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)

# bfs.rb
#ALDS1_11_C

$n = STDIN.gets.split[0].to_i
$rinsetu = Array.new(101).map{Array.new(101,0)}
$d = Array.new(101,9999999)
$q = Array.new

1.upto($n){|i|
  s = STDIN.gets.split
  u = s[0].to_i
  k = s[1].to_i
  0.upto(k-1){|j| 
    v = s[2+j].to_i
    $rinsetu[u][v] = 1
  }
}

$q << 1
$idx = 0
$d[1]=0

while $idx < $q.length
  node = $q[$idx]
#  printf("node=%d\n",node)
  1.upto($n) {|i|
    if i != node && $rinsetu[node][i]==1 && $d[i] > 1+$d[node]
      $d[i] = 1+$d[node] 
      $q << i
    end
  }
  $idx += 1
end

1.upto($n) {|i|
  if $d[i] != 9999999 
    printf("%d %d\n",i,$d[i])
  else
    printf("%d -1\n",i)
  end
}