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)


Vertex = Struct.new(:id, :adj_list, :distance) do
	def to_s
		"#{id} #{distance || -1}"
	end
end

def bfs!(vertexes, distance)
	next_list = vertexes.select{ |v| v.distance.nil? }.inject([]) do |result, v| 
		v.distance = distance
		v.adj_list.select{ |v| v.distance.nil? }.inject(result) { |r, adj| r << adj }
	end

	bfs!(next_list, distance + 1) unless next_list.empty?
end

n = STDIN.gets.to_i
vertex_list = Array.new(n) { |i| Vertex.new(i + 1) }
n.times do
	vertex_no, degree, *adj_list = STDIN.gets.split.map(&:to_i)

	vertex = vertex_list[vertex_no - 1]
	vertex.adj_list = adj_list[0...degree].map! { |adj| vertex_list[adj - 1] }
end

bfs!([vertex_list[0]], 0)
vertex_list.each { |v| puts v }