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)

import java.util.PriorityQueue;
import java.util.Scanner;

class Vertex implements Comparable<Vertex> {
	int no;
	int state;
	int distance;
	static final int INF = 1000000000;
	Vertex(int no) {
		this.no = no;
		state = 0;
		distance = INF;
	}
	@Override
	public int compareTo(Vertex o) {
		return Integer.compare(this.distance, o.distance); 
	}
}
public class Main {
	static int N;
	static int W[][];
	static  Vertex vertex[];

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

		W = new int[N][N];
		vertex = new Vertex[N];

		for (int i = 0; i < N; i++) {
			vertex[i] = new Vertex(i);
			for (int j = 0; j < N; j++) {
				W[i][j] = Vertex.INF;
			}
		}

		for (int i = 0; i < N; i++) {
			sc.nextInt(); // u を読み飛ばし
			int k = sc.nextInt();
			for (int j = 0; j < k; j++) {
				int v = sc.nextInt();
				int c = sc.nextInt();
				W[i][v] = c;
			}
		}
		dijkstra(0);
		for (int i = 0; i < N; i++) {
			System.out.println(i + " " + vertex[i].distance);
		}
	}

	private static void dijkstra(int start) {
		vertex[start].distance = 0;

		PriorityQueue<Vertex> que = new PriorityQueue<Vertex>();
		que.add(vertex[start]);
		for (int step = 0; step < N; step++) {
			Vertex p = que.poll(); // 確定頂点を保存する変数
			p.state = 1;
			for (int x = 0; x < N; x++) {
				if (vertex[x].distance > p.distance + W[p.no][x]) {
					vertex[x].distance = p.distance + W[p.no][x];
					que.add(vertex[x]);
				}
			}
		}

	}
}