[Haskell] Exercise 4.1 - 4.4

○ Exercise 4.1
maxFourを３通りの方法で書く。maxは自分の書いた物を使う様に指定。

import Prelude hiding (max)
max :: Int -> Int -> Int
max x y
  | x >= y    = x
  | otherwise = y

maxThree :: Int -> Int -> Int -> Int
maxThree x y z = max (max x y) z

maxFour1 :: Int -> Int -> Int -> Int -> Int
maxFour1 x y z w = max (max (max x y) z) w

maxFour2 :: Int -> Int -> Int -> Int -> Int
maxFour2 x y z w = max (max x y) (max z w)

maxFour3 :: Int -> Int -> Int -> Int -> Int
maxFour3 x y z w = max (maxThree x y z) w

○ Exercise 4.2
betweenは昇順でも降順でもTrueになる様に作る。

between :: Int -> Int -> Int -> Bool
between x y z = (weakAscendingOrder x y z)
                || (weakAscendingOrder z y x)

weakAscendingOrder :: Int -> Int -> Int -> Bool
weakAscendingOrder x y z = (x<=y) && (y<=z)

Main> between 1 2 3
True
Main> between 3 2 1
True
Main> between 3 2 2
True
Main> between 3 1 2
False
Main> between 1 3 2
False
Main> between 1 3 3
True
Main> 

○ Exercise 4.3
指示通り Exercise 3.7, 3.8 で作った関数を再利用する。

-- from Ex3.8
threeEquals :: Int -> Int -> Int -> Bool
threeEquals m n p = (m==n) && (n==p)

-- from Ex3.7
threeDifferent :: Int -> Int -> Int -> Bool
threeDifferent m n p = (m /= n) && (n /= p) && (p /= m)

howManyEquals :: Int -> Int -> Int -> Int
howManyEquals x y z
  | threeEquals    x y z  = 3
  | threeDifferent x y z  = 0
  | otherwise             = 2

Main> howManyEquals 34 25 36
0
Main> howManyEquals 34 25 34
2
Main> howManyEquals 34 34 34
3
Main> 

○ Exercise 4.4
とりあえずの回答。

howManyOfFourEqual :: Int -> Int -> Int -> Int -> Int
howManyOfFourEqual x y z w
  | (x == y) && (y == z) && (z == w)     = 4
  | threeEquals x y z                    = 3
  | threeEquals y z w                    = 3
  | threeEquals z x y                    = 3
  | threeEquals w x y                    = 3
  | x == y                               = 2
  | x == z                               = 2
  | x == w                               = 2
  | y == z                               = 2
  | y == w                               = 2
  | z == w                               = 2
  | otherwise                            = 0

Main> howManyOfFourEqual 1 2 3 4
0
Main> howManyOfFourEqual 1 2 3 3
2
Main> howManyOfFourEqual 1 3 3 3
3
Main> howManyOfFourEqual 3 3 3 3
4
Main> howManyOfFourEqual 1 3 3 1
2
Main> 

別解：比較の６個の組み合わせの等号の数を数える。（Haskellっぽくない？）

isEq :: Int -> Int -> Int
isEq x y
  | x == y    = 1
  | otherwise = 0

howManyOf4Equal :: Int -> Int -> Int -> Int -> Int
howManyOf4Equal x y z w = 
  case (count x y z w) of
    6 -> 4 -- all combination ==
    3 -> 3 -- x == y == z == x
    2 -> 2 -- example x == y /= z == w
    1 -> 2 -- example x == y only
    0 -> 0
  where count x y z w = (isEq x y) + (isEq x z) + (isEq x w)
                          + (isEq y z) + (isEq y w) + (isEq z w)

Main> howManyOf4Equal 1 2 3 4
0
Main> howManyOf4Equal 1 2 3 3   
2
Main> howManyOf4Equal 1 3 3 3
3
Main> howManyOf4Equal 3 3 3 3
4
Main> howManyOf4Equal 1 3 3 1
2
Main>