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<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<utility>
#include<cmath>
#include<cstring>
#include<queue>
#include<cstdio>
#include<sstream>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define mp make_pair
#define all(in) in.begin(),in.end()
using namespace std;
//kaewasuretyuui
typedef long long ll;
typedef pair<ll,ll> pii;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef pair<int,pii> pip;
typedef vector<pip>vip;
const double PI=acos(-1);
const double EPS=1e-8;
const ll inf=1e18;
struct edge{
	int to,cost;
};
class DIJ{
	public:
	vector<vector<edge> >G;
	int n;
	vi d;//distance
	DIJ(int size){
		n=size;
		G=vector<vector<edge> >(n);
	}
	void add_edge(int a,int b,int c){
		edge e={b,c},ee={a,c};
		G[a].pb(e);
//		G[b].pb(ee);
	}
	void dij(int s){
		d=vi(n,inf);
		d[s]=0;
		priority_queue<pii>q;
		q.push(pii(0,s));
		while(!q.empty()){
			pii p=q.top();
			q.pop();
			int pos=p.second,cost=-p.first;
			if(cost>d[pos])continue;
			rep(i,G[pos].size()){
				edge e=G[pos][i];
				int to=e.to;
				int nowcost=cost+e.cost;
				if(nowcost<d[to]){
					d[to]=nowcost;
					q.push(pii(-d[to],to));
				}
			}
		}
	}
};
int main(){
	int n,m,s;
	cin>>n>>m>>s;
	DIJ dij(n);
	while(m--){
		int a,b,c;
		cin>>a>>b>>c;
		dij.add_edge(a,b,c);
	}
	dij.dij(s);
	rep(i,n)if(dij.d[i]!=inf)cout<<dij.d[i]<<endl;
		else cout<<"INF"<<endl;
}