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Implement solution in Haskell as depth-first-search

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Bill Ewanick 2023-11-17 14:43:01 -05:00
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{-
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