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tomasfdel

Estructuras II Práctica 3

tomasfdel
Apr 11th, 2018
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  1. -- 1)
  2. type Color = (Float, Float, Float)
  3.  
  4. mezclar :: Color -> Color -> Color
  5. mezclar (r1, g1, b1) (r2, g2, b2) = ( (r1 + r2)/2 , (g1 + g2)/2, (b1 + b2)/2 )
  6.  
  7.  
  8. -- 2)
  9. type Linea = (Int, [Char])
  10.  
  11. vacia :: Linea
  12. vacia = (0, [])
  13.  
  14. moverIzq :: Linea -> Linea
  15. moverIzq (cursor, linea) = if cursor == 0 then (0, linea) else (cursor - 1, linea)
  16.  
  17. moverDer :: Linea -> Linea
  18. moverDer (cursor, linea) = if cursor == length(linea) then (cursor, linea) else (cursor + 1, linea)
  19.  
  20. moverIni :: Linea -> Linea
  21. moverIni (cursor, linea) = (0, linea)
  22.  
  23. moverFin :: Linea -> Linea
  24. moverFin (cursor, linea) = (length linea, linea)
  25.  
  26. insertar :: Char -> Linea -> Linea
  27. insertar caracter (cursor, linea) = (cursor, (take cursor linea)++ [caracter] ++ (drop cursor linea))
  28.  
  29. borrar :: Linea -> Linea
  30. borrar (0, linea) = (0, linea)
  31. borrar (cursor, linea) = (cursor - 1, (take (cursor - 1) linea) ++ (drop cursor linea))
  32.  
  33.  
  34.  
  35. -- 3)
  36. data CList a = EmptyCL | CUnit a | Consnoc a (CList a) a
  37.  
  38. headCL :: CList a -> a
  39. headCL (CUnit v) = v
  40. headCL (Consnoc v1 xs v2) = v1
  41.  
  42. rearmar :: CList a -> a -> CList a
  43. rearmar xs v = case xs of
  44.                           EmptyCL            -> (CUnit v)
  45.                           (CUnit v1)         -> (Consnoc v1 EmptyCL v)
  46.                           (Consnoc v1 ys v2) -> (Consnoc v1 (rearmar ys v2) v)
  47.  
  48. rearmar2 :: a -> CList a -> CList a
  49. rearmar2 v xs = case xs of
  50.                           EmptyCL            -> (CUnit v)
  51.                           (CUnit v1)         -> (Consnoc v EmptyCL v1)
  52.                           (Consnoc v1 ys v2) -> (Consnoc v (rearmar2 v1 ys) v2)
  53.  
  54. tailCL :: CList a -> CList a
  55. tailCL (CUnit v) = EmptyCL
  56. tailCL (Consnoc v1 xs v2) = rearmar xs v2
  57.  
  58. isEmptyCL :: CList a -> Bool
  59. isEmptyCL EmptyCL = True
  60. isEmptyCL _ = False
  61.  
  62. isCUnitCL :: CList a -> Bool
  63. isCUnitCL (CUnit v) = True
  64. isCUnitCL _ = False
  65. data CList a = EmptyCL | CUnit a | Consnoc a (CList a) a deriving Show
  66.  
  67. headCL :: CList a -> a
  68. headCL (CUnit v) = v
  69. headCL (Consnoc v1 xs v2) = v1
  70.  
  71. tailCL :: CList a -> CList a
  72. tailCL (CUnit v) = EmptyCL
  73. tailCL (Consnoc v1 xs v2) = snocCL xs v2
  74.  
  75. reverseCL :: CList a -> CList a
  76. reverseCL EmptyCL = EmptyCL
  77. reverseCL (CUnit v) = (CUnit v)
  78. reverseCL (Consnoc v1 xs v2) = Consnoc v2 (reverseCL xs) v1
  79.  
  80. consCL :: a -> CList a -> CList a
  81. consCL x EmptyCL = CUnit x
  82. consCL x (CUnit y) = Consnoc x EmptyCL y
  83. consCL x (Consnoc y1 z y2) = Consnoc x (consCL y1 z) y2
  84.  
  85.  
  86. snocCL :: CList a -> a -> CList a
  87. snocCL EmptyCL x = CUnit x
  88. snocCL (CUnit y) x = Consnoc y EmptyCL x
  89. snocCL (Consnoc y1 z y2) x = Consnoc y1 (snocCL z y2) x
  90.  
  91.  
  92. initsAux :: CList a -> [CList a]
  93. initsAux EmptyCL = [EmptyCL]
  94. initsAux lista = EmptyCL:(map (consCL (headCL lista)) (initsAux (tailCL lista)) )
  95.  
  96. listToCL :: [a] -> CList a
  97. listToCL [] = EmptyCL
  98. listToCL (x:xs) = consCL x (listToCL xs)
  99.  
