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: Time Limit Exceeded)

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

$cache= {}

# $queue = []

def find_min_dist(start_node, target_node)

  queue = []

  queue.push([start_node, 0])

  # min_dis = Float::INFINITY
  dis = 0
  while (n, d = queue.shift)
    if n == target_node
      return d
    else
    nodes = $adj_lists[n]
    nodes.each{|node|
      queue.push([node, dis])
    }
    dis += 1

    $cache[[start_node, target_node]] = dis

  end

  # $cache[[start_node, target_node]] = min_dis

  # return min_dis + 1

  # mins = nodes.map{|n|
  #
  # }
  # dis = mins.min + 1
  # $cache[[start_node, target_node]] = dis
  # return dis
  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
#
#

# Node => min dist
node_to_min_dist_hash = {}

def find(start_node, target_node)
  open_list   = [[start_node, 0]]
  closed_list = []

  while open_list.size != 0
    node, dist = open_list.shift
    if node == target_node
      # puts("Found #{node}, #{target_node}: dist #{dist}")
      return dist
    end
    # puts(node)
    nodes = $adj_lists[node]
    nodes.each{|n|
      open_list.push([n, dist+1])
    }
    closed_list.push(node)
  end

  return -1
end



def find_all(start_node)
  # Node => min dist
  node_to_min_dist_hash = Hash.new(-1)

  open_list   = [[start_node, 0]]
  closed_list = []

  while open_list.size != 0
    node, dist = open_list.shift
    # if node == target_node
    #   # puts("Found #{node}, #{target_node}: dist #{dist}")
    #   return dist
    # end

    if !node_to_min_dist_hash.has_key?(node)
      node_to_min_dist_hash[node] = dist
    end

    # puts(node)
    nodes = $adj_lists[node]
    nodes.each{|n|
      open_list.push([n, dist+1])
    }
    closed_list.push(node)
  end

  return node_to_min_dist_hash
end

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

node_to_min_dist_hash = find_all(1)

# Print
(1...$adj_lists.size).each{|target_node|
  min_dist = node_to_min_dist_hash[target_node]
  puts("#{target_node} #{min_dist}")
}

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