```module CaseBi (
-- * Function that can be used instead of
--
-- > case var of
-- >   a1 -> b1
-- >   a2 -> b2
-- >   a3 -> b3
-- >   ...
-- >   an -> bn
-- >   _  -> def
--
-- for efficiency
getBFst', getBFst, getBFstV,
-- * Additional functions that are used to sort a list of pairs (which can be obtained by e. g. Prelude.zip
sortFst, sortFstV,
-- ** Function that can be used for changing the Vector (a, b) during its creation
filterP
) where

import qualified Data.Vector as V (Vector,head,last,take,drop,length,(!),fromList,map)
import qualified Data.List as L (groupBy)
import Prelude
-- (Bool,Eq,Ord,map,(>=),(<=),(>),(<),(==),(&&),(.),(++),(-),(\$),filter,otherwise,fst,snd,div,not,null,dropWhile,concatMap,take)

-- | The function that can be used instead of the 'case ... of' function
--
-- > case var of
-- >   a1 -> b1
-- >   a2 -> b2
-- >   a3 -> b3
-- >   ...
-- >   an -> bn
-- >   _  -> defaultValue
--
-- The function 'case a of ...' gives the O(n) coplexity of the transformation of a to b here,
-- but the function getBFst' tries to give about O(log n) complexity
-- The Vector v (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use
-- the following functions 'sortFst' and 'sortFstV'.
--
-- b after Vector (a, b) in the type definition of the 'getBFst' must be a defaultValue for case above.
--
-- Vector (a, b) corresponds to
--
-- >  a1 -> b1
-- >  a2 -> b2
-- >  a3 -> b3
-- >  ...
-- >  an -> bn
--
getBFst' :: (Ord a) => b -- ^ a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the 'otherwise' or irrefutable pattern analogue)
-> V.Vector (a, b) -- ^ Vector of the (a, b) tuples that are sorted in ascending order for the first argument. If there are several pairs (a, b) with the same a, the function acts as if there is only the first one
-> a -- ^ an element for which the corresponding resulting b must be found
-> b -- ^ the result
getBFst' def vec l | (l >= vElem0 vec) && (l <= vElemL vec) && (vIL vec >= 3) = if l <= fst (vec V.! (vIL vec `div` 2))
then getBFst' def v1 l
else getBFst' def v2 l
| (l >= vElem0 vec) && (l <= vElemL vec) && (vIL vec == 2) = if l == vElem0 vec
then snd . V.head \$ vec
else if l == vElem1 vec
then snd \$ vec V.! 1
else if l == vElemL vec
then snd . V.last \$ vec
else def
| (l >= vElem0 vec) && (l <= vElemL vec) && (vIL vec == 1) = if l == vElem0 vec
then snd . V.head \$ vec
else if l == vElemL vec
then snd . V.last \$ vec
else def
| (l >= vElem0 vec) && (l <= vElemL vec) && (vIL vec == 0) = snd . V.head \$ vec
| otherwise = def
where vElem0 = fst . V.head
vElem1 v = fst \$ v V.! 1
vElemL = fst . V.last
vIL v = V.length v - 1
v1  = V.take (V.length vec `div` 2) vec
v2 = V.drop (V.length vec `div` 2) vec

-- | The function that uses special kind of bisection to effectively transform the Vector a to Vector b with  instead of simply use
--
-- > case var of
-- >   a1 -> b1
-- >   a2 -> b2
-- >   a3 -> b3
-- >   ...
-- >   an -> bn
-- >   _  -> defaultValue
--
-- The function 'V.map (f (case var of ...)) [a]' gives the O(n*m) coplexity of the transformation of Vector a to Vector b here
-- where m is the length of the Vector a (and Vector b respectively here), but the function 'getBFstV' tries to give about O(m*log n) complexity
-- The Vector (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use
-- the following functions 'sortFst' and 'sortFstV'. If m >> n than the function gives more efficiency. Even otherwise,
-- it can be used to simplify the procedure for optimizing the code for transformation of the Vector data.
--
-- b after Vector (a, b) in the type definition of the 'getBFstV' must be a defaultValue for case above.
--
-- Vector (a, b) corresponds to
--
-- >  a1 -> b1
-- >  a2 -> b2
-- >  a3 -> b3
-- >  ...
