Problem:
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Single Source Shortest Path

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

All vertices are reachable from vertex $0$

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: Wrong Answer)

//Algorithms and Data Structures I - Graph II - Single Source Shortest Path I
import java.util.HashMap;
import java.util.PriorityQueue;
import java.util.Scanner;

class Node implements Comparable<Node> {
	public  int     u,
		            k,
			        d = Integer.MAX_VALUE;
	public  int[][] adj;
	boolean S;

	Node(int u, int k) {
		this.u = u;
		this.k = k;
		adj    = new int[2][k];
	}

	public int compareTo(Node n) {
		return this.d - n.d;
	}
}

class Main {

	private static PriorityQueue<Node>    Q   = new PriorityQueue<Node>();
	private static HashMap<Integer, Node> map = new HashMap<Integer, Node>();

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Node source = null,
			 nd;
		for(int i=0;i<n;i++){
			nd = new Node(sc.nextInt(), sc.nextInt());
			for (int j = 0; j < nd.k; j++) {
				nd.adj[0][j] = sc.nextInt();
				nd.adj[1][j] = sc.nextInt();
			}
			if (nd.u == 0) { nd.d   = 0 ;
			                 source = nd;}
			else           { Q.add(nd)  ;}
			map.put(nd.u, nd);
		}
		relax(source);

		while(!Q.isEmpty()){
			relax(Q.poll());
		}

		for(int i=0;i<n;i++){
			nd = map.get(i);
			System.out.println(nd.u+" "+nd.d);
		}
	}

	private static void relax(Node n){
		Node t;
		int  l;
		for(int i=0;i<n.k;i++){
			t = map.get(n.adj[0][i]);
			l = n.d+n.adj[1][i];
			if(!t.S && l<t.d){
				t.d=l;
			}
		}
		n.S = true;
	}
}