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: Wrong Answer)

import scala.io.StdIn._

object Main extends App {
  val max = 1000000000
  val n = readInt()
  var graph = collection.mutable.Seq.fill(n, n)(max)

  for (i <- 1 to n) {
    val input = readLine().split(" ").toList.map(_.toInt)
    val u = input.head - 1
    val k = input(1)
    for (j <- 1 to k) {
      graph(u)(input(1 + j) - 1) = 1
    }
  }

  graph.head(0) = 0

  for (k <- 0 until n) {
    for (i <- 0 until n) {
      for (j <- 0 until n) {
        graph(i)(j) = math.min(graph(i)(j), graph(i)(k) + graph(k)(j))
      }
    }
  }

  graph.head.zipWithIndex.foreach {
    case (v, i) =>
      val n = if (v == max) -1 else v
      println(s"$i $n")
  }
}