[Haskell] FLOLAC - Functional Programming Practicals 3 - Lists and Recursive Function 遞回函數

在上 FLOLAC 的課程時，老師出了一些 Haskell 的練習題給我們練習。
這邊我列出第三部分的題目跟我作的參考答案~ (練習使用 List 跟寫遞回函數!)
但我還是建議你看原版的PDF (有全部的題目) 會比較清楚XD

When I am studying in the FLOLAC, the teacher gave us some Haskell exercises to practice.
I put the problems and my answer of section 3 to this article! ( for List and recursive functions.)
But I think you should see the original practicals PDF, which is more clear.

練習題目 Practicals: 3 Inductively Defined Functions on Lists

1. Define a function fstEven :: [Int] → Int that returns the first even number of the input list.

2. Define a function hasZero :: [Int] → Bool that returns True if and only if there is a 0 in the input list.

3. Define a function myLast that takes a list and returns the last (rightmost) element.
(a) Let the type be myLast :: [a] → a. Define myLast.
(b) What happens in the previous definition of the input list is empty?
(c) Define myLast :: [a] → Maybe a, which returns Nothing if the list is empty.

4. Define a function pos such that pos x xs looks for x in xs and returns its position.
For example, find 'a' "abc" yields 0, and find 'a' "bac" yields 1.
(a) Let the type be pos :: Eq a ⇒ a → [a] → Int. In your definition, what happens if x is not in the list?
(b) Let the type be pos :: Eq a ⇒ a → [a] → Maybe Int, such that pos x xs returns Nothing if x is not in the list.

5. Define myConcat :: [[a]] → [a] such that, for example myConcat [[1,2,3], [], [4], [5,6]] = [1,2,3,4,5,6]. Hint: use (++).

6. Define double :: [a] → [a] such that, for example, double [1,2,3] = [1,1,2,2,3,3].

7. Define interleave :: [a] → [a] → [a] such that, for example, interleave [1,2,3,4] [5,6,7] = [1,5,2,6,3,7,4].

8. Define splitLR :: [Either a b] → ([a], [b]) such that, for example:
splitLR [Left 1, Left 3, Right 'a', Left 2, Right 'b'] = ([1,3,2], "ab") .

9. Define a function fan :: a → [a] → [[a]] such that fan x xs inserts x into the 0th, 1st. . . nth positions of xs, where n is the length of xs. For example:
fan 5 [1,2,3,4] = [[5,1,2,3,4], [1,5,2,3,4], [1,2,5,3,4], [1,2,3,5,4], [1,2,3,4,5]] .

10. Define perms :: [a] → [[a]] that returns all permutations of the input list. For example:
perms [1,2,3] = [[1,2,3], [2,1,3], [2,3,1], [1,3,2], [3,1,2], [3,2,1]] .

11. Try to define functions inits and tails yourself, and make sure you understand them. Recall that inits [1,2,3] = [[ ], [1], [1,2], [1,2,3]], and tails [1,2,3] = [[1,2,3], [2,3], [3], [ ]].

---

我作的參考解答(有給老師改過了XD，應該沒有問題~)
Here is my answer. (The teacher has saw that so I think it's correct.)

