The whole point here is to evaluate both lists inside the list comprehension only once. There is a very simple way to accomplish this:

[q:qs | let qss = queens' (k-1), q <- [1..n], qs <- qss]

Here, queens' (k-1) is only evaluated once, and is shared for all q.

(Note: If queens' (k-1) is polymorphic (which it is) and you use -XNoMonomorphismRestriction, then you better add a type annotation to qss to ensure sharing.)

Adrian

On 2013/01/30 1:51, Doaitse Swierstra wrote:

From the conclusion that both programs compute the same result it can be concluded that  the fact that you have made use of a list comprehension has forced  you to make a choice which should not matter, i.e. the order in which to place the generators. This should be apparent from your code.

My approach is such a situation is to "define your own generator" (assuming here that isSafe needs both its parameters):

pl `x` ql = [ (p,q) | p <-pl, q <- ql]

queens3 n =  map reverse $ queens' n

    where queens' 0       = [[]]                                                                                                

          queens' k       = [q:qs | (qs, q) <- queens' (k-1) `x` [1..n], isSafe q qs]                                              

          isSafe   try qs = not (try `elem` qs || sameDiag try qs)                                                              

          sameDiag try qs = any (\(colDist,q) -> abs (try - q) == colDist) $ zip [1..] qs

Of course you can make more refined versions of `x`, which perform all kinds of fair enumeration, but that is not the main point here. It is the fact that the parameters to `x` are only evaluated once which matters here.

 Doaitse

On Jan 29, 2013, at 10:25 , Junior White <efiish@gmail.com> wrote:

Hi Cafe,

   I have two programs for the same problem "Eight queens problem",

the link is http://www.haskell.org/haskellwiki/99_questions/90_to_94.

   My two grograms only has little difference, but the performance, this is my solution:

-- solution 1------------------------------------------------------------

queens1 :: Int -> [[Int]]                                                                                                       

queens1 n = map reverse $ queens' n                                                                                             

    where queens' 0       = [[]]                                                                                                

          queens' k       = [q:qs | q <- [1..n], qs <- queens' (k-1), isSafe q qs]                                              

          isSafe   try qs = not (try `elem` qs || sameDiag try qs)                                                              

          sameDiag try qs = any (λ(colDist, q) -> abs (try - q) == colDist) $ zip [1..] qs 

-- solution 2--------------------------------------------------------------

queens2 :: Int -> [[Int]]                                                                                                       

queens2 n = map reverse $ queens' n                                                                                             

    where queens' 0       = [[]]                                                                                                

          queens' k       = [q:qs | qs <- queens' (k-1), q <- [1..n], isSafe q qs]                                              

          isSafe   try qs = not (try `elem` qs || sameDiag try qs)                                                              

          sameDiag try qs = any (λ(colDist,q) -> abs (try - q) == colDist) $ zip [1..] qs 

the performance difference is: (set :set +s in ghci)

*Main> length (queens1 8)

92

(287.85 secs, 66177031160 bytes)

*Main> length (queens2 8)

92

(0.07 secs, 17047968 bytes)

*Main> 

The only different in the two program is in the first is "q <- [1..n], qs <- queens' (k-1)," and the second is "qs <- queens' (k-1), q <- [1..n]".

Does sequence in list comprehansion matter? And why?

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