// Implementation of Dijkstra's algorithm using adjacency lists
// and priority queue for efficiency.
// Running time: O(|E| log |V|)
// USAGE: edges: pair of weight/destination, source, target
void Dijkstra(VVPII edges, int s, int t) {
  // use priority queue in which top element has the "smallest" priority
  priority_queue<PII, VPII, greater<PII> > Q;
  VI dist(edges.size(), INF), dad(edges.size(), -1);
  Q.push(make_pair (0, s));
  dist[s] = 0;
  while(!Q.empty()){
    PII p = Q.top();
    if (p.second == t) break;
    Q.pop();
    int here = p.second;
    for(VPII::iterator it=edges[here].begin(); it!=edges[here].end(); it++){
      if(dist[here] + it->first < dist[it->second]){
        dist[it->second] = dist[here] + it->first;
        dad[it->second] = here;
        Q.push (make_pair (dist[it->second], it->second));
      }
    }
  }
  // dist contains distances
}