module ConvexHull where

import Data.List (foldl', sort)
import Queries


addNewPoint :: (Ord a, Num a) => [Point a] -> Point a -> [Point a]
addNewPoint (p2:p1:rest) p = if (makesRightTurn p1 p2 p)
                                then p : p2 : p1 : rest
                                else addNewPoint (p1 : rest) p
addNewPoint ps p = p:ps

convexHull :: (Ord a, Show a, Num a) => [Point a] -> [Point a]
convexHull [] = []
convexHull points =
    let sortedPoints  = sort points
        upperHull = foldl' addNewPoint [] sortedPoints
        lowerHull = foldr (flip addNewPoint) [] sortedPoints
    -- Remove initial point from upperHull because it is the last point of lowerHull
    -- Remove initial point from lowerHull because it is the last point of upperHull
    in  tail upperHull ++ tail lowerHull


convexHull' :: (Ord a, Show a, Num a) => [Point a] -> [Point a]
convexHull' [] = []
convexHull' points =
    let sortedPoints  = sort points
        upperHull = foldl' addNewPoint [] sortedPoints
        lowerHull = foldl' (addNewPoint) [] (reverse sortedPoints)
    -- Remove initial point from upperHull because it is the last point of lowerHull
    -- Remove initial point from lowerHull because it is the last point of upperHull
    in  tail upperHull ++ tail lowerHull