	------------practice 3--------------------------------------
	--author: Yao-Jen Chang
	--Email: autek.roy@gmail.com
	--purpose: answers for practicals section 3 in FLOLAC 2014
	--language: haskell
	--Date: 07/02/2014
	------------------------------------------------------------
	--1 先不考慮失敗的input
	fstEven :: [Int] -> Int
	fstEven (x : xs) = if even x then x else fstEven xs
	--2
	hasZero :: [Int] -> Bool
	hasZero [] = False
	hasZero (x :xs) = if x ==0 then True else hasZero xs
	--3 (a)
	myLast :: [a] -> a --any type will work
	myLast[x] = x
	myLast(x :xs) = myLast xs
	--3 (b) it will crash
	--3 (c)
	myLast2 :: [a] -> Maybe a --any type will work
	myLast2[]=Nothing
	myLast2[x] = Just x
	myLast2(x :xs) = myLast2 xs
	--4
	pos :: Eq a => a -> [a] -> Int
	pos y (x: xs) = if x==y then 0 else
	case pos y xs of
	n -> n + 1
	--4 (a) it will crash
	--4 (b)
	pos2 :: Eq a => a -> [a] -> Maybe Int
	pos2 y [] = Nothing
	pos2 y (x: xs) = if x==y then Just 0 else
	case pos2 y xs of
	Nothing -> Nothing
	Just n -> Just (n + 1)
	--5
	--test input: myConcat [[12, 4], [], [4], [65,9,3], [7]]
	myConcat :: [[a]] -> [a]
	myConcat[] = []
	myConcat (x :xs) = x ++ myConcat xs
	--6
	double::[a] -> [a]
	double[] = []
	double (x: xs) = x : x : double xs
	--7
	--test input: interleave [1, 2, 3, 4][5, 6, 7, 8]
	interleave :: [a] -> [a] -> [a]
	interleave [] x = x
	interleave x [] = x
	interleave (x:xs) (y:ys) = x : y : interleave xs ys
	--same as above
	--interleave2 [5,6,7] [2,3,4] = [5,2,6,3,7,4]
	--interleave2 (1:[2,3,4]) [5,6,7] = 1 : interleave2 [5,6,7] [2,3,4]
	interleave2 :: [a] -> [a] -> [a]
	interleave2 [] x = x
	interleave2 (x:xs) ys = x : interleave2 ys xs
	--8
	--test input: splitLR [Left 1, Left 3, Right 'a', Left 2, Right 'b'] = ([1, 3, 2], "ab")
	splitLR ::[Either a b] -> ([a], [b])
	splitLR [] = ([], [])
	splitLR (x:xs) = case x of
	Left a -> (a:fst(rs), snd(rs))
	Right a -> (fst(rs), a:snd(rs))
	where rs = (splitLR xs)
	--9
	--fan 5 [2, 3] = [[5, 2, 3], [2, 5, 3], [2, 3, 5]]
	--fan 5 [1, 2, 3] = [[5,1,2,3],[1,5,2,3],[1,2,5,3],[1,2,3,5]]
	--test input: fan 5 [1, 2, 3, 4]
	fan :: a -> [a] -> [[a]]
	fan y [] = [[y]]
	fan y (x: xs) = (y:x:xs): map (x:) rs --map example: map (9:)[[1,2], [4, 5]] -> [[9,1,2],[9,4,5]]
	where rs = (fan y xs)
	--10
	--perms [3] = [[3]]
	--perms [2, 3] = [[2, 3], [3, 2]]
	--perms [1, 2, 3] = [[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 3, 2], [3, 1, 2]]
	--perms (1:[2, 3]) = [[2, 3], [3, 2]]
	--test input: perms [1,2,3]
	perms :: [a] -> [[a]]
	perms [x] = [[x]]
	perms (x:xs) = myConcat rs
	where rs = map (fan x) (perms xs)
	--11 寫完之後，發現跟講義一模一樣XD
	--inits [2, 3] = [[], [2], [2, 3]]
	--inits [1, 2, 3] = [[],[1],[1,2],[1,2,3]]
	inits :: [a] -> [[a]] --all prefixes
	inits [] = [[]]
	inits (x:xs) = []: (map (x:) (inits xs))--map example: map (9:)[[1,2], [4, 5]] -> [[9,1,2],[9,4,5]]
	--tails [2, 3] =[[2,3],[3],[]]
	--tails [1, 2, 3] = [[1,2,3],[2,3],[3],[]]
	tails :: [a] -> [[a]] --all suffixes
	tails [] = [[]]
	tails (x:xs) = (x:xs) : tails xs -- (x:xs) means the original element

view raw Haskell_Lists and Recursive Function.hs hosted with ❤ by GitHub

推薦相關文章給您:
1. 安裝Haskell環境與基本操作教學 - 使用GHCi
2. Haskell Practicals 1 - Functions 函數
3. Haskell Practicals 2 - Products and Sums 乘積和合
4. Haskell Practicals 3 - Lists and Recursive Function 遞回函數

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