Problem:
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Breadth First Search

Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1, 2, ... n$.

Input

In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:

$u$ $k$ $v_1$ $v_2$ ... $v_k$

$u$ is ID of the vertex and $k$ denotes its degree.$v_i$ are IDs of vertices adjacent to $u$.

Constraints

$1 \leq n \leq 100$

Output

For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.

Sample Input 1

4
1 2 2 4
2 1 4
3 0
4 1 3

Sample Output 1

1 0
2 1
3 2
4 1

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;
using System.IO;

namespace ConsoleApplication1
{
    class Program
    {
        static readonly int INFTY = int.MaxValue;

        static void Main(string[] args)
        {
            //StreamReader inputfile = new StreamReader("input.txt");
            int n = int.Parse(Console.ReadLine());
            int[,] table = new int[n, n];

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

                for (int j = 0; j < k; j++)
                {
                    int v = int.Parse(input[2 + j]) - 1;

                    table[u, v] = 1;
                }
            }

            Dijkstra(table, n);
        }

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

            minCostArr[0] = 0;

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

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

                if (u == -1) break;

                isVisit[u] = true;

                for (i = 0; i < n; i++)
                {
                    int w = table[u, i];

                    if (w > 0)
                    {
                        int c = minCostArr[u] + w;

                        if (c < minCostArr[i])
                        {
                            minCostArr[i] = c;
                        }
                    }
                }
            }

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