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)

#encoding: utf-8

$map = []
$vis = [false] * 100
$depth = [0] * 100

def build_map
  $n = gets.rstrip.to_i
  $map = []
  $n.times { $map << [0] * $n}
  (1..$n).each do |node|
    arr = gets.rstrip.split(/\s/).map(&:to_i)
    u, k = arr[0], arr[1]
    node = arr[2..-1]
    node.each { |v| $map[u - 1][v - 1] = 1}
  end
end

def bfs(x)
  $depth[x] = 0
  que = [x]
  $vis[x] = true
  while not que.empty?
    u, que = que.first, que.drop(1)
    $map[u].each_with_index do |node, idx|
      if node == 1 and not $vis[idx]
        $depth[idx] = $depth[u] + 1
        $vis[idx] = true
        que << idx
      end
    end
  end
end

def solve
  build_map
  bfs(0)
end

solve

(0..$n - 1).each do |node|
  puts "#{node + 1} #{$depth[node]}"
end