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 <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <utility>
#include <functional>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int INF = 1000000010;

struct edge{
    int to,cost;
};
class Dijkstra{
    public:
        vector<int> d;//始点からの距離
        vector<vector<edge>> G;//辺とそのコスト
        int s;
        priority_queue<P,vector<P>,greater<P>> q;
        Dijkstra(int n,int _s):d(n,INF),G(n),s(_s){
            d[s] = 0;
        }

        void solve(){
            q.push(P(0,s));
            while(q.size()){
                P p = q.top();
                q.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;
                        q.push(P(d[e.to],e.to));
                    }
                }
            }
        }
};


int main(){
    int v,e,s;
    cin >> v >> e >> s;

    Dijkstra dij(v,s);

    for(int i = 0;i < e;i++){
        int a,b,d;
        cin >> a >> b >> d;
        dij.G[a].push_back(edge{b,d});
    }

    dij.solve();

    for(int i = 0;i < v;i++){
        if(dij.d[i] != INF)cout << dij.d[i] << endl;
        else cout << "INF" << endl;
    }
}