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;

namespace Graph_I
{
    class Breadth_First_Search
    {

        static int[] dist;

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

            for (int i = 0; i < n; i++)
            {
                var token = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                var row = token[0] - 1;
                G[row] = new bool[n];
                for (int j = 0; j < token[1]; j++)
                    G[row][token[2 + j] - 1] = true;
            }

            var str = new StringBuilder();

            for (int i = 0; i < n; i++)
                str.Append(i + 1).Append(" ").Append(BreadthFirstSearch(G, i)).Append("\n");
            Console.Write(str.ToString());
        }

        static int BreadthFirstSearch(bool[][] graph, int destination)
        {
            if (dist[destination] != 0) return dist[destination];
            var n = graph.Length;
            var done = new bool[n];
            var queue = new Queue<int>();

            done[0] = true;
            dist[0] = 0;
            queue.Enqueue(0);

            while (queue.Count > 0)
            {
                var r = queue.Dequeue();
                if (r == destination) return dist[r];
                for (int i = 0; i < n; i++)
                {
                    if (graph[r][i] && !done[i])
                    {
                        done[i] = true;
                        dist[i] = dist[r] + 1;
                        queue.Enqueue(i);
                    }
                }
            }

            return -1;

        }
    }
}