Local maxima of list using fold

Question

Is there any way to find out local maxima of a list using foldr or foldl or maybe I have to use unfoldr because of first and last elements of list aren't local maximums?

I understand how to find it using recursion with guards, e.g.

localMax :: [Int] -> [Int]
localMax []       = []
localMax (x:[])   = []
localMax (x:y:[]) = []
localMax (x:y:z:zs)
    | y > z && y > x = y:localMax (y:z:zs)
    | otherwise = localMax (y:z:zs)

Answer 1

You could, but itd be very ugly. Mostly because to find the local maximum, you'll need to know the previous and next elements.

The previous element is no problem, but a fold isn't supposed to know anything about the elements after it.

As a possible approach

 import Data.List (zip3)

 localMax xs = map proj2
               . filter isLocalMax
               $ zip3 xs (tail xs) (drop 2 xs)
   where isLocalMax (x, y, z) = x < y && z < y
         proj2 (_,x,_) = x

So we shift the list by one and two and zip it all together so [a, b, c, d, e] becomes [(a, b, c), (b, c, d), (c, d, e)] then we just use map and filter to select the appropriate elements.

Do note though that map and filter could be smashed into one foldr if you really wanted to.