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: Memory Limit Exceeded)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);

		int numOfVertex = scanner.nextInt();
		int numOfEdge = scanner.nextInt();
		int source = scanner.nextInt();
		int[][] weightedAdjacencyMatrix = new int[numOfVertex][numOfVertex];
		
		for(int i=0; i<numOfVertex; i++) {
			for(int j=0; j<numOfVertex; j++) {
				weightedAdjacencyMatrix[i][j] = -1;
			}
		}

		for(int i=0; i<numOfEdge; i++) {
			int s = scanner.nextInt();
			int t = scanner.nextInt();
			int weight = scanner.nextInt();

			weightedAdjacencyMatrix[s][t] = weight;
		}

		int[][] shortestPathMatrix = new int[numOfVertex][numOfVertex];
		final int INF = 100000000;
		for(int i=0; i<numOfVertex; i++) {
			for(int j=0; j<numOfVertex; j++) {
				if(i!=j) {
					int cost = weightedAdjacencyMatrix[i][j];
					shortestPathMatrix[i][j] = (cost>-1) ? cost : INF;
				}
			}
		}


		for(int k=0; k<numOfVertex; k++) {
			for(int i=0; i<numOfVertex; i++) {
				for(int j=0; j<numOfVertex; j++) {
					int distance = shortestPathMatrix[i][k] + shortestPathMatrix[k][j];
					if (distance <  shortestPathMatrix[i][j]) {
						shortestPathMatrix[i][j] = distance;
					}
				}
			}
		}


		for(int i=0; i<numOfVertex; i++) {
			String cost = shortestPathMatrix[source][i]!=INF ? String.valueOf(shortestPathMatrix[source][i]) : "INF";
			System.out.println(cost);
		}

		scanner.close();
	}

}