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

public class Program
{

    public void Proc() {
        int pointCount = int.Parse(Reader.ReadLine());
        for (int i = 0; i < pointCount; i++) {
            int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a) - 1).Skip(2).ToArray();
            Path.Add(i, new List<int>());
            Path[i].AddRange(inpt);
        }

        Nullable<int>[] ans = new Nullable<int>[pointCount];
        ans[0] = 0;
        Queue<int> q = new Queue<int>();
        q.Enqueue(0);
        while(q.Count > 0) {
            int pos = q.Dequeue();

            if(!Path.ContainsKey(pos)) {
                continue;
            }
            int nextStep = ans[pos].Value + 1;
            foreach(int nextPos in Path[pos]) {
                if(ans[nextPos] == null || ans[nextPos] > nextStep) {
                    ans[nextPos] = nextStep;
                    q.Enqueue(nextPos);
                }
            }
        }
        for (int i = 0; i < pointCount; i++) {
            if(ans[i] == null) {
                Console.WriteLine((i+1) + " " + -1);
            } else {
                Console.WriteLine((i + 1) + " " + ans[i].Value);
            }
        }
    }
    private Dictionary<int, List<int>> Path = new Dictionary<int, List<int>>();


    public class Reader
    {
        private static StringReader sr;
        public static bool IsDebug = false;
        public static string ReadLine() {
            if(IsDebug) {
                if(sr == null) {
                    sr = new StringReader(InputText.Trim());
                }
                return sr.ReadLine();
            } else {
                return Console.ReadLine();
            }
        }
        private static string InputText = @"


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

";
    }

    public static void Main(string[] args)
    {
#if DEBUG
        Reader.IsDebug = true;
#endif
        Program prg = new Program();
        prg.Proc();
	}
}