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.Generic;
using System.Linq;
class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        Graph g = new Graph(n);
        for (int i = 0; i < n; i++)
        {
            int[] s = Console.ReadLine().Split(' ').Select(p => int.Parse(p)).ToArray();
            int u = s[0];
            for (int j = 2; j < s.Length; j++)
                g.SetEdge(u, s[j]);
        }
        g.BFS(1);
        for (int i = 0; i < n; i++)
            Console.WriteLine("{0} {1}", i + 1, g.d[i]);
    }
}
class Graph
{
    private int n;
    private List<int>[] adj;
    public int[] d;
    public Graph(int n)
    {
        this.n = n;
        adj = new List<int>[n];
        d = new int[n];
        for (int i = 0; i < n; i++)
        {
            adj[i] = new List<int>();
            d[i] = -1;
        }
    }
    public void SetEdge(int s, int g)
    {
        if (s > n || g > n)
            return;
        adj[s - 1].Add(g);
    }
    public List<int> GetEdge(int i)
    {
        return adj[i - 1];
    }
    public void BFS(int s)
    {
        d[s - 1] = 0;
        Queue<int> q = new Queue<int>();
        q.Enqueue(s);
        while (q.Count != 0)
        {
            int u = q.Dequeue();
            foreach (var v in GetEdge(u))
            {
                if (d[v - 1] == -1)
                {
                    d[v - 1] = d[u - 1] + 1;
                    q.Enqueue(v);
                }
            }
        }
    }
}