Haskell Language Sorting Algorithms Merge Sort
Example
Ordered merging of two ordered lists
Preserving the duplicates:
merge :: Ord a => [a] -> [a] -> [a]
merge xs [] = xs
merge [] ys = ys
merge (x:xs) (y:ys) | x <= y = x:merge xs (y:ys)
| otherwise = y:merge (x:xs) ys
Top-down version:
msort :: Ord a => [a] -> [a]
msort [] = []
msort [a] = [a]
msort xs = merge (msort (firstHalf xs)) (msort (secondHalf xs))
firstHalf xs = let { n = length xs } in take (div n 2) xs
secondHalf xs = let { n = length xs } in drop (div n 2) xs
It is defined this way for clarity, not for efficiency.
Example use:
> msort [3,1,4,5,2]
Result:
[1,2,3,4,5]
Bottom-up version:
msort [] = []
msort xs = go [[x] | x <- xs]
where
go [a] = a
go xs = go (pairs xs)
pairs (a:b:t) = merge a b : pairs t
pairs t = t
