Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: Runtime Error)

import scala.io.StdIn.{readInt,readLine}
  
object Main {
  def main(args:Array[String]) = {
    val n = readInt
    val d = (1 to n).map(_ => -1).toArray

    val g = {
      for(i<-0 until n) yield {
        val v = readLine.split(" ").map(_.toInt)
        (for(j<-2 until 2+v(1)) yield v(j) ).toArray
      }
    }.toArray

    var list = Array(1)
    var cnt = 0
    while(list.length > 0 && cnt <= n) {
      list = (for(e <- list) yield {
        if(d(e-1) == -1) { d(e-1) = cnt }
        g(e-1)
      }).toArray.flatten
      cnt += 1
    }

    for(i<-0 until n) println((i+1) + " " + d(i))
  }
}