Haskell函数式编程基础习题(3)

墨蓝 2022-08-06 06:04 154阅读 0赞

import Data.Char
    ---------------------------
    --Exercise 5.26
    --Exercise 5.25
    --Exercise 5.24
    --Exercise 5.23
    duplicate :: String -> Int -> String
    duplicate s 1 = s
    duplicate s n = s  ++ (duplicate s (n-1))
    
    
    --Exercise 5.22
    onSeparateLines :: [String] ->  String
    onSeparateLines (x:xx) = x ++ (onSeparateLines xx)
    onSeparateLines [] = []
    
    
    --Exercise 5.21
    matches :: Int -> [Int] -> [Int]
    matches n xs = [x | x <- xs , x ==n ]
    
    myElem ::Int -> [Int] -> Bool
    myElem n xs = length (matches n xs) /= 0
    
    
    --Exercise 5.20
    isPrime :: Int -> Bool
    isPrime n 
    	| n == 1 = False
    	| otherwise = length ( divisors n) == 2
    
    divisors :: Int -> [Int]
    divisors n = 1: myDivisors n 2
    
    myDivisors::Int -> Int -> [Int]
    myDivisors m n 
    	| n <=1  =  [1]
    	| n >= m = [m]
    	| m `mod` n == 0  = n : (myDivisors m (n+1))
    	| otherwise = myDivisors m (n+1)
    	
    
    
    --Exercise 5.19-1
    capitalizeLetters :: String->String
    capitalizeLetters xs = [myIsChar x | x <- xs ]
    
    myIsChar :: Char -> Char
    myIsChar c 
    	| ((ord 'a') <= (ord c)) && ((ord c) <= (ord 'z')) = ' '
    	| otherwise = c
    	
    --Exercise 5.19
    capitalize :: String -> String 
    capitalize xs = [myToUpper x | x <- xs ]
    
    
    myToUpper :: Char -> Char
    myToUpper c
    	| ((ord 'a') <= (ord c)) && ((ord c) <= (ord 'z')) = chr (ord c -((ord 'z') - (ord 'Z')))
    	| otherwise = c
    	
    
    
    --Exercise 5.18
    doubleAll :: [Int] ->[Int]
    doubleAll xs = [x*2 | x <-xs]
    
    --Exercise 5.17
    
    --Exercise 5.16
    
    --Exercise 5.15
    
    --Exercise 5.14
    
    --Exercise 5.13
    isOverlap :: NewShape -> NewShape -> Bool
    isOverlap s1 s2 = s1 == s2
    
    
    --Exercise 5.12
    data NewShape = NewShape Float Float Shape
    					deriving (Show,Eq)
    
    move :: Float -> Float -> NewShape -> NewShape
    move dx dy (NewShape x y shape)= NewShape (x+dx) (y+dy) shape
    
    --Exercise 5.11
    
    --Exercise 5.10
    
    --Exercise 5.9
    
    --Exercise 5.8
    isRegular :: Shape -> Bool 
    isRegular (Circle _) = True
    isRegular ( Rectagle width height) 
    	| width == height = True 
    	| otherwise = False
    isRegular _ = False
    
    --Exercise 5.7
    isRound :: Shape -> Bool
    isRound (Circle _) = True
    isRound _ = False
    
    area :: Shape -> Float
    area (Circle radiu) = 3.14 * radiu * radiu
    area ( Rectagle width height) = width * height
    area _ = 0
    
    --Exercise 5.6
    type Name = String
    type Weight = String
    type Price = Float 
    
    data Item = Item Name Weight Price
    
    --Exercise 5.5
    data Shape = Circle Float 
    			| Rectagle Float Float
    			| Triangles Float Float Float 
    			deriving (Eq,Ord,Show)
    			
    			
    perimeter:: Shape -> Float
    perimeter (Circle radiu) = 2* 3.14 * radiu 
    perimeter (Rectagle width height) = 2 * (width + height)
    
    --Exercise 5.4
    
    --Exercise 5.3
    isCrossXAxis :: (Int,Int) -> Bool
    isCrossXAxis sl 
    		| (fst sl) /= 0  = True
    		| otherwise  = False
    --Exercise 5.2
    
    --Exercise 5.1
    maxOccurs :: Int -> Int ->(Int,Int)
    maxOccurs m n 
    	| m == n  =  (m,2)
    	| m > n = (m,1)
    	| otherwise = (n,1)
    	
    maxThreeOccures:: Int -> Int -> Int -> (Int,Int)
    maxThreeOccures x y z 
    	| x ==  (fst tempMax) = (x ,1 + (snd tempMax) )
    	| x< (fst tempMax) = tempMax
    	| otherwise = (x,1)
    	where tempMax = maxOccurs y z 
    
