Pares como sumas de pares

3 Comentarios

1. Haskell

   descomposicionesDecrecientes :: Integer -> [[Integer]] descomposicionesDecrecientes n = reverse [xs | xs <- sumasPares n m, esDecreciente xs] where m = length $ pares n pares n = [x | x <- [1..n], even x] sumasPares n 0 = [] sumasPares n m = [xs | xs <- variaciones m (pares n), sum xs == n] ++ sumasPares n (m-1) variaciones 0 xs = [[]] variaciones x xs = [z:ys | z <- xs, ys <- variaciones (x-1) xs] esDecreciente [x] = True esDecreciente (x:y:xs) | x >= y = esDecreciente (y:xs) | otherwise = False

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   descomposicionesDecrecientes :: Integer -> [[Integer]] descomposicionesDecrecientes n =     reverse [xs | xs <- sumasPares n m, esDecreciente xs]     where m = length $ pares n           pares n = [x | x <- [1..n], even x]           sumasPares n 0 = []           sumasPares n m = [xs | xs <- variaciones m (pares n), sum xs == n] ++                            sumasPares n (m-1)           variaciones 0 xs = [[]]           variaciones x xs = [z:ys | z <- xs, ys <- variaciones (x-1) xs]           esDecreciente [x] = True           esDecreciente (x:y:xs) | x >= y    = esDecreciente (y:xs)                                  | otherwise = False

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2. Haskell

   descomposicionesDecrecientes :: Integer -> [[Integer]] descomposicionesDecrecientes n = reverse $ sort $ map reverse (aux n [2,4..n]) where aux n [] = [] aux n [a] = [[a]] aux n (a:b:bs) = [a:xs | xs <- aux (n-a) (takeWhile (<=(n-a)) (a:b:bs))] ++ aux n (b:bs)

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   descomposicionesDecrecientes :: Integer -> [[Integer]] descomposicionesDecrecientes n = reverse $ sort $ map reverse (aux n [2,4..n])     where aux n [] = []           aux n [a] = [[a]]           aux n (a:b:bs) =               [a:xs | xs <- aux (n-a) (takeWhile (<=(n-a)) (a:b:bs))] ++               aux n (b:bs)

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3. Haskell

   import Control.Monad -- realiza la acción solicitada pero no sobre pares, sino sobre todos los naturales sumDec m n | n < 1 = [[]] | otherwise = let z = min m n in [i:k | i <- [z, z-1 .. 1], k <- sumDec i (n-i)] -- llevamos `sumDec` al espacio de los pares descomposicionesDecrecientes = map (map (2*)) . join sumDec . flip div 2

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   import Control.Monad   -- realiza la acción solicitada pero no sobre pares, sino sobre todos los naturales sumDec m n | n < 1     = [[]]            | otherwise = let z = min m n                          in  [i:k | i <- [z, z-1 .. 1], k <- sumDec i (n-i)]   -- llevamos `sumDec` al espacio de los pares descomposicionesDecrecientes = map (map (2*)) . join sumDec . flip div 2

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