# how can I select all the 3-element-combination out of a list efficiently Classic List Threaded 13 messages Open this post in threaded view
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## how can I select all the 3-element-combination out of a list efficiently

 hi dear haskell lover ;) what I want to do is simply this: select3 :: [a] -> [(a, a, a)] and how can it be done efficiently? thanks in advance!
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## Re: how can I select all the 3-element-combination out of a list efficiently

 geniusfat wrote: > hi dear haskell lover ;) > what I want to do is simply this: > select3 :: [a] -> [(a, a, a)] > and how can it be done efficiently? > thanks in advance! >   What, as in   select3 [1..10] -> [(1,2,3),(2,3,4),(3,4,5),(4,5,6),(5,6,7),(6,7,8),(7,8,9),(8,9,10)] ? How about like this:   select3 = map (\[x,y,z] -> (x,y,z)) . filter ((2 <) . length) . take 3 . tails _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 In reply to this post by geniusfat geniusfat wrote: > hi dear haskell lover ;) > what I want to do is simply this: > select3 :: [a] -> [(a, a, a)] > and how can it be done efficiently? > thanks in advance! If, given [1,2,3,4,5,6,7,8,9,10,11,12] you want [(1,2,3),(4,5,6),(7,8,9)....] then: map (take 3) . iterate (drop 3) is very nearly what you need. Two problems: (a) it gives you [[1,2,3],[4,5,6]..] instead (b) it carries on with an infinite number of [] empty lists you can fix both of these: map (\[a,b,c]->(a,b,c)) . takeWhile (not.null) . map (take 3) . iterate (drop 3) Prelude> map (\[a,b,c] -> (a,b,c)) . takeWhile (not.null) . map (take 3) . iterate (drop 3) \$ [1..12] [(1,2,3),(4,5,6),(7,8,9),(10,11,12)] Hope that helps. Jules _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 In reply to this post by geniusfat geniusfat wrote: > hi dear haskell lover ;) > what I want to do is simply this: > select3 :: [a] -> [(a, a, a)] > and how can it be done efficiently? > thanks in advance! Oh, hang on. I just read your subject line. Do you really mean all the 3-elem combinations? that's much easier: Prelude> let l = [1,5,9,15] in [(a,b,c) | a <- l, b <- l, c <- l] [(1,1,1),(1,1,5),(1,1,9),(1,1,15),(1,5,1),(1,5,5),(1,5,9),(1,5,15),(1,9,1),(1,9,5),(1,9,9),(1,9,15),(1,15,1),(1,15,5),(1,15,9),(1,15,15),(5,1,1),(5,1,5),(5,1,9),(5,1,15),(5,5,1),(5,5,5),(5,5,9),(5,5,15),(5,9,1),(5,9,5),(5,9,9),(5,9,15),(5,15,1),(5,15,5),(5,15,9),(5,15,15),(9,1,1),(9,1,5),(9,1,9),(9,1,15),(9,5,1),(9,5,5),(9,5,9),(9,5,15),(9,9,1),(9,9,5),(9,9,9),(9,9,15),(9,15,1),(9,15,5),(9,15,9),(9,15,15),(15,1,1),(15,1,5),(15,1,9),(15,1,15),(15,5,1),(15,5,5),(15,5,9),(15,5,15),(15,9,1),(15,9,5),(15,9,9),(15,9,15),(15,15,1),(15,15,5),(15,15,9),(15,15,15)] Jules _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 > Oh, hang on. I just read your subject line. Do you really mean all the > 3-elem combinations? Ah, Haskell... So many ways to do the same thing, so many possible meanings to every apparently innocuous statement. ;-) _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 with which model in Combinatorics in mind do you want that function? with or without repetition?    the order matters and each object can be chosen more than once the order matters and each object can be chosen only once the order does not matter and each object can be chosen only once    the order does not matter and each object can be chosen more than once -------------------------------------------------- import Data.List perm3_with_rep,perm3_without_rep,comb3_with_rep,comb3_without_rep :: [a] -> [(a, a, a)] perm3_with_rep    es = [(x,y,z)|x<-es,y<-es,z<-es] perm3_without_rep es = [(x,y,z)|let it s=zip s \$ zipWith (++) (inits s) (tail \$ tails s),(x,xr)<-it es,(y,yr)<-it xr,z<-yr] comb3_with_rep    es = [(x,y,z)|let it=init.tails,xs@(x:_)<-it es,ys@(y:_)<-it xs,z<-ys] comb3_without_rep es = [(x,y,z)|let it=init.tails,(x:xr)<-it es,(y:yr)<-it xr,z<-yr] comb3_to_perm3 :: [(a, a, a)] -> [(a, a, a)] comb3_to_perm3 xyz = concat[perm_without_rep [x,y,z]|(x,y,z)<-xyz] -------------------------------------------------- - marc _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe attachment0 (196 bytes) Download Attachment
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## Re: how can I select all the 3-element-combination out of a list efficiently

