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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Practice
{
    class Program
    {
        const int WHITE = 0;
        const int GRAY = 1;
        const int BLACK = 2;
        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        static void SolveA(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[,] m = new int[n, n];
            for(int i=0;i<n;++i)
            {
                string[] szarr = Console.ReadLine().Split(' ');
                //int u = int.Parse(szarr[0]);
                int k = int.Parse(szarr[1]);
                for(int j=0;j<k;++j)
                {
                    int v =int.Parse( szarr[j+ 2]);
                    int idx = v - 1;
                    m[i, idx] = 1;
                }
            }
            int[] color = new int[n];
            int[] d = new int[n];
            for(int i=0;i<d.Length;++i)
            {
                d[i] = -1;
            }
            var q = new Queue<int>();
            for(int i=0;i<n;++i)
            {
                if(d[i] == -1)
                {
                    BFS(i, color, d, q, m);
                }
            }
            for(int i=0;i<n;++i)
            {
                string sz = string.Format("{0} {1}", i + 1, d[i]);
                Console.WriteLine(sz);
            }
        }
        static void BFS(int s, int[] color, int[] d, Queue<int> q, int[,] m)
        {
            color[s] = GRAY;
            d[s] = 0;
            q.Enqueue(s);
            while(q.Count >= 1)
            {
                int u = q.Dequeue();
                for(int v = 0;v<d.Length;++v)
                {
                    if(m[u,v] != 0 && color[v] == WHITE)
                    {
                        color[v] = GRAY;
                        d[v] = d[u] + 1;
                        q.Enqueue(v);
                    }
                }
                color[u] = BLACK;
            }
         }
        static int Next(int[,] m , int u, int[] color)
        {
            for(int i=0;i<m.GetLength(0);++i)
            {
                if(m[u,i] == 1 && color[i] == WHITE)
                {
                    return i;
                }
            }
            return -1;
        }
    }

}