Día: 6 de julio de 2022

   interseccionParcial :: Ord a => Int -> [[a]] -> [a]

   interseccionParcial 1 [[3,4],[4,5,9],[5,4,7]]  == [3,4,5,9,7]
   interseccionParcial 2 [[3,4],[4,5,9],[5,4,7]]  == [4,5]
   interseccionParcial 3 [[3,4],[4,5,9],[5,4,7]]  == [4]
   interseccionParcial 4 [[3,4],[4,5,9],[5,4,7]]  == []

import Data.List (foldl', nub, union, sort)
import Test.QuickCheck
 
-- 1ª solución
-- ===========
 
interseccionParcial1 :: Ord a => Int -> [[a]] -> [a]
interseccionParcial1 n xss = 
  [x | x <- sort (elementos xss)
     , pertenecenAlMenos n xss x]
 
elementos :: Ord a => [[a]] -> [a]
elementos []       = []
elementos (xs:xss) = xs `union` elementos xss
 
pertenecenAlMenos :: Ord a => Int -> [[a]] -> a -> Bool
pertenecenAlMenos n xss x =
  length [xs | xs <- xss, x `elem` xs] >= n
 
-- 2ª solución
-- ===========
 
interseccionParcial2 :: Ord a => Int -> [[a]] -> [a]
interseccionParcial2 n xss = 
  [x | x <- sort (elementos2 xss)
     , pertenecenAlMenos2 n xss x]
 
elementos2 :: Ord a => [[a]] -> [a]
elementos2 = foldl' union []
 
pertenecenAlMenos2 :: Ord a => Int -> [[a]] -> a -> Bool
pertenecenAlMenos2 n xss x =
  length (filter (x `elem`) xss) >= n
 
-- 3ª solución
-- ===========
 
interseccionParcial3 :: Ord a => Int -> [[a]] -> [a]
interseccionParcial3 n xss = 
  [x | x <- sort (nub (concat xss))
     , length [xs | xs <- xss, x `elem` xs] >= n]
 
-- Comprobación de equivalencia
-- ============================
 
-- La propiedad es
prop_interseccionParcial :: Positive Int -> [[Int]] -> Bool
prop_interseccionParcial (Positive n) xss =
  all (== interseccionParcial1 n yss)
      [interseccionParcial2 n yss,
       interseccionParcial3 n yss]
  where yss = map nub xss
 
-- La comprobación es
--    λ> quickCheck prop_interseccionParcial
--    +++ OK, passed 100 tests.