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++ (judge verdict: Time Limit Exceeded)

#include<cstdio>
#include<vector>
#include<map>
#include<iostream>
#include<queue>
#include<algorithm>

using namespace std;

#define INF 100000000
typedef pair<int,int> P;
int v,e,r;
int s[1000000],t[1000000],d[10000000];

void dijkstra(){
  priority_queue<P,vector<P>,greater<P> > pq;
  pq.push(P(0,r));
  int res[v];
  fill(res,res+v,INF);
  res[r]=0;

  while(!pq.empty()){
    P tmp=pq.top(); pq.pop();
    for(int i=0;i<e;i++){
      if(tmp.second==s[i]){
        if(res[t[i]]>res[s[i]]+d[i]){
          res[t[i]]=res[s[i]]+d[i];
          pq.push(P(res[t[i]],t[i]));
        }
      }
    }
  }
  for(int i=0;i<v;i++){
    if(res[i]==INF) printf("INF\n");
    else  printf("%d\n",res[i]);
  }
}




int main(){
  scanf("%d%d%d",&v,&e,&r);
  for(int i=0;i<e;i++){
    scanf("%d%d%d",&s[i],&t[i],&d[i]);
  }

/*  for(int i=0;i<e;i++){
    s[i+e]=t[i];
    t[i+e]=s[i];
    d[i+e]=d[i];
  }
*/
  dijkstra();

  return 0;
}