  100.  
  101. inits :: CList a -> CList (CList a)
  102. inits lista = listToCL (initsAux lista)
  103.  
  104. lasts:: CList a -> CList (CList a)
  105. lasts lista = listToCL (map reverseCL (initsAux (reverseCL lista)))
  106.  
  107. concatDosCL :: CList a -> CList a -> CList a
  108. concatDosCL l1 EmptyCL = l1
  109. concatDosCL EmptyCL l2 = l2
  110. concatDosCL (CUnit v1) (CUnit v2) = Consnoc v1 EmptyCL v2
  111. concatDosCL (Consnoc v11 xs v12) (CUnit v2) = Consnoc v11 (rearmar xs v12) v2
  112. concatDosCL (CUnit v1) (Consnoc v21 xs v22) = Consnoc v1 (rearmar2 v21 xs) v22
  113. concatDosCL (Consnoc v11 xs v12) (Consnoc v21 ys v22) = Consnoc v11 (concatDosCL (rearmar xs v12) (rearmar2 v21 ys)) v22
  114.  
  115. concatCL :: CList (CList a) -> CList a
  116. concatCL EmptyCL = EmptyCL
  117. concatCL (CUnit l) = l
  118. concatCL (Consnoc l1 xs l2) = (concatDosCL((concatDosCL l1 (concatCL xs))) l2)
  119.  
  120.  
  121.  
  122. -- 4)
  123. import Prelude
  124. data Aexp = Num Int | Prod Aexp Aexp | Div Aexp Aexp
  125. --data Maybe a = Nothing | Just a
  126.  
  127. eval :: Aexp -> Int
  128. eval (Num n) = n
  129. eval (Prod n1 n2) = (eval n1) * (eval n2)
  130. eval (Div n1 n2) = div (eval n1) (eval n2)
  131.  
  132. seval :: Aexp -> Maybe Int
  133. seval (Num n) = Just n
  134. seval (Prod n1 n2) = case ((seval n1), (seval n2)) of
  135.                                                       (Nothing, v2) -> Nothing
  136.                                                       (v1, Nothing) -> Nothing
  137.                                                       ((Just v1), (Just v2)) -> Just (v1*v2)
  138. seval (Div n1 n2) = case ((seval n1), (seval n2)) of
  139.                                                       (Nothing, v2) -> Nothing
  140.                                                       (v1, Nothing) -> Nothing
  141.                                                       ((Just v1), (Just v2)) -> if v2 == 0 then Nothing else Just (div v1 v2)
  142.  
  143.  
  144.  
  145. -- 5)
  146. data Tree a = Hoja | Nodo (Tree a) a (Tree a) deriving Show
  147.  
  148. completo :: a -> Int -> Tree a
  149. completo dato 0 = Hoja
  150. completo dato n = let subarbol = (completo dato (n - 1))
  151.                   in (Nodo subarbol dato subarbol)
  152.  
  153. balanceado :: a -> Int -> Tree a
  154. balanceado dato 0 = Hoja
  155. balanceado dato 1 = Nodo Hoja dato Hoja
  156. balanceado dato n = if (mod (n - 1) 2) == 0 then let subarbol = (balanceado dato (div n 2))
  157.                                            in (Nodo subarbol dato subarbol)
  158.                                       else let subI = (balanceado dato (div n 2))
  159.                                                subD = (balanceado dato ((div n 2) - 1))
  160.                                            in (Nodo subI dato subD)
  161.  
  162.  
  163.  
  164.  
  165. -- 6)
  166. data GenTree a = EmptyG | NodeG a [GenTree a]
  167. data BinTree a = EmptyB | NodeB (BinTree a) a (BinTree a)
  168.  
  169. checkBT :: Eq a => BinTree a -> BinTree a -> Bool
  170. checkBT EmptyB EmptyB = True
  171. checkBT (NodeB l1 v1 r1) EmptyB = False
  172. checkBT EmptyB (NodeB l2 v2 r2) = False
  173. checkBT (NodeB l1 v1 r1) (NodeB l2 v2 r2) = (v1 == v2) && (checkBT l1 l2) && (checkBT r1 r2)
  174.  
  175.  
  176. g2btAux :: GenTree a -> [GenTree a] -> BinTree a
  177. g2btAux (NodeG v []) [] = (NodeB EmptyB v EmptyB)
  178. g2btAux (NodeG v []) (y:ys) = (NodeB EmptyB v (g2btAux y ys) )
  179. g2btAux (NodeG v (x:xs)) [] = (NodeB (g2btAux x xs) v EmptyB)
  180. g2btAux (NodeG v (x:xs)) (y:ys) = (NodeB (g2btAux x xs) v (g2btAux y ys))
  181.  
  182.  
