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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

import static java.lang.Integer.parseInt;

/**
 * Graph II - Single Source Shortest Path I
 */
public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;

		int n = parseInt(br.readLine());

		Graph G = new Graph(n);

		for (int i = 0; i < n; i++) {
			StringTokenizer st = new StringTokenizer(br.readLine());
			int u, k;
			u = parseInt(st.nextToken());
			k = parseInt(st.nextToken());
			for (int j = 0; j < k; j++) {
				int v, c;
				v = parseInt(st.nextToken());
				c = parseInt(st.nextToken());
				Edge e = new Edge();
				e.s = G.vs[u];
				e.t = G.vs[v];
				e.cost = c;
				G.es.get(e.s).add(e);
			}
		}

		//
		G.vs[0].cost = 0;

		Queue<Vertex> pq = new PriorityQueue<>();
		pq.offer(G.vs[0]);

		while (!pq.isEmpty()) {

			Vertex s = pq.poll();
			s.passed = true;

			pq.clear();
			for (Edge e : G.es.get(s)) {
				if (!e.t.passed && e.t.cost > s.cost + e.cost) {
					e.t.cost = s.cost + e.cost;
					pq.offer(e.t);
				}
			}
		}

		for (int i = 0; i < n; i++) {
			System.out.println(i + " " + G.vs[i].cost);
		}

	} //end main
}

class Graph {
	Vertex[] vs;
	Map<Vertex, List<Edge>> es;

	Graph(int n) {
		vs = new Vertex[n];
		for (int i = 0; i < n; i++) {
			vs[i] = new Vertex();
		}
		es = new HashMap<>();
		for (int i = 0; i < n; i++) {
			es.put(vs[i], new ArrayList<>());
		}
	}
}

class Vertex implements Comparable<Vertex> {
	int cost = Integer.MAX_VALUE;
	boolean passed = false;

	@Override
	public int compareTo(Vertex o) {
		return Integer.compare(this.cost, o.cost);
	}
}

class Edge {
	Vertex s, t;
	int cost;
}