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<vector>
#include<queue>
using namespace std;
typedef pair<long long, long long> P;
int v,e,r;
struct edge{
    int to;
    long long cost;
    edge(int _to, long long _cost) :to(_to),cost(_cost){}
};
vector <edge> G[100010];
long long d[100100];

void dijkstra(int start){
    priority_queue<P,vector<P>,greater<P> > que;
    for(int i=0;i<v;i++) d[i]=1e12;
    d[start]=0;
    que.push(P(d[r],r) );

    while(!que.empty()) {
        P p=que.top();
        que.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;
                que.push(P(d[e.to],e.to));
            }
        }
    }
}
int main(){
    cin>>v>>e>>r;
    for(int i=0;i<e;i++){
        int s,t,d;
        cin>>s>>t>>d;
        G[s].push_back(edge(t,d));
    }

dijkstra(r);
for(int i=0;i<v;i++){
    if(d[i]!=1e12) cout<<d[i]<<endl;
    else cout<<"INF"<<endl;
}
}