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.ArrayList;
import java.util.Scanner;

public class Main {
    
    public long[] result;     
    class edge {
        public int a;  
        public int b;  
        public int value;  
        
        edge(int a, int b, int value) {
            this.a = a;
            this.b = b;
            this.value = value;
        }
    }
 
    public boolean getShortestPaths(int n, int s, edge[] A) {
        ArrayList<Integer> list = new ArrayList<Integer>();
        result = new long[n];
        boolean[] used = new boolean[n];
        int[] num = new int[n];
        for(int i = 0;i < n;i++) {
            result[i] = Integer.MAX_VALUE;
            used[i] = false;
        }
        result[s] = 0;    
        used[s] = true;   
        num[s] = 1;       
        list.add(s);      
        while(list.size() != 0) {
            int a = list.get(0);  
            list.remove(0);         
            for(int i = 0;i < A.length;i++) {
           
                if(a == A[i].a && result[A[i].b] > result[A[i].a] + A[i].value) { 
                    result[A[i].b] = result[A[i].a] + A[i].value;
                    if(!used[A[i].b]) {
                        list.add(A[i].b);
                        num[A[i].b]++;
                        if(num[A[i].b] > n)
                            return false;
                        used[A[i].b] = true;   
                    }
                }
            }
            used[a] = false;     
        }
        return true;
    }
    
    public static void main(String[] args) throws IOException {
    	Main test = new Main();
        BufferedReader BR = new BufferedReader(new InputStreamReader(System.in));
		String str = BR.readLine();
		String [] arr = str.split("\\s+");
        int n = Integer.parseInt(arr[0]);;
        int s = Integer.parseInt(arr[2]);;
        int p = Integer.parseInt(arr[1]);;        
        edge[] A = new edge[p];
        for(int i = 0;i < p;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]);
             A[i] = test.new edge(p1, p2, w);
        }
        if(test.getShortestPaths(n, s, A)) {
             for(int i = 0;i < test.result.length;i++){
            	 if(test.result[i]==Integer.MAX_VALUE){
            		 System.out.println("INF");
            	 }else{
            		 System.out.println(test.result[i]);
            	 } 
             }
                 
        } else
             System.out.println("null");
    }
}