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 C# (judge verdict: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
static long n = long.Parse(Console.ReadLine());//頂点数
static long[,] nextMatrix = new long[n,n];//隣接行列

	static void Main()
	{
    for(long i = 0; i < n; i++)
    {
      for(long j = 0; j < n; j++)
      {
        nextMatrix[i,j] = long.MaxValue;//隣接しない頂点は距離無限と仮定
      }
    }

    for(long i = 0; i < n; i++)
    {
      long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
      for(long j = 0; j < nums[1]; j++)
      {
        nextMatrix[i,nums[2*(j+1)]] = nums[2*(j+1)+1];//隣接行列の作成
      }
    }

    Dijkstra();

  }

    static void Dijkstra()
    {
      long minDistance;//更新する頂点の中での最短距離
      long[] distances = new long[n];//最短距離のメモ
      long[] colors = new long[n];//0で未確認、2で最短距離確定

      for(long i = 0; i < n; i++)
      {
        distances[i] = long.MaxValue;
        colors[i] = 0;
      }

      distances[0] = 0;
      colors[0] = 1;
      while(true)
      {
        minDistance = long.MaxValue;
        long minVertex = -1;//最短距離を更新した頂点番号
        for(long i = 0; i < n; i++)
        {
          if(distances[i] < minDistance && colors[i] != 2)
          {
            minVertex = i;
            minDistance = distances[i];
          }
        }

        if(minVertex == -1) break;//最短距離の更新がなかった場合
        colors[minVertex] = 2;
        for(long i = 0; i < n; i++)
        {
          if(colors[i] != 2 && nextMatrix[minVertex,i] != long.MaxValue)//未確定の頂点
          {
            if(distances[i] > distances[minVertex] + nextMatrix[minVertex,i])
            {
              distances[i] = distances[minVertex] + nextMatrix[minVertex,i];
              colors[i] = 1;
            }
          }
        }
      }

      for(long i = 0; i < n; i++)
      {
        Console.WriteLine(i + " " + (distances[i] == long.MaxValue? "-1" : distances[i].ToString()));
      }
      
    }
    
}