  183. g2bt:: GenTree a -> BinTree a
  184. g2bt EmptyG = EmptyB
  185. g2bt (NodeG x lista) = g2btAux (NodeG x lista) []
  186.  
  187. test1 = (NodeB (NodeB (NodeB EmptyB 'M' (NodeB EmptyB 'N' EmptyB)) 'G' (NodeB EmptyB 'H' (NodeB EmptyB 'I' EmptyB))) 'B' EmptyB)
  188. test2 = (NodeG 'B' [(NodeG 'G' [(NodeG 'M' []), (NodeG 'N' [])]), (NodeG 'H' []), (NodeG 'I' []) ])
  189.  
  190.  
  191. -- 7 y 8)
  192. data Bin a = Hoja | Nodo (Bin a) a (Bin a)
  193.  
  194. minimumBST :: Bin a -> a
  195. minimumBST (Nodo Hoja a r) = a
  196. minimumBST (Nodo l a r) = minimumBST l
  197.  
  198. maximumBST :: Bin a -> a
  199. maximumBST (Nodo l a Hoja) = a
  200. maximumBST (Nodo l a r) = maximumBST r
  201.  
  202. checkBST :: Ord a => Bin a -> Bool
  203. checkBST Hoja = True
  204. checkBST (Nodo Hoja a Hoja) = True
  205. checkBST (Nodo l a Hoja) = (a >= (maximumBST l)) && (checkBST l)
  206. checkBST (Nodo Hoja a r) = (a <= (minimumBST r)) && (checkBST r)
  207. checkBST (Nodo l a r) = (a <= (maximumBST l)) && (a <= (minimumBST r)) && (checkBST l) && (checkBST r)
  208.  
  209. memberAux :: (Num a, Ord a) => a -> Bin a -> a -> Bool
  210. memberAux valor Hoja candidato = valor == candidato
  211. memberAux valor (Nodo l a r) candidato = if valor <= a then (memberAux valor l a) else (memberAux valor r candidato)
  212.  
  213.  
  214. member :: (Num a, Ord a) => a -> Bin a -> Bool
  215. member valor arbol = memberAux valor arbol (valor + 1)
  216.  
  217.  
  218.  
  219. -- 9)
  220. data Color = R | B
  221. data RBT a = E | T Color (RBT a) a (RBT a)
  222.  
  223. makeBlack :: RBT a -> RBT a
  224. makeBlack E = E
  225. makeBlack (T _ l x r) = T B l x r
  226.  
  227. lbalance :: Color -> RBT a -> a -> RBT a -> RBT a
  228. lbalance B (T R (T R a x b) y c) z d = T R (T B a x b) y (T B c z d)
  229. lbalance B (T R a x (T R b y c)) z d = T R (T B a x b) y (T B c z d)
  230. lbalance c l a r = T c l a r
  231.  
  232. rbalance :: Color -> RBT a -> a -> RBT a -> RBT a
  233. rbalance B a x (T R (T R b y c) z d) = T R (T B a x b) y (T B c z d)
  234. rbalance B a x (T R b y (T R c z d)) = T R (T B a x b) y (T B c z d)
  235. rbalance c l a r = T c l a r
  236.  
  237. insert :: Ord a => a -> RBT a -> RBT a
  238. insert x t = makeBlack (ins x t)
  239.        where ins x E = T R E x E
  240.              ins x (T c l y r) | x < y = lbalance c (ins x l) y r
  241.                                | x > y = rbalance c l y (ins x r)
  242.                                | otherwise = T c l y r
  243.  
  244.  
  245.  
  246. -- 10)
  247.  
  248. type Rank = Int
  249. data Heap a = E | N Rank a (Heap a) (Heap a)
  250.  
  251. rank :: Heap a -> Rank
  252. rank E = 0
  253. rank (N r _ _ _) = r
  254.  
  255. makeH:: a -> Heap a -> Heap a -> Heap a
  256. makeH x a b = if rank a >= rank b then N (rank b + 1) x a b
  257.                                   else N (rank a + 1) x b a
  258.  
  259. merge :: Ord a => Heap a -> Heap a -> Heap a
  260. merge h1 E = h1
  261. merge E h2 = h2
  262. merge h1@(N _ x a1 b1) h2@(N _ y a2 b2) =
  263.     if x <= y then makeH x a1 (merge b1 h2)
  264.               else makeH y a2 (merge h1 b2)
  265.  
  266.  
  267. fromHeapList :: Ord a => [Heap a] -> [Heap a]
  268. fromHeapList [] = []
  269. fromHeapList [x] = [x]
  270. fromHeapList (x:y:xs) = fromHeapList ( (merge x y) : (fromHeapList xs) )
  271.  
  272.  
  273. fromList :: Ord a => [a] -> Heap a
  274. fromList [] = E
  275. fromList xs = let [x] = fromHeapList (map (\x -> N 1 x E E) xs) in x
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