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++14 (judge verdict: Accepted)

#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
 
#define MAX 100000
#define INFTY 1 << 30
int v,r;
vector<pair<int,int> > adj[MAX];
 
void dijkstra(){
  priority_queue<pair<int,int> > PQ;
  int d[MAX];
  for(int i = 0; i < v; i++){
    d[i] = INFTY;
  }    
  d[r] = 0;
  PQ.push(make_pair(0,r));
  
  while(!PQ.empty()){
    pair<int,int> m = PQ.top(); PQ.pop();
    int u = m.second;
    
    if(d[u] < m.first*(-1)) continue;
    
    for(int i = 0; i < adj[u].size(); i++){
      int v = adj[u][i].first;
      if(d[u]+adj[u][i].second < d[v]){
	d[v] = d[u]+adj[u][i].second;
	PQ.push(make_pair(d[v]*(-1),v));
      }
    }
  }
  for(int i = 0; i < v; i++){
    if(d[i] < INFTY) cout << to_string(d[i]) << endl;
    else cout << "INF" << endl;
  }
}

int main(){
  int e,s,t,d;
  cin >> v >> e >> r;
  for(int i = 0; i < e; i++){
    cin >> s >> t >> d;
    adj[s].push_back(make_pair(t,d));
  }
  dijkstra();
  
  return 0;
}