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

namespace ALDS1_11_C_BreadthFirstSearch
{
	class Program
	{
		static void Main ( string[] args )
		{
			int vertexCount = int.Parse (Console.ReadLine ());
			Graph graph = new Graph (vertexCount);

			for (int lp = 0; lp < vertexCount; lp++)
			{
				int[] inputNum = Array.ConvertAll (Console.ReadLine ().Split (' '), int.Parse);

				for (int lp2 = 0; lp2 < inputNum[1]; lp2++)
				{
					graph.GetPath (inputNum[0], inputNum[lp2 + 2]);
				}
			}

			int[] result = graph.BreadthFirstSeach (1);
			StringBuilder output = new StringBuilder (result.Length * 2);

			for (int lp = 0; lp < result.Length; lp++)
			{
				output.Append (lp + 1);
				output.Append (" ");
				output.Append (result[lp]);
				output.AppendLine ();
			}

			Console.Write (output);
		}
	}

	class Graph
	{
		public Graph ( int size )
		{
			this.Size = size;
			this.Path = new bool[this.Size][];

			for (int lp = 0; lp < this.Path.Length; lp++)
			{
				this.Path[lp] = new bool[this.Size];	
			}
		}

		private bool[][] Path { set; get; }
		private int Size { set; get; }
		private const bool Exist = true;

		public void GetPath ( int beginPoint, int adjacencyPoint )
		{
			Path[beginPoint - 1][adjacencyPoint - 1] = Exist;
		}

		public int[] BreadthFirstSeach ( int beginSearchPoint )
		{
			beginSearchPoint -= 1;

			//initialize
			Queue<int> searchQueue = new Queue<int> (Size);

			const int CannotVisit = -1;
			int[] distance = Enumerable.Repeat (CannotVisit, Size).ToArray ();

			//process
			searchQueue.Enqueue (beginSearchPoint);
			distance[beginSearchPoint] = 0;

			while (searchQueue.Count != 0)
			{
				int item = searchQueue.Dequeue ();

				for (int lp = 0; lp < Size; lp++)
				{
					//??£??\????????????
					if (Path[item][lp] == Exist)
					{
						//????¨??????????
						if (distance[lp] == CannotVisit)
						{
							//????´¢????±??????\??????
							searchQueue.Enqueue (lp);
							distance[lp] = distance[item] + 1;
						}
					}
				}
			}

			return distance;
		}
	}
}