209 lines
6.6 KiB
Haskell
209 lines
6.6 KiB
Haskell
import Data.List (nub, tails)
|
|
import Debug.Trace (traceShow, traceShowId)
|
|
import Parsing (splitByString)
|
|
|
|
type Line = ((Int, Int), (Int, Int))
|
|
type Vector = (Int, Int)
|
|
|
|
fromLine :: Line -> Vector
|
|
fromLine ((x1, y1), (x2, y2)) = (x2 - x1, y2 - y1)
|
|
|
|
vCross2D :: Vector -> Vector -> Int
|
|
vCross2D (x1, y1) (x2, y2) = x1 * y2 - y1 * x2
|
|
|
|
vSubtract :: Vector -> Vector -> Vector
|
|
vSubtract (x1, y1) (x2, y2) = (x2 - x1, y2 - y1)
|
|
|
|
vAdd :: Vector -> Vector -> Vector
|
|
vAdd (x1, y1) (x2, y2) = (x1 + x2, y1 + y2)
|
|
|
|
sMult :: Int -> Vector -> Vector
|
|
sMult s (x, y) = (s * x, s * y)
|
|
|
|
sDiv :: Int -> Vector -> Vector
|
|
sDiv s (x, y) = (x `quot` s, y `quot` s)
|
|
|
|
main :: IO ()
|
|
main = do
|
|
input <- getContents
|
|
let
|
|
vents = parseVents input
|
|
putStrLn (show (solution1 vents))
|
|
putStrLn (show (solution2 vents))
|
|
|
|
solution1 :: [Line] -> Int
|
|
solution1 = length . nub . intersectAll . filterDiagonal
|
|
|
|
solution2 :: [Line] -> Int
|
|
solution2 = length . nub . traceShowId . intersectAll
|
|
|
|
intersectAll :: [Line] -> [Vector]
|
|
intersectAll =
|
|
flatten . (map intersectOne) . (combinations 2)
|
|
where
|
|
intersectOne :: [Line] -> [Vector]
|
|
intersectOne [] = []
|
|
-- "other" is a vector of size 1, so (head other) is fine
|
|
intersectOne (vent:other) = intersect vent (head other)
|
|
|
|
intersect :: Line -> Line -> [Vector]
|
|
intersect l1@(p, _) l2@(q, _)
|
|
-- Colinear
|
|
| rsAngle == 0 && qprAngle == 0 =
|
|
intersect1D l1 l2
|
|
|
|
-- Parallel, non-intersecting
|
|
| rsAngle == 0 && qprAngle /= 0 =
|
|
[]
|
|
|
|
-- Intersecting
|
|
| rsAngle /= 0
|
|
&& qpsAngle `dividesUnit` rsAngle
|
|
&& qprAngle `dividesUnit` rsAngle =
|
|
[intersection]
|
|
|
|
-- Non-parllel, non-intersecting
|
|
| otherwise =
|
|
[]
|
|
|
|
where
|
|
r = fromLine l1
|
|
s = fromLine l2
|
|
rsAngle = r `vCross2D` s
|
|
qprAngle = (p `vSubtract` q) `vCross2D` r
|
|
qpsAngle = (p `vSubtract` q) `vCross2D` s
|
|
intersection = q `vAdd` (rsAngle `sDiv` (qprAngle `sMult` s))
|
|
|
|
intersect1D :: Line -> Line -> [Vector]
|
|
intersect1D l1@((x1, y1), (x1', y1')) l2@((x2, y2), (x2', y2'))
|
|
-- Note that when we're here all cases are colinear (and perhaps
|
|
-- overlapping). This means that the lines must occupy the same
|
|
-- axes, and we only need to check the orientation of one.
|
|
|
|
-- Diagonal lines; if these overlap, they overlap in a range
|
|
-- given by the overlap in their projections on the x and y axis
|
|
| isDiagonal l1 = zip (overlap (x1, x1') (x2, x2')) (overlap (y1, y1') (y2, y2'))
|
|
-- Others overlap in the range where their respective x/y axis
|
|
-- projection overlaps, and the other doesn't change
|
|
| isHorizontal l1 = zip (repeat x1) (overlap (y1, y1') (y2, y2'))
|
|
| isVertical l1 = zip (overlap (x1, x1') (x2, x2')) (repeat y1)
|
|
where
|
|
isDiagonal :: Line -> Bool
|
|
isDiagonal ((x, y), (x', y')) = x /= x' && y /= y'
|
|
isHorizontal :: Line -> Bool
|
|
isHorizontal ((x, y), (x', y')) = x == x'
|
|
isVertical :: Line -> Bool
|
|
isVertical ((x, y), (x', y')) = y == y'
|
|
overlap :: Vector -> Vector -> [Int]
|
|
overlap (a, b) (c, d) =
|
|
let
|
|
(a', b') = sortedTuple (a, b)
|
|
(c', d') = sortedTuple (c, d)
|
|
start = max a' c'
|
|
end = min b' d'
|
|
in
|
|
[start..end]
|
|
where
|
|
sortedTuple :: Vector -> Vector
|
|
sortedTuple (a, b)
