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;
import java.util.Arrays;

public class Main {

    static class edge{
        int from, to, cost;
    }
    
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        int v = Integer.parseInt(str[0]);
        int e = Integer.parseInt(str[1]);
        int r = Integer.parseInt(str[2]);

        edge[] es = new edge[e];
        for (int i=0; i<e; i++){
            str = br.readLine().split(" ");
            edge ed = new edge();
            ed.from = Integer.parseInt(str[0]);
            ed.to = Integer.parseInt(str[1]);
            ed.cost = Integer.parseInt(str[2]);
            
            es[i] = ed;
        }

        long[] distance = new long[v];
        Arrays.fill(distance, Long.MAX_VALUE);
        distance[r] = 0;
        for(int i=0; i<v; i++){
            for(int j=0; j<e; j++){
                edge ed = es[j];
                if(distance[ed.from] != Long.MAX_VALUE)
                    distance[ed.to] = Long.min(distance[ed.to], distance[ed.from] + ed.cost);
            }
        }
        for(int i=0; i<distance.length; i++) {
            if(distance[i] == Long.MAX_VALUE){
                System.out.println("INF");
            } else {
                System.out.println(distance[i]);
            }
        }
    }
}