Problem:
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Single Source Shortest Path II

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

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

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)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;


public class Main{

	@SuppressWarnings("unchecked")
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int edgeCnt = Integer.parseInt(s.nextLine());
		ArrayList[] list = new ArrayList[edgeCnt];
		for(int i=0 ; i<edgeCnt ; i++) {
			list[i] = new ArrayList();
			String[] input = s.nextLine().split(" ");
			for(int j=0 ; j<Integer.parseInt(input[1]) ; j++) {
				list[Integer.parseInt(input[0])].add(new Main().new Edge(Integer.parseInt(input[0]), Integer.parseInt(input[j*2+2]),Integer.parseInt(input[j*2+3])));
			}
		}
		int[] result = daikusutora(list);
		for(int k=0 ; k<result.length ; k++) {
			System.out.println(result[k]);
		}
	}

	@SuppressWarnings("unchecked")
	public static int[] daikusutora(ArrayList[] list) {
		int[] result = new int[list.length];
		Arrays.fill(result, Integer.MAX_VALUE);
		boolean[] visited = new boolean[list.length];
		Queue queue = new PriorityQueue();
		queue.offer(new Main().new Edge(0, 0, 0));
		result[0] = 0;
		while(! queue.isEmpty()) {
			Edge edge = (Edge) queue.poll();


			if(result[edge.endNo] < edge.weight)
				continue;

			for(int i=0 ; i<list[edge.endNo].size() ; i++) {
				Edge e = (Edge)list[edge.endNo].get(i);

				if(!visited[e.endNo]) {
					if((result[e.endNo] > result[e.startNo] + e.weight)) {
						result[e.endNo] = result[e.startNo] + e.weight;
						queue.offer(e);
					}
				}
			}
			visited[edge.startNo] = true;
		}
		return result;
	}

	class Edge implements Comparable<Edge> {

		int startNo;
		int endNo;
		int weight;

		public Edge(int startNo, int endNo, int weight) {
			this.startNo = startNo;
			this.endNo = endNo;
			this.weight = weight;
		}

		public int compareTo(Edge obj) {
			return this.weight - obj.weight;
		}
	}
}