|
|
| a > b = (b, a)
|
|
| otherwise = (a, b)
|
|
|
|
-- Whether a division will give a number 0 <= x <= 1
|
|
dividesUnit :: Int -> Int -> Bool
|
|
dividesUnit a b
|
|
| a == 0 = True
|
|
| a > 0 = a <= b
|
|
| a < 0 = a >= b && b < 0
|
|
|
|
filterDiagonal :: [Line] -> [Line]
|
|
filterDiagonal = filter (not . isDiagonal)
|
|
where
|
|
isDiagonal :: Line -> Bool
|
|
isDiagonal ((x, y), (x', y')) = x /= x' && y /= y'
|
|
|
|
parseVents :: String -> [Line]
|
|
parseVents = tupelize . splitUp
|
|
where
|
|
tupelize :: [[[Int]]] -> [Line]
|
|
tupelize = map subTupelize
|
|
where
|
|
subTupelize :: [[Int]] -> Line
|
|
subTupelize [[a, b], [c, d]] = ((a, b), (c, d))
|
|
-- For our parsing purposes, we don't need to cover error
|
|
-- cases
|
|
subTupelize _ = undefined
|
|
splitUp :: String -> [[[Int]]]
|
|
splitUp = (map (map (map read))) . (map (map (splitByString ","))) . (map (splitByString " -> ")) . lines
|
|
|
|
-- Missing stdlib functions
|
|
|
|
combinations :: Int -> [a] -> [[a]]
|
|
combinations 0 _ = [[]]
|
|
combinations n xs = [y:ys | y:xs' <- tails xs
|
|
, ys <- combinations (n-1) xs']
|
|
|
|
flatten :: [[a]] -> [a]
|
|
flatten = foldr1 (++)
|
|
|
|
-- Tests
|
|
|
|
testInput1 :: String
|
|
testInput1 = unlines [
|
|
"0,9 -> 5,9",
|
|
"8,0 -> 0,8",
|
|
"9,4 -> 3,4",
|
|
"2,2 -> 2,1",
|
|
"7,0 -> 7,4",
|
|
"6,4 -> 2,0",
|
|
"0,9 -> 2,9",
|
|
"3,4 -> 1,4",
|
|
"0,0 -> 8,8",
|
|
"5,5 -> 8,2"
|
|
]
|
|
|
|
test1 = solution1 (parseVents testInput1)
|
|
test2 = solution2 (parseVents testInput1)
|
|
|
|
testIntersect1 = intersect ((0, 0), (0, 5)) ((0, 2), (0, 4)) == [(0, 2), (0, 3), (0, 4)]
|
|
testIntersect2 = intersect ((0, 0), (0, 5)) ((0, 5), (0, 6)) == [(0, 5)]
|
|
testIntersect3 = intersect ((0, 0), (0, 5)) ((0, 6), (0, 7)) == []
|
|
testIntersect4 = intersect ((0, 0), (5, 0)) ((2, 0), (4, 0)) == [(2, 0), (3, 0), (4, 0)]
|
|
testIntersect5 = intersect ((0, 0), (0, 5)) ((0, 2), (4, 2)) == [(0, 2)]
|
|
testIntersect6 = intersect ((0, 0), (0, 5)) ((0, 3), (4, 3)) == [(0, 3)]
|
|
testIntersect7 = intersect ((1, 0), (1, 5)) ((0, 2), (4, 2)) == [(1, 2)]
|
|
testIntersect8 = intersect ((4, 0), (4, 5)) ((0, 2), (4, 2)) == [(4, 2)]
|
|
testIntersect9 = intersect ((1, 0), (1, 5)) ((2, 2), (4, 2)) == []
|
|
testIntersect10 = intersect ((9, 4), (3, 4)) ((7, 0), (7, 4)) == [(7, 4)]
|
|
testIntersect11 = intersect ((2, 2), (2, 1)) ((3, 4), (1, 4)) == []
|
|
testIntersect12 = intersect ((0, 9), (5, 9)) ((7, 0), (7, 4)) == []
|
|
testIntersect13 = intersect ((9, 4), (3, 4)) ((3, 4), (1, 4)) == [(3, 4)]
|
|
testIntersect14 = intersect ((0, 0), (1, 1)) ((1, 1), (2, 2)) == [(1, 1)]
|
|
testIntersect15 = intersect ((0, 0), (3, 3)) ((1, 1), (3, 3)) == [(1, 1), (2, 2), (3, 3)]
|
|
testIntersect16 = intersect ((0, 0), (3, 3)) ((4, 4), (8, 8)) == []
|
|
testIntersect17 = intersect ((0, 1), (1, 2)) ((1, 2), (3, 4)) == [(1, 2)]
|
|
testIntersect18 = intersect ((0, 1), (3, 4)) ((1, 2), (3, 4)) == [(1, 2), (2, 3), (3, 4)]
|
|
testIntersect19 = intersect ((0, 1), (3, 4)) ((0, 0), (3, 3)) == []
|
|
|
|
testIntersect =
|
|
all (== True) [
|
|
testIntersect1,
|
|
testIntersect2,
|
|
testIntersect3,
|
|
testIntersect4,
|
|
testIntersect5,
|
|
testIntersect6,
|
|
testIntersect7,
|
|
testIntersect8,
|
|
testIntersect9,
|
|
testIntersect10,
|
|
testIntersect11,
|
|
testIntersect12,
|
|
testIntersect13,
|
|
testIntersect14,
|
|
testIntersect15,
|
|
testIntersect16,
|
|
testIntersect17,
|
|
testIntersect18
|
|
]
|