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: Wrong Answer)

# NOTE: 1-origin (not 0-origin)
$adj_lists = []

def find_min_dist(start_node, target_node)
  if start_node == target_node
    0
  else
    nodes = $adj_lists[start_node]
    if nodes == []
      return Float::INFINITY
    else
      mins = nodes.map{|n|
        find_min_dist(n, target_node)
      }
      # p ['nodes', nodes, 'min', mins]
      return mins.min + 1
    end
  end
end

_ = gets


while line = gets
  i, _, *nodes= line.split(' ').map(&:to_i)
  $adj_lists[i] = nodes
end

# # NOTE: 1-origin
# distances = [nil] * $adj_lists.size
#
# distances[1] = 0
#
# # (1..$adj_lists.size).each{|i|
# #
# # }
#
# # p $adj_lists

# Print
(1...$adj_lists.size).each{|target_node|
  min_dist = find_min_dist(1, target_node)
  puts("#{target_node} #{min_dist}")

}

# p find_node(1, 2)
# p find_node(1, 3)
# p find_node(1, 4)
#
# # p distances