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: Time Limit Exceeded)

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

public class Node
{
    public int nno { get; set; }
    public List<int> child { get; set; }
}
public class Ball
{
    public int step { get; set; }
    public int node { get; set; }
}

public class hello
{
    public static void Main()
    {
        var nodes = new List<Node>();
        var n = int.Parse(Console.ReadLine().Trim());
        for (int i = 0; i < n; i++)
        {
            string[] s = Console.ReadLine().Trim().Split(' ');
            var u = int.Parse(s[0]);
            var k = int.Parse(s[1]);
            var a = new Node { child = new List<int>(), nno = u };
            for (int j = 0; j < k; j++) a.child.Add(int.Parse(s[j + 2]));
            nodes.Add(a);
        }
        var bfs = new int[n + 1];
        for (int targ = 1; targ <= n; targ++)
        {
            var q = new Queue<Ball>();
            var qq = new Ball { node = 1, step = 0 };
            q.Enqueue(qq);
            while (true)
            {
                if (GetBFS(nodes, q, bfs, targ)) break;
            }
        }
        for (int i = 1; i <= n; i++) Console.WriteLine("{0} {1}", i, bfs[i]);
    }
    public static bool GetBFS(List<Node> node, Queue<Ball> q, int[] b, int targ)
    {
        if (q.Count() == 0)
        {
            b[targ] = -1;
            return true;
        }
        var tq = q.Dequeue();
        var tq2 = node[tq.node - 1];
        if (targ == tq.node)
        {
            b[targ] = tq.step;
            return true;
        }
        foreach (var x in tq2.child)
        {
            var tx = new Ball { step = tq.step + 1, node = x };
            q.Enqueue(tx);
        }
        return false;
    }
}