.js

class Intersection {
  constructor(id) {
    this.id = id
    this.roads = []
    this.timeBeforeArrival = Infinity
  }
  
  addRoad({ destination, drivingTime }) {
    this.roads.push({ destination, drivingTime })
  }
  
  startDriving(newTimeBeforeArrival = 0) {
    this.timeBeforeArrival = newTimeBeforeArrival
    
    for (const { destination, drivingTime } of this.roads) {
      const destinationTimeBeforeArrival = this.timeBeforeArrival + drivingTime
      
      if (destination.timeBeforeArrival > destinationTimeBeforeArrival) {
        destination.startDriving(destinationTimeBeforeArrival)
      }
    }
  }
  
  getPathTo(start) {
    if (this === start) {
      return [this.id]
    }
    
    let closestIntersection
    
    for (const { destination, drivingTime } of this.roads) {
      if (destination.timeBeforeArrival + drivingTime === this.timeBeforeArrival) {
        closestIntersection = destination
        break
      }
    }
    
    return [...closestIntersection.getPathTo(start), this.id]
  }
}

function navigate(numberOfIntersections, roads, startID, finishID) {
  const intersections = Array.from(
    new Array(numberOfIntersections),
    (_, id) => new Intersection(id)
  )
  
  const start  = intersections[startID]
  const finish = intersections[finishID]
    
  for (const { from, to, drivingTime } of roads) {
    intersections[from].addRoad({ destination: intersections[ to ], drivingTime })
    intersections[ to ].addRoad({ destination: intersections[from], drivingTime })
  }
  
  start.startDriving()
  
  if (finish.timeBeforeArrival === Infinity) {
    return null
  } else {
    return finish.getPathTo(start)
  }
}