpreted as accessibility: if two nodes are connected, you can get from one to the other. Every node is accessible to itself: to get where you already are, stay there. Also, If you can get from A to B, you can go back from B to A. And if you can get from A to B and from B to C, then you can get from A to C. As a consequence, the connection between nodes divides the grid into regions of mutually accessible nodes. You can travel from any node in a given region to any other node in that region -- but not to any nodes outside that region (exercise to reader -- proof by contradiction). The problem has two parts. First, find a way to represent this grid structure and the accessibility relation; second, use your schema to efficiently calculate whether two given nodes are accessible to each other. ...