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 C# (judge verdict: Time Limit Exceeded)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;

public class Program
{

	public void Proc()
	{
        int pointCount = int.Parse(Reader.ReadLine());
        Dictionary<int, Dictionary<int, int>> path = new Dictionary<int, Dictionary<int, int>>();
        for (int i = 0; i < pointCount; i++) {
            int[] inpt = Reader.ReadLine().Split(' ').Skip(2).Select(a => int.Parse(a)).ToArray();
            for (int j = 0; j < inpt.Length; j+=2) {
                if(!path.ContainsKey(i)) {
                    path.Add(i, new Dictionary<int, int>());
                }
                path[i][inpt[j]] = inpt[j + 1];
            }
        }
        Queue<int> que = new Queue<int>();
        Nullable<int>[] steps = new Nullable<int>[pointCount];
        steps[0] = 0;
        que.Enqueue(0);
        while(que.Count() > 0) {
            int current = que.Dequeue();
            if(!path.ContainsKey(current)) {
                continue;
            }
            path[current].Keys.ToList().ForEach(a =>
            {
                int nextStep = steps[current].Value + path[current][a];
                if (steps[a] == null || steps[a] > nextStep)
                {
                    steps[a] = nextStep;
                    que.Enqueue(a);
                }
            });
        }

        System.Text.StringBuilder ans = new System.Text.StringBuilder();
        for (int i = 0; i < pointCount; i++) {
            ans.AppendLine(i + " " + steps[i]);
        }
        Console.Write(ans.ToString());
    }


	public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"


10
0 2 1 1 2 3
1 2 3 3 2 1
2 2 3 1 6 10
3 1 4 1
4 1 7 1
5 2 3 1 6 1
6 2 3 1 8 1
7 2 5 1 8 4
8 1 9 100000
9 0

";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}