Haskell学习笔记8 - 训练题

这是之前一些学习haskell过程中做过的题

Q1 把每一个元音字母大写

vTest :: Bool
vTest = (capVowels "mmh"    == "mmh") &&
         (capVowels "learn" == "lEArn") &&
         (capVowels "Only"  == "Only") &&
         (capVowels "holy"   == "hOly")
capVowels :: String -> String

capVowels xs = [if x `elem` "aeiou" then toUpper x else x | x <- xs]

Q2 模拟实现平方根

a*x^2 + b*x + c =0

qrTest :: Bool
qrTest = and (map isQR [
        (2, (-8), 8, Just (2.0,2.0)),
        (5, 2, 1, Nothing),
        (5, 6, 1, Just (-0.2,-1.0)),
        (1, (-4), 6.25, Nothing)])
   where
   isQR (i, j, k, l) = qRoots i j k == l

qRoots :: (Ord z, Floating z) => z -> z -> z -> Maybe (z, z)

qRoots a b c = if d >= 0
      then Just (x1,x2)
      else Nothing
   where
    d = b^2 - 4*a*c
    x1 = (-b + sqrt d) / (2*a)
    x2 = (-b - sqrt d) / (2*a)

Q3 返回两个变量中有几个一样，几个不一样的元素

mTest :: Bool
mTest = (tMatch [1, 2, 3] [2, 2, 3]     == Just (2,1)) &&
         (tMatch [1, 2, 3] [2, 2, 3, 4] == Nothing)    &&
         (tMatch "soft2" "soft3"        == Just (4,1)) &&
         (tMatch "THE2" "SOF3"          == Just (0,4)) &&
         (tMatch " " " "                == Just (1,0))


tMatch :: (Eq a) => [a] -> [a] -> Maybe (Int,Int)

tMatch xs ys = if length xs /= length ys then Nothing
  else Just (same,diff)
  where
    same = length $ filter (\(x,y) -> x == y) $ zip xs ys
    diff = length $ filter (\(x,y) -> x /= y) $ zip xs ys

Q4 最长连续次数
例如：abcddddefgaaaabb，最长连续次数=4，贡献者是 a 和 d

maxRepeat :: String -> Int
maxRepeat = maximum . map length . group

Q5 输出所有连续出现次数最多的字母

maxE :: String -> String
maxE s = let n = maximum . map length . group $ s
   in [ head xs | xs <- group s, length xs == n]

Q6 第1格放1粒麦子，第2格放2粒，第3格4粒，第4格8粒，每格都加倍

total :: Int -> Integer
total n = sum $ take n (iterate (*2) 1) -- take,取前n个数

Q7 角谷定理

jiao :: Int -> [Int]
jiao 1 = [1]
jiao n 
   | even n = n : jiao (n `div` 2)
   | otherwise = n : jiao (n*3+1)

jiaoLen :: Int -> Int
jiaoLen n = maximum [length (jiao x) | x <- [1..n]] - 1