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;

namespace Graph_II
{
    class Single_Source_Shortest_Path_I
    {
        struct Edge
        {
            public int to;
            public int cost;
        }

        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var graph = new Edge[n][];

            for (int i = 0; i < n; i++)
                graph[i] = Console.ReadLine().Trim(' ').Split(' ')
                    .Skip(2)
                    .Select((s, index) => new { val = int.Parse(s), index})
                    .GroupBy(x => x.index / 2)
                    .Select(group => group.Select(g => g.val))
                    .Select(vc => new Edge { to = vc.First(), cost = vc.Last() })
                    .ToArray();

            var used = new bool[n];
            var mincost = Enumerable.Repeat(int.MaxValue, n).ToArray();
            mincost[0] = 0;

            while (true)
            {
                var v = -1;
                for (int i = 0; i < n; i++)
                    if (!used[i] && (v == -1 || mincost[i] < mincost[v])) v = i;

                if (v == -1) break;
                used[v] = true;

                for (int i = 0; i < graph[v].Length; i++)
                    mincost[graph[v][i].to] = Math.Min(mincost[graph[v][i].to], mincost[v] + graph[v][i].cost);
            }

            for (int i = 0; i < mincost.Length; i++)
                Console.WriteLine($"{i} {mincost[i]}");
        }
    }
}