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: Accepted)

#include <iostream>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
 
#define numof(array)  (sizeof (array) / sizeof *(array))

const int INF = 1000000007;
const int MAX_V = 1000007;
 
typedef long long ll;
typedef pair<int, int> P; //first: ???????????¢???second: ??????????????? 

struct edge{
    int to;
    int cost;
};

int V=0;
vector<edge > G[MAX_V];
int d[MAX_V];

void dijkstra(int s){
  priority_queue<P, vector<P>, greater<P> > qu;
  fill(d, d + V, INF);
  d[s] = 0;
  qu.push(P(0,s));
  while(!qu.empty()){
    P p = qu.top(); qu.pop();
    int v = p.second;    
    if(d[v] < p.first) continue;
    for(int i = 0; i < G[v].size(); i++){
      edge e = G[v][i];
      if(d[e.to] > d[v] + e.cost){
	d[e.to] = d[v] + e.cost;
	qu.push(P( d[e.to], e.to ));
      }
    }
  }
}


int main(){

  int E,r;
  cin >> V >> E >> r;
  for(int i = 0 ; i < E; i++){
    int s , t , d;
    cin >> s >> t >> d;
    edge e = {t,d};
    //    e.to = t; e.cost = d;
    G[s].push_back(e);
  }
  dijkstra(r);
  for(int i = 0; i < V ; i++){
    if (d[i] == INF) cout << "INF" << endl;
    else cout << d[i] << endl;
  }

  return 0;
}