# Cookbook/Other data structures

GHC comes with some handy data-structures by default. If you want to use a Map, use Data.Map. For sets, you can use Data.Set. A good way to find efficient data-structures is to take a look at the hierarchical libraries, see Haskell Hierarchical Libraries and scroll down to 'Data'.

## Map

A naive implementation of a map would be using a list of tuples in the form of (key, value). This is used a lot, but has the big disadvantage that most operations take O(n) time.

Using Data.Map we can construct a fast map using this data-structure:

```
import qualified Data.Map as Map
myMap :: Map.Map String Int
myMap = Map.fromList [("alice", 111), ("bob", 333), ("douglas", 42)]
```

We can then do quick lookups:

```
bobsPhone :: Maybe Int
bobsPhone = Map.lookup "bob" myMap
```

Map is often imported `qualified`

to avoid name-clashing with the Prelude. See Import for more information.

## Set

TODO

## Tree

TODO

## ByteString

TODO

## Arrays

Arrays are generally eschewed in Haskell. However, they are useful if you desperately need constant lookup or update or if you have huge amounts of raw data.

Immutable arrays like `Data.Array.IArray.Array i e`

offer lookup in constant time but they get copied when you update an element. Use them if they can be filled in one go.
The following example groups a list of numbers according to their residual after division by `n`

in one go.

```
bucketByResidual :: Int -> [Int] -> Array Int [Int]
bucketByResidual n xs = accumArray (\xs x -> x:xs) [] (0,n-1) [(x `mod` n, x) | x <- xs]
Data.Arra.IArray> bucketByResidual 4 [x*x | x <- [1..10]]
array (0,3) [(0,[100,64,36,16,4]),(1,[81,49,25,9,1]),(2,[]),(3,[])]
Data.Arra.IArray> amap reverse it
array (0,3) [(0,[4,16,36,64,100]),(1,[1,9,25,49,81]),(2,[]),(3,[])]
```

Note that the array can fill itself up in a circular fashion. Useful for dynamic programming. Here is the Edit distance between two strings without array updates.

```
editDistance :: Eq a => [a] -> [a] -> Int
editDistance xs ys = table ! (m,n)
where
(m,n) = (length xs, length ys)
x = array (1,m) (zip [1..] xs)
y = array (1,n) (zip [1..] ys)
table :: Array (Int,Int) Int
table = array bnds [(ij, dist ij) | ij <- range bnds]
bnds = ((0,0),(m,n))
dist (0,j) = j
dist (i,0) = i
dist (i,j) = minimum [table ! (i-1,j) + 1, table ! (i,j-1) + 1,
if x ! i == y ! j then table ! (i-1,j-1) else 1 + table ! (i-1,j-1)]
```

Mutable arrays like `Data.Array.IO.IOArray i e`

are updated in place, but they have to live in the IO-monad or the ST-monad in order to not destroy referential transparency. There are also diff arrays like `Data.Array.Diff.DiffArray i e`

that look like immutable arrays but do updates in place if used in a single threaded way. Here is depth first search with diff arrays that checks whether a directed graph contains a cycle. *Note: this example really belongs to Map or Set.*

```
import Control.Monad.State
type Node = Int
data Color = White | Grey | Black
hasCycle :: Array Node [Node] -> Bool
hasCycle graph = runState (mapDfs $ indices g) initSeen
where
initSeen :: DiffArray Node Color
initSeen = listArray (bounds graph) (repeat White)
mapDfs = fmap or . mapM dfs
dfs node = get >>= \seen -> case (seen ! node) of
Black -> return False
Grey -> return True -- we found a cycle
White -> do
modify $ \seen -> seen // [(node,Grey )]
found <- mapDfs (graph ! node)
modify $ \seen -> seen // [(node,Black)]
return found
```