    --Exercise 4.39
    --Exercise 4.38
    --Exercise 4.37
    --Exercise 4.36
    --Exercise 4.35
    --Exercise 4.34
    --Exercise 4.33
    --Exercise 4.32
    myPower :: Int -> Int -> Int 
    myPower num mi 
    	| mi == 1 = num
    	| mi == 2  = num * num
    	| mi `mod` 2 == 0  = numbSpeed * numbSpeed 
    	| otherwise  = 	num * (myPower num (mi -1))				
    		where  numbSpeed = myPower num (mi `div` 2)
    
    --Exercise 4.31
    commonFactor :: Int -> Int -> Int
    commonFactor m n = myCommonFactor m n (m+n - max m n )
    
    	
    myCommonFactor :: Int -> Int -> Int -> Int
    myCommonFactor m n fac 
    	| fac == 1 = 1
    	| (m `mod` fac == 0)   &&  (n `mod` fac == 0)  = fac
    	| otherwise = myCommonFactor m n (fac-1)
    
    --Exercise 4.30
    
    --Exercise 4.29
    myCube :: Int -> String 
    myCube n = (myLeft2Rgith n n ++ myRight2Left n n) `above` (myRight2Left n n ++ myLeft2Rgith n n) 
    
    --Exercise 4.28
    myRight2Left :: Int -> Int  -> String 
    myRight2Left m n  
    	|	n <= m = myBlackWhite m (m-n) `above`  myLeft2Rgith m (m-n+1)
    	| 	otherwise =""
    
    
    --Exercise 4.27
    myLeft2Rgith :: Int -> Int  -> String 
    myLeft2Rgith m n  
    	|	n>0 = myBlackWhite m n `above`  myLeft2Rgith m (n-1)
    	| 	otherwise =""
    myBlackWhite:: Int -> Int -> String
    myBlackWhite total index
    	| index == total =  "1" ++ myBlackWhite (total -1) index
    	| total <= 0  = ""
    	| otherwise = "0" ++ myBlackWhite (total -1) index
    
    
    --Exercise 4.26
    above::String ->String -> String 
    above m n = m ++"\n" ++ n
    
    
    cloumn :: String -> Int -> String
    cloumn s n 
    	| n <=1  = s
    	| otherwise = s `above` (cloumn s (n-1))
    
    
    --Exercise 4.25
    beside :: String -> String -> String 
    beside n m = m ++ n ++ m
    blackSquares :: Int -> String
    blackSquares n
    	| n <=1    = "1"
    	| otherwise = "1" `beside` blackSquares (n-1)
    	
    whiteBlack :: Int -> String 
    whiteBlack n
    	| n <=1  = "0"
    	| otherwise = "0" `beside` whiteBlack (n-1)
    
    	
    blackWhite :: Int -> String
    blackWhite n 
    	| n <=1  = "1"
    	| otherwise = "1" `beside` whiteBlack (n-1)
    
    --Exercise 4.24
    	
    --Exercise 4.23
    regions :: Int -> Int 
    regions n  = sumFun (\x->x) n
    
    sumFun :: (Int->Int) -> Int ->Int
    sumFun f n
    	| n == 0 = f 0
    	| n > 0 = sumFun f (n-1) + f n 
    
    --Exercise 4.22
    myBoolF :: Int -> Bool
    myBoolF n = boolF f n
    
    boolF :: (Int -> Int) -> Int -> Bool
    boolF f n 
    	| f n ==0  = True
    	| n == 0 = False
    	| otherwise = boolF f (n-1)
    
    --Exercise 4.21
    myMaxF :: Int -> Int 
    myMaxF n = maxF f n
    
    maxF :: (Int -> Int) -> Int -> Int
    maxF f n 
    	| n == 0 = f n
    	| otherwise = max (f n) (maxF f (n-1))
    
    
    f :: Int -> Int
    f 0 = 0
    f 1 = 44
    f 2 = 17
    f _ = 0
    
    --Exercise 4.20
    intSquareRoot ::Int -> Int 
    intSquareRoot n 
    		| n == 1 =1
    		| n == 2 = 1
    		| n == 3 = 1
    		| otherwise = nearNumber n (n `div` 2)  
    
    nearNumber :: Int -> Int -> Int 
    nearNumber	n t  
    	| n < t*t = nearNumber n (t-1)
    	| otherwise = t
    		
    --Exercise 4.19
    multipNautureNumber:: Int->Int
    multipNautureNumber n 
    	| n == 1  = 1
    	| n > 1 = n * multipNautureNumber(n-1)
    	| otherwise = 0