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 Ruby (judge verdict: Accepted)

class Node
  attr_reader :id, :siblings
  attr_accessor :state, :distance

  def initialize(id)
    @id = id
    @siblings = []
    @state = :white
    @distance = nil
  end

  def <<(sibling)
    @siblings << sibling
  end
end

if $PROGRAM_NAME == __FILE__
  n = gets.to_i

  temp = Hash.new {|hash, id| hash[id] = Node.new(id) }

  n.times do
    id, _, *sibling_ids = gets.chomp.split.map(&:to_i)

    node = temp[id]

    sibling_ids.each do |sibling_id|
      node << temp[sibling_id]
    end
  end

  nodes = temp.values.sort_by(&:id)

  first_node = nodes.first
  first_node.distance = 0

  queue = [first_node]

  until queue.empty?
    current = queue.shift

    current.siblings.each do |sibling|
      next unless sibling.state == :white

      sibling.state = :gray
      sibling.distance = current.distance + 1

      queue << sibling
    end

    current.state = :black
  end

  nodes.each do |node|
    puts "#{node.id} #{node.distance || -1}"
  end
end