trait KeyNeighborsSolution extends Solution {

case class PathData(distance: Int, pathDoors: Set[Pos], pathKeys: Set[Pos])

// https://en.wikipedia.org/wiki/Transit_node_routing

def getKeyNeighbors(input: Input): collection.Map[Pos, collection.Map[Pos, PathData]]

override def collectKeysSteps(input: Input): Int = {

private case class PathData(length: Int, pathPoss: Set[Pos])

// https://en.wikipedia.org/wiki/Transit_node_routing

private val posNeighbors: collection.Map[Pos, collection.Map[Pos, PathData]] = {

val allPoss: Set[Pos] = hallways ++ room2amphipod.keySet

case class ValveData(flowRate: Int, tunnels: Seq[Valve])

// https://en.wikipedia.org/wiki/Transit_node_routing

def valveDists(valves: Map[Valve, ValveData]): collection.Map[Valve, collection.Map[Valve, Int]] = {

val dists: mutable.Map[Valve, mutable.Map[Valve, Int]] = valves.view.mapValues(_.tunnels.map(_ -> 1).to(mutable.Map)).to(mutable.Map)

// Floyd-Warshall