{-# LANGUAGE DeriveDataTypeable #-}
{-|
Module      : $Header$
Description : Calculate schedules
Copyright   : (c) Justus Adam, 2015
License     : LGPL-3
Maintainer  : development@justusadam.com
Stability   : experimental
Portability : POSIX

This module provides functions for calculating possibilities for an ideal
schedule layout from weighted Lessons as well as providing functions for
converting them into readable/printable format.
-}
module SchedulePlanner.Calculator.Solver
  ( calcFromMap
  , calcFromList
  , mapToSubject
  , totalWeight
  , time
  , MappedSchedule(..)
  , MappedLessons(..)
  ) where

import           Control.Arrow         ((&&&))
import           Data.List             as List (sortBy, uncons)
import qualified Data.Map              as Map (Map, empty, foldl, fromListWith,
                                               insert, keys, lookup, map, null)
import           Data.Maybe            (fromMaybe)
import qualified Data.Ord              as Ord (comparing)
import           SchedulePlanner.Types



{-|
  type Alias for readability
  maps lessons to their respective subject
-}
newtype MappedLessons s  = MappedLessons { unMapLessons :: Map.Map s [Lesson s] }


{-|
  type Alias for readability
  represents a schedule
-}
newtype MappedSchedule s = MappedSchedule { unMapSchedule :: Map.Map Cell (Lesson s) }


-- | Convenience function extracing the (day, timeslot) 'Tuple' from a 'Lesson'
time :: Lesson a -> Cell
time = Cell . (day &&& timeslot)


-- | Convenience function to obtain the total weight of a particular Schedule
totalWeight :: MappedSchedule a -> Int
totalWeight = Map.foldl (+) 0 . Map.map weight . unMapSchedule


{-|
  Map a List of 'Lesson's to their respective subjects
-}
mapToSubject :: Ord s => [Lesson s] -> MappedLessons s
mapToSubject = MappedLessons . Map.fromListWith (++) . map (subject &&& (:[]))


{-|
  Same as 'calcFromMap' but operates on a List of 'Lesson's
-}
calcFromList :: Ord s => [Lesson s] -> Maybe [MappedSchedule s]
calcFromList = calcFromMap . mapToSubject


{-|
  Main evaluation function
  Transforms a map of weighted 'Lesson's of a particular subject into a list
  of lightest schedules by branching the evaluation at avery point
  where there is a timeslot collision
-}
calcFromMap :: Ord s
            => MappedLessons s
            -> Maybe [MappedSchedule s]
calcFromMap (MappedLessons mappedLessons)
  | Map.null mappedLessons  = Nothing
  | otherwise               = reduceLists subjX (MappedLessons sortedLessons) (MappedSchedule Map.empty) minList
  where
    sortedLessons     = Map.map (List.sortBy (Ord.comparing weight)) mappedLessons
    (subjX : minList) = Map.keys sortedLessons


{-|
  One of the essential calculation steps, reducing the subject lists and
  recursing the calculation
-}
reduceLists :: Ord s
            => s
            -> MappedLessons s
            -> MappedSchedule s
            -> [s]
            -> Maybe [MappedSchedule s]
reduceLists s (MappedLessons mappedLessons) schedules subjects =
  Map.lookup s mappedLessons >>= uncons >>=
    \(c, cs)  -> calc' c (MappedLessons $ Map.insert s cs mappedLessons) schedules subjects


{-|
  Helper function for 'calcFromMap'
  represents a recusively called and forking calculation step
-}
calc' :: Ord s
      => Lesson s
      -> MappedLessons s
      -> MappedSchedule s
      -> [s]
      -> Maybe [MappedSchedule s]
calc' x lists (MappedSchedule hourMap) minList =
  maybe
    maybeEnd
    splitCalc
    (Map.lookup (time x) hourMap)

  where
    maybeEnd = maybe
                (return [newMap])
                (\(c, cs) -> reduceLists c lists newMap cs)
                (uncons minList)

    sideCalc element aMap = fromMaybe [] (reduceLists (subject element) lists aMap minList)

    splitCalc old         = return $ sideCalc x (MappedSchedule hourMap) ++ sideCalc old newMap

    newMap                = MappedSchedule $ Map.insert (time x) x hourMap