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.Collections.Generic;
using System.Linq;
using System.Diagnostics;

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());

        // 隣接行列を用いる
        var matrix = new long[n, n];

        for (int i = 0; i < n; i++)
        {
            string[] cin = Console.ReadLine().Split();
            for (int j = 0; j < int.Parse(cin[1]); j++)
            {
                matrix[i, int.Parse(cin[2 + 2 * j])] = long.Parse(cin[3 + 2 * j]);
            }
        }
        long[] dist = Dijkstra(n, 0, matrix);

        // [高速化]出力多いのでまとめてFlushする
        Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        for (int i = 0; i < n; i++)
        {
            Console.WriteLine(i + " " + dist[i]);
        }
        Console.Out.Flush();
    }
    static long[] Dijkstra(int n, int s, long[,] matrix)
    {
        var dist = new long[n];
        for (int i = 0; i < n; i++)
        {
            dist[i] = long.MaxValue;
        }
        dist[s] = 0;

        var fix = new bool[n];

        while (true)
        {
            int p = int.MaxValue;
            long q = long.MaxValue;
            for (int i = 0; i < n; i++)
            {
                if (!fix[i] && dist[i] <= q)
                {
                    p = i;
                    q = dist[i];
                }
            }
            if (p == int.MaxValue) break;
            fix[p] = true;
            for (int i = 0; i < n; i++)
            {
                if (!fix[i] && matrix[p, i] != 0) dist[i] = Math.Min(dist[i], dist[p] + matrix[p, i]);
            }
        }
        return dist;
    }
}