Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in C++11 (judge verdict: Accepted)

#include <bits/stdc++.h>

std::vector< std::tuple<long, long> > graph[112345];
int V, E, r;
long dist[112345];
const long INF = (1LL << 60);

int main() {
  for(long& I : dist) I = INF;
  scanf("%d %d %d", &V, &E, &r);
  for(int i = 0; i < E; ++i) {
    int s, t, d;
    scanf("%d %d %d", &s, &t, &d);
    graph[s].push_back(std::tuple<long, long>(t, d));
  }

  // node cost / id
  std::priority_queue< std::tuple<long, long> >q;
  dist[r] = 0;
  q.push(std::tuple<long, long>(0, r));
  while( not q.empty() ) {
    long cost, id;
    std::tie(cost, id) = q.top(); q.pop();
    cost = -cost;
    for(int i = 0; i < (int)graph[id].size(); ++i) {
      long next, edgecost;
      std::tie(next, edgecost) = graph[id][i];
      if( dist[next] > cost + edgecost ) {
        dist[next] = cost + edgecost;
        q.push(std::tuple<long, long>(-dist[next], next));
      }
    }
  }

  for(int i = 0; i < V; ++i) {
    if( dist[i] == INF ) {
      puts("INF");
    }
    else {
      printf("%ld\n", dist[i]);
    }
  }
  
  return 0;
}