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 JAVA (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Edge{
	int u,v;
	int weight;
}

public class Main{
	int nodenum, edgenum, source;
	int[] dist;
	Edge[] edge;
	public static void main(String[] args) throws IOException{
		Main f = new Main();
		f.init();
		if (f.Bellman_Ford()){
			for(int i=0;i<f.nodenum;i++){
				if(f.dist[i]==500000000){
					System.out.println("INF");
				}else{
					System.out.println(f.dist[i]);
				}
			}
		}
	}
	public void init() throws IOException{
		BufferedReader BR = new BufferedReader(new InputStreamReader(System.in));
		String str = BR.readLine();
		String [] arr = str.split("\\s+");
		this.nodenum = Integer.parseInt(arr[0]);
		this.edgenum = Integer.parseInt(arr[1]);
		this.source = Integer.parseInt(arr[2]);
		dist = new int[nodenum];
		edge = new Edge[edgenum];
		for(int i=0;i<edgenum;i++){
			edge[i] = new Edge();
		}
		for(int i=0;i<nodenum;i++){
			dist[i] = 500000000;
		}
		dist[source] = 0;
		for(int i=0;i<edgenum;i++){
			String tempstr = BR.readLine();
			String [] temparr = tempstr.split("\\s+");
			int p1 = Integer.parseInt(temparr[0]);
			int p2 = Integer.parseInt(temparr[1]);
			int w = Integer.parseInt(temparr[2]);
			edge[i].u = p1;
			edge[i].v = p2;
			edge[i].weight = w;
			if(edge[i].u == source){
				dist[edge[i].v] = edge[i].weight;
			}
		}
	}
	
	public void relax(int u, int v, int weight){
		if(dist[v]>dist[u] + weight){
			//System.out.println(dist[v]+" "+dist[u]+" "+weight);
			dist[v] = dist[u] + weight;
			//System.out.println(dist[v]);
		}
	}
	
	public boolean Bellman_Ford(){
		for(int i=0;i<nodenum-1;i++){
			for(int j=0;j<edgenum; j++){
				relax(edge[j].u, edge[j].v, edge[j].weight);
			}
		}
		boolean flag = true;
		for(int i=0;i<edgenum;i++){
			if(dist[edge[i].v] > dist[edge[i].u] + edge[i].weight){
				flag = false;
				break;
			}
		}
		return flag;
	}
}