{-
Keys and Rooms

Instructions:
There are n rooms labelled from 0 to n - 1 and all the rooms are locked except for room 0. Your goal is to visit all the rooms. However, you cannot enter a locked room without having its key.

When you visit a room, you may find a set of distinct keys in it. Each key has a number on it, denoting which room it unlocks, and you can take all of them with you to unlock the other rooms.

Given an array rooms where rooms[i] is the set of keys that you can obtain if you visited room i, return true if you can visit all the rooms, or false otherwise.

Constraints:
    n == rooms.length
    2 <= n <= 1000
    0 <= rooms[i].length <= 1000
    1 <= sum(rooms[i].length) <= 3000
    0 <= rooms[i][j] < n
    All the values of rooms[i] are unique.
-}
module Main where

import           Data.List (genericIndex, genericLength)

input1Rooms :: [[Integer]]
input1Rooms = [[1],[2],[3],[]]

input2Rooms :: [[Integer]]
input2Rooms = [[1,3],[3,0,1],[2],[0]]

main :: IO ()
main = do
  print $ "Example 1 is: " <> show (canVisitAll input1Rooms)
  print $ "Example 2 is: " <> show (canVisitAll input2Rooms)

canVisitAll :: [[Integer]] -> Bool
canVisitAll rooms = [0..l] == dfs rooms 0 []
  where
    l = l' rooms - 1

dfs :: [[Integer]] -> Integer -> [Integer] -> [Integer]
dfs graph current visited =
    foldl (\visited next ->
              if next `elem` visited
                then visited
                else dfs graph next visited)
           (visited ++ [current])
           (graph !!! current)

l' :: [a] -> Integer
l' = genericLength

(!!!) :: [a] -> Integer -> a
(!!!) = genericIndex