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 <queue>
#include <algorithm>
#include <cstdio>
#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define llong long long
#define pb(a) push_back(a)
#define INF 999999999
using namespace std;
typedef pair<int, int> P;

int dy[]={0, 0, 1, -1};
int dx[]={1, -1, 0, 0};

struct edge{
	int to, cost;
};

int V, E, s;
vector<edge> e[100000];

vector<int> bellman_ford(){
	vector<int> d(V, INF);
	d[s]=0;
	
	while(1){
		bool flag=0;
		
		REP(i, V){
			REP(j, e[i].size()){
				edge ne=e[i][j];
				if(ne.cost!=INF && d[ne.to]>d[i]+ne.cost){
					d[ne.to]=d[i]+ne.cost;
					flag=1;
				}
			}
		}
		
		if(!flag) break;
	}
	
	return d;
}

int main(){
	cin >> V >> E >> s;
	
	REP(i, E){
		int f, t, d;
		cin >> f >> t >> d;
		e[f].push_back((edge){t, d});
	}
	
	vector<int> d;
	d=bellman_ford();
	
	REP(i, V){
		if(d[i]==INF) cout << "INF";
		else cout << d[i];
		cout << endl;
	}
}