notebook/code/FastDijkstra.cc

// Implementation of Dijkstra's algorithm using adjacency lists
// and priority queue for efficiency.
//
// Running time: O(|E| log |V|)

#include <queue>
#include <stdio.h>

using namespace std;
const int INF = 2000000000;
typedef pair<int,int> PII;

int main(){
  
  int N, s, t;
  scanf ("%d%d%d", &N, &s, &t);
  vector<vector<PII> > edges(N);
  for (int i = 0; i < N; i++){
    int M;
    scanf ("%d", &M);
    for (int j = 0; j < M; j++){
      int vertex, dist;
      scanf ("%d%d", &vertex, &dist);
      edges[i].push_back (make_pair (dist, vertex)); // note order of arguments here
    }
  }
  
  // use priority queue in which top element has the "smallest" priority
  priority_queue<PII, vector<PII>, greater<PII> > Q;
  vector<int> dist(N, INF), dad(N, -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 (vector<PII>::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));
      }
    }
  }
  
  printf ("%d\n", dist[t]);
  if (dist[t] < INF)
    for(int i=t;i!=-1;i=dad[i])
      printf ("%d%c", i, (i==s?'\n':' '));
    
  return 0;
}