プログラミング Haskell の 5 章を読みました

遅々として進まない プログラミング Haskell ですが、5 章を読んで練習問題解いた。

square_sum :: Int -> Int
square_sum n = sum [ x^2 | x <- [1 .. n]]

replicate :: Int -> a -> [a]
replicate n a = [ a | x <- [1 .. n]]

pyths :: Int -> [(Int, Int, Int)]
pyths n = [ (x, y, z) | x <- [1 .. n], y <- [1 .. n], z <- [1 .. n], x^2 + y^2 == z^2 ]

perfects :: Int -> [Int]
perfects n = [ x | x <- [ 1 .. n ], sum [ y | y <- factors x, y /= x ] == x ]
             where factors n = [ x | x <- [1 .. n], n `mod` x == 0 ]

concat [[ (x,y) | y <- [4..6] ] | x <- [1..3]]

positions :: Eq a => a -> [a] -> [Int]
positions x xs = [ i | i <- find x (zip xs [ 1 .. n ]) ]
                 where 
                   find k ts = [ b | (a, b) <- ts, a == k ]
                   n = length xs

scalarproduct :: [Int] -> [Int] -> Int
scalarproduct xs ys = sum [ a * b | (a, b) <- zip xs ys ]

perfects は指定した値までの完全数をリストとして返す関数なんだけど、まさかこれだけシンプルに書けるとは正直思いませんでした。リスト内包表記の強力さが良くわかります。

perfects :: Int -> [Int]
perfects n = [ x | x <- [ 1 .. n ], sum [ y | y <- factors x, y /= x ] == x ]
             where factors n = [ x | x <- [1 .. n], n `mod` x == 0 ]

*Main> perfects 500
[6,28,496]