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)

n = gets.to_i
m = Array.new(n) # adjacency matrix
for i in 0..n-1
  m[i] = Array.new(n,0)
end
for i in 0..n-1
  temp = gets.chomp.split(" ").map(&:to_i)
  if temp[1] != 0
    for j in 0..temp[1]-1
      m[i][temp[j+2]-1] = 1
    end
  end
end

q = [0] # queue
d = Array.new(n,-1)
d[0] = 0
while q.length > 0
  #p ["debug", q]
  cur = q.shift
  (0..n-1).each do |dst|
    if m[cur][dst] == 1 && d[dst] == -1
      d[dst] = d[cur] + 1
      q << dst
    end
  end
end

for i in 0..n-1
  print i+1, " ", d[i], "\n"
end