-- >  an -> bn
--
getBFstV :: (Ord a) => V.Vector (a, b) -- ^ Vector of the (a, b) tuples that are sorted in ascending order for the first argument
-> b -- ^ a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the 'otherwise' or irrefutable pattern analogue)
-> V.Vector a -- ^ a Vector needed to be transformed accordingly to the correct (a, b) tuple pairs
-> V.Vector b -- ^ the resulting Vector
getBFstV c y = V.map (getBFst' y c)

-- | The function that uses special kind of bisection to effectively transform the [a] to [b] with  instead of simply use
--
-- > case var of
-- >   a1 -> b1
-- >   a2 -> b2
-- >   a3 -> b3
-- >   ...
-- >   an -> bn
-- >   _  -> defaultValue
--
-- The function 'map (f (case var of ...)) [a]' gives the O(n*m) coplexity of the transformation of [a] to [b] here
-- where m is the length of the [a] (and [b] respectively here), but the function 'getBFst' tries to give about O(m*log n) complexity
-- The Vector (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use
-- the following functions 'sortFst' and 'sortFstV'. If m >> n than the function gives more efficiency. Even otherwise,
-- it can be used to simplify the procedure for optimizing the code for transformation of the list data.
--
-- b after Vector (a, b) in the type definition of the 'getBFst' must be a defaultValue for case above.
--
-- Vector (a, b) corresponds to
--
-- >  a1 -> b1
-- >  a2 -> b2
-- >  a3 -> b3
-- >  ...
-- >  an -> bn
--
getBFst :: (Ord a) => V.Vector (a, b) -- ^ Vector of the (a, b) tuples that are sorted in ascending order for the first argument
-> b -- ^ a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the 'otherwise' or irrefutable pattern analogue)
-> [a] -- ^ a list of values needed to be transformed accordingly to the correct (a, b) tuple pairs
-> [b] -- ^ the resulting list
getBFst c y = map (getBFst' y c)

-- | Function that sorts a list of (a, b) tuples by the first argument (|@a@| must be an instance of class Ord)
-- and is inspired by Data.List.sort function (the last one can be used for sorting the (a, b) tuples where both the types of a and b
-- have instances of the class Ord).
sortFst :: (Ord a) => [(a, b)] -> [(a, b)]
sortFst xs | not . null \$ xs = let z = fst . head \$ xs in sortFst (filter (\(x, _) -> x < z) xs) ++ filter (\(x, _) -> x == z) xs ++ sortFst (filter (\(x, _) -> x > z) xs)
| otherwise = []

-- | Function that prepares the list of (a, b) tuples representing the
--
-- > case var of
-- >   a1 -> b1
-- >   a2 -> b2
-- >   a3 -> b3
-- >    ...
-- >   an -> bn
-- >   _  -> defaultValue
--
-- for usage in the 'getBFst' and 'getBFstV' functions. |@a@| must be an instance of class Ord.
--
sortFstV :: (Ord a) => [(a, b)] -> V.Vector (a, b)
sortFstV = V.fromList . sortFst

-- | The function that is used to filter a list [(a, b)] of the corresponding values for getFstB' to obtain the Vector (a, b)
-- such that the b element for the sequence of pairs (a, b) with the same a is selected by the predicate p and is not necessarily the first one
-- as it is for the getFstB' function and its successors by default.
filterP :: (Ord a) => ((a, b) -> Bool) -- ^ The predicate p used to select the only one value of b in the pairs (a, b) with the same a.
-- ^ If there are several pairs (a, b) for the same a that satisfies a predicate then the first one is used. For large [(a, b)]
-- ^ it can be rather complex.
-> [(a, b)] -- ^ The list of (a, b) sorted in the ascending order by the first element a (e. g. by the 'sortFst' function)
-> V.Vector (a, b) -- ^ The resulting filtered Vector (a, b) that can be used for getFstB' and its successor functions
--
-- Example:
--
-- > filterP (\(t, w) -> (t == "1") || (w > 'f')) . sortFst \$ [("1",'a'),("4a",'k'),("4a",'b'),("4a",'c'),("4a",'d'),("4a",'e'),("b7",'c'),("b7",'k')] = [("1",'a'),("4a",'k'),("b7",'k')]
--
filterP p xs = V.fromList . concatMap (\x -> take 1 . dropWhile (not . p) \$ x) \$ L.groupBy (\(x1,_) (x2,_) -> x1 == x2) xs

```