 In reply to this post by geniusfat What I meant is this:   the order does not matter and each object can be chosen only once. But thank all those who have offered help, it helps a lot ;)
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## Re: how can I select all the 3-element-combination out of a list efficiently

 geniusfat wrote: > What I meant is this: > > the order does not matter and each object can be chosen only once. > But thank all those who have offered help, it helps a lot ;) > Then you want "triples1" from the code below. The idea for triples1, triples2, and triples3 is that each pickOne returns a list of pairs.  The first element of each pair is the chosen element and the second element of each pair is the list of choices for the next element (given the current choice). import Data.List -- Order does not matter, no repetition -- preserves sorting triples1 xs = do   (x,ys) <- pickOne xs   (y,zs) <- pickOne ys   z <- zs   return (x,y,z)  where pickOne [] = []        pickOne (x:xs) = (x,xs) : pickOne xs        -- Alternative        -- pickOne xs = map helper . init . tails \$ xs        -- helper (x:xs) = (x,xs) -- Order does matter, no repetition -- does not preserve sorting triples2 xs = do   (x,ys) <- pickOne xs   (y,zs) <- pickOne ys   z <- zs   return (x,y,z)  where pickOne xs = helper [] xs        helper bs [] = []        helper bs (x:xs) = (x,bs++xs) : helper (x:bs) xs        -- Alternative (produces results in different order        --              and preserves sorting)        -- pickOne xs = zipWith helper (inits xs) (init (tails xs))        -- helper pre (x:post) = (x,pre++post) -- Order does not matter, repetition allowed -- preserves sorting triples3 xs = do   (x,ys) <- pickOne xs   (y,zs) <- pickOne ys   z <- zs   return (x,y,z)  where pickOne [] = []        pickOne a@(x:xs) = (x,a) : pickOne xs        -- Alternative        -- pickOne xs = map helper . init . tails \$ xs        -- helper xs@(x:_) = (x,xs)         -- Order does matter, repetition allowed -- preserves sorting triples4 xs = do   x <- xs   y <- xs   z <- xs   return (x,y,z) temp = map (\$ [1..4]) \$ [triples1,triples2,triples3,triples4] preservesSorting = map (\xs -> xs == sort xs) temp test1 = putStr . unlines . map show \$ temp test2 = putStr . unlines . map show . map length \$ temp _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 [hidden email] wrote: > Then you want "triples1" from the code below. > > The idea for triples1, triples2, and triples3 is that each pickOne returns a > list of pairs.  The first element of each pair is the chosen element and the > second element of each pair is the list of choices for the next element (given > the current choice). In the spirit of multiple implementations; another approach is to note that you're really asking for all 3-element sublists: power [] = [[]] power (x:xs) = power xs ++ map (x:) (power xs) triples1' l = [ t | t <- power l, length t == 3] (this implementation also preserves sorting) Jules _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 In reply to this post by geniusfat geniusfat <[hidden email]> writes: (snip) > the order does not matter and each object can be chosen only once. (snip) In that case, with the help of Data.List.tails, one can do: threeOf :: [a] -> [(a,a,a)] threeOf xs =     [ (p,q,r) | (p:ps) <- tails xs, (q:qs) <- tails ps, r <- qs ] (the r <- qs is a simpler version of (r:rs) <- tails qs) or maybe, nOf :: Int -> [a] -> [[a]] nOf _    []  = [] nOf 1    xs  = map return xs nOf n (x:xs) = map (x:) (nOf (n-1) xs) ++ nOf n xs (These are fairly naive versions that just took me a few minutes, but perhaps they'll do.) -- Mark _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: how can I select all the 3-element-combination out of a list efficiently

 In reply to this post by Jules Bean Jules Bean wrote: > In the spirit of multiple implementations; another approach is to note > that you're really asking for all 3-element sublists: > > power [] = [[]] > power (x:xs) = power xs ++ map (x:) (power xs) > > triples1' l = [ t | t <- power l, length t == 3] > > (this implementation also preserves sorting) ...but is exponentially slower than necessary, and fails on infinite lists. Try this one: sublistsN 0 _      = [[]] sublistsN n (x:xs) = map (x:) (sublistsN (n-1) xs) ++ sublistsN n xs sublistsN _ _      = [] triples = sublistsN 3 BR, -- -- Mirko Rahn -- Tel +49-721 608 7504 -- --- http://liinwww.ira.uka.de/~rahn/ --- _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe