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 Haskell (judge verdict: Accepted)

import qualified Data.Array.IArray as IA
import Data.Array.ST
import Control.Monad
import Control.Applicative
import Control.Monad.ST

type Graph = IA.Array Int [Int]
type Result = IA.Array Int Int
type STResult s = STArray s Int Int

main :: IO ()
main = do
  n <- readLn :: IO Int
  ns <- replicateM n $ do
    (n:_:ns') <- getInts
    return (n, ns')
  let g = makeGraph n ns
  mapM_ putStrLn $ res2str $ solve n g

getInts :: IO [Int]
getInts = map read . words <$> getLine

makeGraph :: Int -> [(Int, [Int])] -> Graph
makeGraph n = IA.accumArray (++) [] (1, n)  

res2str :: Result -> [String]
res2str res = map (\i ->
                     show i
                     ++ " "
                     ++ show (let r = res IA.! i in
                                 if r == n+1
                                 then (-1)
                                 else r))
              [1..n]
              where
                n = snd (IA.bounds res)

solve :: Int -> Graph -> Result
solve n graph = runSTArray $ do
  res <- newArray (1, n) (n+1) 
  bfs 1 0 res
  return res
  where
    bfs :: Int -> Int -> STResult s -> ST s Int
    bfs current depth res
      | depth == (n+1) = return current
      | otherwise = do
          writeArray res current depth
          cs <- filterM
                (\i -> do
                    s <- readArray res i
                    return (s > depth)) $ graph IA.! current
          if null cs
            then return current
            else do
            mapM_ (\i -> bfs i (depth+1) res) cs
            return current