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: Accepted)

import java.util.Comparator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	class Edge {
		int to, dist;
		Edge(int to, int dist) {
			this.to = to; this.dist = dist;
		}
	}
	class Pair {
		int f, s;
		Pair(int f, int s) {
			this.f = f; this.s = s;
		}
	}
	class Graph {
		LinkedList<Edge> edges = new LinkedList<Edge>();
	}

	final int INF = Integer.MAX_VALUE;
	final int MAX_V = 10000;

	void run() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		
		Graph[] g = new Graph[MAX_V];
		for (int i = 0; i < MAX_V; i++)
			g[i] = new Graph();
		
		for (int i = 0; i < n; i++) {
			int u = scan.nextInt();
			int k = scan.nextInt();
			for (int j = 0; j < k; j++) {
				int v = scan.nextInt();
				int c = scan.nextInt();
				g[u].edges.add(new Edge(v, c));
			}
		}

		int[] dist = new int[MAX_V];
		for (int i = 0; i < MAX_V; i++)
			dist[i] = INF;

		Queue<Pair> que = new PriorityQueue<Pair>(new Comparator<Pair>() {
			@Override
			public int compare(Pair p1, Pair p2) {
				return p1.f - p2.f;
			}
		});
		
		dist[0] = 0;
		que.add(new Pair(0, 0));
		
		while (!que.isEmpty()) {
			Pair p = que.poll();
			int v = p.s;
			if (dist[v] < p.f) continue;
			for (int i = 0; i < g[v].edges.size(); i++) {
				Edge e = g[v].edges.get(i);
				if (dist[e.to] > dist[v] + e.dist) {
					dist[e.to] = dist[v] + e.dist;
					que.add(new Pair(dist[e.to], e.to));
				}
			}
		}
		for (int i = 0; i < n; i++)
			System.out.println(i + " " + dist[i]);
	}
	public static void main(String[] args) {
		new Main().run();
	}
}