Am Montag 04 Januar 2010 02:17:06 schrieb Patrick LeBoutillier:
> Hi,
>
> This question didn't get any replies on the beginners list, I thought
> I'd try it here...
Sorry, been occupied with other things. I already took a look, but hadn't anything conclusive enough to reply yet.
>
> I've written (and improved using other solutions I've found on the
> net) a simple sudoku solver which I'm trying to profile. Here is the
> code:
>
>
> import Array
Better
import Data.Array.Unboxed
*much* faster
> import List (transpose, nub, (\\))
> import Data.List
>
> data Sudoku = Sudoku { unit :: Int, cells :: Array (Int, Int) Int,
cells :: UArray (Int,Int) Int
> holes :: [(Int, Int)] }
>
> cell :: Sudoku -> (Int, Int) -> Int
> cell s i = (cells s) ! i
>
> instance Read Sudoku where
> readsPrec _ s = [(Sudoku unit cells holes, "")]
> where unit = length . words . head . lines $ s
> cells = listArray ((1, 1), (unit, unit)) (map read . words $ s)
> holes = [ c | c <- indices cells, (cells ! c) == 0]
>
> instance Show Sudoku where
> show s = unlines [unwords [show $ cell s (x,y) | x <- [1 .. unit s]]
>
> | y <- [1 .. unit s]]
>
> genNums :: Sudoku -> (Int, Int) -> [Int]
> genNums s c@(i,j) = ([1 .. u] \\) . nub $ used
> where
nub isn't nice. It's quadratic in the length of the list. Use e.g.
map head . group . sort
or
Data.[Int]Set.toList . Data.[Int]Set.fromList
if the type is in Ord (and you don't need the distinct elements in the order they come in). That gives an O(n*log n) nub with a sorted result.
And (\\) isn't particularly fast either (O(m*n), where m and n are the lengths of the lists). If you use one of the above instead of nub, you can use the O(min m n) 'minus' for sorted lists:
xxs@(x:xs) `minus` yys@(y:ys)
| x < y = x : xs `minus` yys
| x == y = xs `minus` ys
| otherwise = xxs `minus` ys
xs `minus` _ = xs
Here, you can do better:
genNums s c@(i,j) = nums
where
nums = [n | n <- [1 .. u], arr!n]
arr :: [U]Array Int Bool
arr = accumArray (\_ _ -> False) True (0,u) used
> used = (row s u i j) ++ (col s u i j) ++ (square s sq u i j)
> u = unit s
Not good to calculate sq here. You'll use it many times, calculate once and store it in s.
> sq = truncate . sqrt . fromIntegral $ u
>
> row s u i j = [cell s (i, y) | y <- [1 .. u]]
>
> col s u i j = [cell s (x, j) | x <- [1 .. u]]
>
> square s sq u i j = [cell s (x, y) | y <- [1 .. u], x <- [1 .. u], f x i, f
> y j] where f a b = div (a-1) sq == div (b-1) sq
Test for f y j before you generate x to skip early.
square s sq u i j = [cell s (ni+x,nj+y) | x <- [1 .. sq], y <- [1 .. sq]]
where
qi = (i-1) `div` sq
qj = (j-1) `div` sq
ni = qi*sq
nj = qj*sq
>
> solve :: Sudoku -> [Sudoku]
> solve s =
> case holes s of
> [] -> [s]
> (h:hs) -> do
> n <- genNums s h
> let s' = Sudoku (unit s) ((cells s) // [(h, n)]) hs
> solve s'
>
> main = print . head . solve . read =<< getContents
>
>
> When I compile as such:
>
> $ ghc -O2 --make Sudoku.hs -prof -auto-all -caf-all -fforce-recomp
>
> and run it on the following puzzle:
>
> 0 2 3 4
> 3 4 1 0
> 2 1 4 0
> 0 3 2 1
>
> I get the following profiling report:
>
> Fri Jan 1 10:34 2010 Time and Allocation Profiling Report (Final)
>
> Sudoku +RTS -p -RTS
>
> total time = 0.00 secs (0 ticks @ 20 ms)
That means the report is basically useless. Not entirely, because the allocation figures may already contain useful information. Run on a 9x9 puzzle (a not too hard one, but not trivial either).
Also, run the profiling with -P instead of -p, you'll get more info about time and allocation then.
> total alloc = 165,728 bytes (excludes profiling overheads)
>
> COST CENTRE MODULE %time %alloc
>
> CAF GHC.Handle 0.0 10.7
> CAF Text.Read.Lex 0.0 2.1
> CAF GHC.Read 0.0 1.2
> square Main 0.0 2.8
> solve Main 0.0 1.3
> show_aVx Main 0.0 3.7
> readsPrec_aYF Main 0.0 60.6
> main Main 0.0 9.6
> genNums Main 0.0 5.0
> cell Main 0.0 1.2
>
>
>
> individual inherited
> COST CENTRE MODULE
> no. entries %time %alloc %time %alloc
>
> MAIN MAIN
> 1 0 0.0 0.3 0.0 100.0
> main Main
> 186 1 0.0 9.6 0.0 85.6
> show_aVx Main
> 196 2 0.0 3.7 0.0 3.7
> cell Main
> 197 16 0.0 0.0 0.0 0.0
> solve Main
> 188 5 0.0 1.3 0.0 11.8
> genNums Main
> 189 8 0.0 5.0 0.0 10.4
> square Main
> 194 88 0.0 2.8 0.0 3.2
> cell Main
> 195 16 0.0 0.4 0.0 0.4
> col Main
> 192 4 0.0 0.7 0.0 1.1
> cell Main
> 193 16 0.0 0.4 0.0 0.4
> row Main
> 190 4 0.0 0.7 0.0 1.1
> cell Main
> 191 16 0.0 0.4 0.0 0.4
> readsPrec_aYF Main
> 187 3 0.0 60.6 0.0 60.6
> CAF GHC.Read
> 151 1 0.0 1.2 0.0 1.2
> CAF Text.Read.Lex
> 144 8 0.0 2.1 0.0 2.1
> CAF GHC.Handle
> 128 4 0.0 10.7 0.0 10.7
> CAF GHC.Conc
> 127 1 0.0 0.0 0.0 0.0
>
> Does the column 'entries' represent the number of times the function
> was called?
Number of times it was 'entered', not quite the same as the number of times it was called.
I think (Warning: speculation ahead, I don't *know* how the profiles are generated) it's thus:
Say you call a function returning a list. One call, first entry. It finds the beginning of the list, the first k elements and hands them to the caller. Caller processes these, asks "can I have more, or was that it?". Same call, second entry: f looks for more, finds the next m elements, hands them to caller. Caller processes. Repeat until whatever happens first, caller doesn't ask whether there's more or callee finds there's nothing more (or hits bottom).
> If so, I don't understand how the 'square' function could
> be called 88 times when it's caller is only called 8 times. Same thing
> with 'genNums' (called 8 times, and solve called 5 times)
>
> What am I missing here?
>
> Patrick