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

class Program
{
    // Nodeのリスト
    static List<Node> nodes = new List<Node>();
    // 辿っているQueue
    static Queue<Node> queue = new Queue<Node>();

    // Node
    class Node
    {
        public int dist = -1;
        public List<int> adjacentIds;
    }

    static void Main(string[] args)
    {
    	// 行数を取得
        int n = int.Parse(Console.ReadLine().Split()[0]);

        // nodeを作成
        for (int i = 0; i < n; i++)
        {
            nodes.Add(new Node());
        }

        // nodeの中身設定
        for (int i = 0; i < n; i++)
        {
            List<int> nums = Console.ReadLine().Split().Select(str => int.Parse(str)).ToList();
            nodes[nums[0] - 1].adjacentIds = nums.GetRange(2, nums[1]).Select(id => id - 1).ToList();
        }

        // bfs
        
        Bfs(nodes[0]);

        // 出力
        for (int i = 0; i < n; i++)
        {
            System.Console.WriteLine(string.Format("{0} {1}", i + 1, nodes[i].dist));
        }
    }

    static void Bfs(Node start)
    {
        start.dist = 0;
        queue.Enqueue(start);
        while (queue.Count() > 0)
        {
            Node node = queue.Dequeue();
            foreach (var id in node.adjacentIds)
            {
                if (nodes[id].dist == -1)
                {
                    nodes[id].dist = node.dist + 1;
                    queue.Enqueue(nodes[id]);
                }
            }
        }
    }
}