Лабораторная №1 Haskell

--Задача №1

--1-ый способ:
max31 :: Int -> Int -> Int -> Int
max31 x y z = max x (max y z)

--2-ой способ:
max32 :: Int -> Int -> Int -> Int
max32 =(max .) .max

--Задача №2
min3 :: Int -> Int -> Int -> Int
min3 x y z = min x (min y z)

--Задача №3
sort2 :: Int -> Int -> (Int, Int)
sort2 x y = (min x y, max x y)

--Задача №4

--1-ый способ:
bothTrue1 :: Bool -> Bool -> Bool
bothTrue1 True True = True
bothTrue1 True False = False
bothTrue1 False True = False
bothTrue1 False False = False

--2-ой способ:
bothTrue2 :: Bool -> Bool -> Bool
bothTrue2 True x = x
bothTrue2 _ _ = False

--Задача №5
solve2 :: Double -> Double -> (Bool,Double)
solve2 0 _ = (False, 0.0)
solve2 a b = (True, -b/a)

--Задача №6

--1-ый способ:
isParallel1 :: (Int, Int) -> (Int, Int) -> (Int, Int) -> (Int, Int) -> Bool
isParallel1 (x1, y1) (x2, y2) (x3, y3) (x4, y4) = (y2 - y1) * (x4 - x3) == (x2 - x1) * (y4 - y3)

--2-ой способ:
isParallel2 :: (Int, Int) -> (Int, Int) -> (Int, Int) -> (Int, Int) -> Bool
isParallel2 (x1, y1) (x2, y2) (x3, y3) (x4, y4) = a*b == c*d
    where a = y2 - y1
          b = x4 - x3
          c = x2 - x1
          d = y4 - y3

--3-ий способ:
isParallel3 :: (Int, Int) -> (Int, Int) -> (Int, Int) -> (Int, Int) -> Bool
isParallel3 x y w z = (fst y - fst x) * (snd z - snd w) == (fst z - fst w) * (snd y - snd x)

--4-ый способ:
isParallel4 :: (Int, Int) -> (Int, Int) -> (Int, Int) -> (Int, Int) -> Bool
isParallel4 x y w z = a*b == c*d
    where a = fst y - fst x
          b = snd z - snd w
          c = fst z - fst w
          d = snd y - snd x

-- Задание №7
isIncluded :: (Double, Double) -> Double -> (Double, Double) -> Double -> Bool
isIncluded (x1, y1) r1 (x2, y2) r2 = d + r2 <= r1
    where dx = x2 - x1
          dy = y2 - y1
          d = sqrt( dx*dx + dy*dy )

{- Примеры выполнения:
isIncluded (2, 2) 5 (4, 2) 3
True
isIncluded (2, 2) 4 (3, 4) 1
True
isIncluded (2, 2) 3 (3, 4) 1
False -}

-- Задание №8
isRectangular :: (Double, Double) -> (Double, Double) -> (Double, Double) -> Bool
isRectangular (x1, y1) (x2, y2) (x3, y3) = d1 + d2 == d3 || d1 + d3 == d2 || d2 + d3 == d1
    where d1 = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1)
          d2 = (x3 - x2)*(x3 - x2) + (y3 - y2)*(y3 - y2)
          d3 = (x3 - x1)*(x3 - x1) + (y3 - y1)*(y3 - y1)

{- Примеры выполнения:
isRectangular (0, 0) (0, 10) (4, 2)
True
isRectangular (0, 0) (4, 0) (0, 6)
True
isRectangular (1, 2) (3, 6) (4, 5)
True -}

-- Задание №9
isTriangle :: Double -> Double -> Double -> Bool
isTriangle x y z = x + y + z > 2 * max x (max y z)

{- Примеры решения:
isTriangle 8 6 8
True
isTriangle 4 10 6
False
isTriangle 5 1 2
False -}

-- Задание №10
isSorted :: Double -> Double -> Double -> Bool
isSorted a b c = (a >= b && b >= c) || (a <= b && b <= c)

{- Примеры решения:
isSorted 1 2 3
True
isSorted 2 6 4
False
isSorted 10 9 7
True -}