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.io.StdIn.{readLine, readInt};
import scala.collection.immutable.Queue;
object Main {
    def main(args: Array[String]): Unit = {
        val n = readInt;
        val graph: Array[List[Int]] = new Array[List[Int]](n + 1);
        for (i <- (1 to n)) {
            graph(i) = readLine.split(" ").drop(2).map(_.toInt).toList;
        }
        val ret: Array[Int] = bfs(1, n + 1, graph);
        for (i <- (1 to n)) {println("%d %d".format(i, ret(i)))}
    }
    def bfs(start: Int, size: Int, graph: Array[List[Int]]): Array[Int] = {
        val status = new Array[Int](size).map(a => -1);
        def go(q: Queue[Int]): Unit = {
            q.dequeueOption match {
                case None => ();
                case Some((src, rest)) => {
                    val newQ = graph(src).foldLeft(rest) { (nq, dst) =>
                        if (status(dst) == -1) {
                            status(dst) = status(src) + 1;
                            nq.enqueue(dst);
                        } else {
                            nq;
                        }
                    }
                    go(newQ);
                }
            }
        }
        status(start) = 0;
        go(Queue[Int](start));
        status;
    }
}