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 Scala (judge verdict: Accepted)

import scala.collection.mutable.ListBuffer
import scala.io.StdIn

object Main extends App {

  val n = StdIn.readLine().toInt
  val result = Array.ofDim[Int](n, n)
  (0 until n).foreach { _ =>
    val a = StdIn.readLine().split(' ').map(_.toInt)
    (0 until a(1)).foreach { k =>
      result(a(0) - 1)(a(2 + k) - 1) = 1
    }
  }
  
  //(0 until n).foreach(i => println((i+1) + ": " +result(i).mkString(" ")))
  val color = Array.ofDim[Int](n) // 0: ini, 1: current, 9: finish
  val distance = Array.fill(n)(-1)
  var queue = ListBuffer.empty[Int]

  private val WHITE = 0
  private val GRAY = 1
  private val BLACK = 9

  color(0) = GRAY
  queue += 0 // start node
  distance(0) = 0
  while(queue.nonEmpty){
    val u = queue.head
    queue = queue.drop(1)
    (0 until n).foreach { v =>
      if(result(u)(v) == 1 && color(v) == WHITE){
        color(v) = GRAY
        distance(v) = distance(u) + 1
        queue += (v)
      }
    }
    color(u) = BLACK
  }
    

  val r = (0 until n).map(v => s"${v+1} ${distance(v)}")
  
  println(r.mkString(f"%n"))
  
}