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.Text;

namespace ConsoleApplication1
{
    enum Color { white, gray, black }

    class Program
    {
        static readonly int INFTY = int.MaxValue;

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

            int[][] table = new int[n][];
            for (int i = 0; i < n; i++)
            {
                table[i] = Enumerable.Repeat(INFTY, n).ToArray();
            }

            for (int i = 0; i < n; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                int u = int.Parse(input[0]);
                int k = int.Parse(input[1]);

                for (int j = 0; j < k; j++)
                {
                    int v = int.Parse(input[2 + j * 2]);
                    int c = int.Parse(input[3 + j * 2]);

                    table[u][v] = c;
                }
            }

            Dijkstra(table, n);
        }

        static void Dijkstra(int[][] table, int n)
        {
            int i, minCost;
            int[] minCostArr = Enumerable.Repeat(INFTY, n).ToArray();
            Color[] colors = new Color[n];

            minCostArr[0] = 0;
            colors[0] = Color.gray;

            while (true)
            {
                minCost = INFTY;
                int u = -1;

                for (i = 0; i < n; i++)
                {
                    if (minCost > minCostArr[i] && colors[i] != Color.black)
                    {
                        u = i;
                        minCost = minCostArr[i];
                    }
                }

                if (u == -1) break;

                colors[u] = Color.black;

                for (i = 0; i < n; i++)
                {
                    if (colors[i] != Color.black && table[u][i] != INFTY)
                    {
                        if (minCostArr[i] > minCostArr[u] + table[u][i])
                        {
                            minCostArr[i] = minCostArr[u] + table[u][i];
                            colors[i] = Color.gray;
                        }
                    }
                }
            }

            StringBuilder sb = new StringBuilder();
            for (i = 0; i < n; i++)
            {
                int temp = minCostArr[i] == INFTY ? -1 : minCostArr[i];
                sb.AppendLine(i + " " + temp);
            }
            Console.Write(sb);
        }
    }
}