# [Haskell-cafe] Combine list of sorted lists

Quan Ta quancta at gmail.com
Fri Dec 29 02:21:02 EST 2006

```Hi all,

I have this function which combines (zip) list of sorted lists into a sorted
list (sorted by sum).  The function works with infinite list and seems to
give correct result.  But after I see the code for the Hamming sequence from
the Wiki, I wonder if it can be written better, or more clearly, or succint?

import Data.List

comb [] = []
comb (a:as) = foldl f2 (f1 a) as
where
f1 :: [Int] -> [[Int]]
f1 []     = []
f1 (a:as) = [a] : f1 as

f2 :: [[Int]] -> [Int] -> [[Int]]
f2 la        []        = []
f2 []        lb        = []
f2 la@(a:as) lb@(b:bs) = (a ++ [b]) : (f3 (f2 [a] bs) (f2 as lb))

f3 :: [[Int]] -> [[Int]] -> [[Int]]
f3 [] lb = lb
f3 la [] = la
f3 la lb = let a = head la
in if sum a <= sum b then
a : f3 (tail la) lb
else
b : f3 la (tail lb)

t1 = take 500 (comb [[1,2..],[1,23..],[1,5..],[1,9..]])

t2 = take 500 (sortBy (\x y -> compare (sum x) (sum y))
[[a,b,c,d] | a<-[1,2..80],b<-[1,23..80],
c<-[1,5..80],d<-[1,9..80]])

--t3 = take 500 (sortBy (\x y -> compare (sum x) (sum y))
--              [[a,b,c,d] | a<-[1,2..],b<-[1,23..],
--                           c<-[1,5..],d<-[1,9..]])

main = print (show ((map sum t1) == (map sum t2)))

-- thanks for looking,
-- Quan
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