Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
public static class P
{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());

        int[][] childs = new int[n][];
        for (int i = 0; i < n; i++)
        {
            var data = Console.ReadLine().Split().Select(int.Parse).ToArray();
            childs[data[0] - 1] = data.Skip(2).Select(x => x - 1).OrderBy(x => x).ToArray();
        }

        int[] dist = Enumerable.Repeat(-1, n).ToArray();
        Queue<int> queue = new Queue<int>();
        dist[0] = 0;
        queue.Enqueue(0);
        while (queue.Count > 0)
        {
            var elem = queue.Dequeue();
            foreach (var item in childs[elem])
            {
                if (dist[item] != -1) continue;
                dist[item] = dist[elem] + 1;
                queue.Enqueue(item);
            }
        }
        for (int i = 0; i < n; i++)
        {
            Console.WriteLine($"{i + 1} {dist[i]}");
        }
    }
}