adventofcode-2021/5/ventnavigator.hs

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import Data.List (nub, tails)
import Debug.Trace (traceShow, traceShowId)
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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)
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main :: IO ()
main = do
input <- getContents
let
vents = parseVents input
putStrLn (show (solution1 vents))
putStrLn (show (solution2 vents))
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solution1 :: [Line] -> Int
solution1 = length . nub . intersectAll . filterDiagonal
solution2 :: [Line] -> Int
solution2 = length . nub . traceShowId . intersectAll
intersectAll :: [Line] -> [Vector]
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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 =
[]
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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
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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)
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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)) == []
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testIntersect =
all (== True) [
testIntersect1,
testIntersect2,
testIntersect3,
testIntersect4,
testIntersect5,
testIntersect6,
testIntersect7,
testIntersect8,
testIntersect9,
testIntersect10,
testIntersect11,
testIntersect12,
testIntersect13,
testIntersect14,
testIntersect15,
testIntersect16,
testIntersect17,
testIntersect18
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]