Я пытаюсь исправить утечку памяти в этом коде. Он не завершается в течение десяти минут на небольших входах и выдает ошибку «недостаточно памяти» при запуске с stack exec
. Я думаю, что утечка памяти находится в конструкции newMap. Я думаю, что это может быть утечка, потому что это внутри рекурсивной функции. Я попытался использовать расширение Strict GH C и использовать seq и deepseq и варианты кода ниже.
Я думаю, что утечка здесь:
!existingPolysets <- get
let newMap = (List.foldl' (\accumulator coefficient ->
let newMonomial = (Monomial coefficient degree)
innerMap = addOneMonomialToPolySets newMonomial (PolynomialConstraints x y bound maxDegree) existingPolysets accumulator in
Map.union innerMap accumulator) Map.empty [-bound..bound])
($!!) modify' (const newMap)
Ниже приведен остальной код:
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE BangPatterns #-}
module Dag where
import Control.Monad.State.Strict
import Control.Monad (liftM, ap)
import qualified Data.List as List
import qualified Data.Map.Strict as Map
import qualified Data.Set as Set
import GHC.Generics (Generic)
import Data.Hashable
import Control.DeepSeq
data PolynomialConstraints = PolynomialConstraints Integer Integer Integer Integer
-- x y bound degree
deriving (Show, Eq, Ord, Generic)
data Index = Index Integer Integer -- degree, output
deriving (Show, Eq, Ord, Generic)
type MyState = Map.Map Index PolynomialSetWithIdentifier
instance NFData Index
instance NFData Monomial
instance NFData Identifier
instance NFData SubPolynomialSetWithIdentifier
instance NFData PolynomialSetWithIdentifier
instance NFData PolynomialConstraints
instance Hashable Monomial
instance Hashable Identifier
instance Hashable SubPolynomialSetWithIdentifier
instance Hashable PolynomialSetWithIdentifier
data PolynomialSetWithIdentifier = PolynomialSetWithIdentifier [SubPolynomialSetWithIdentifier] Identifier
deriving (Show, Eq, Ord, Generic)
data SubPolynomialSetWithIdentifier = SubPolynomialSetWithIdentifier Monomial PolynomialSetWithIdentifier Identifier
deriving (Show, Eq, Ord, Generic)
data Identifier = Identifier Int
deriving (Show, Eq, Ord, Generic)
type PolynomialsSolutions a = State MyState a
data Monomial = Monomial Integer Integer
-- coeff, degree
deriving (Show, Eq, Ord, Generic)
emptyPolynomialSetWithID = (PolynomialSetWithIdentifier [] (Identifier $ hash $ getSubPolynomialSetsIdentifiers []))
getSubPolynomialSetsIdentifiers :: [SubPolynomialSetWithIdentifier] -> [Identifier] -- is this good or should it be [Int] ? more typing seems safer
-- returns a list the identifiers of the SubPolynomialSets in subPolynomialSetsWithID
getSubPolynomialSetsIdentifiers = List.map (\(SubPolynomialSetWithIdentifier monomial polynomialSetWithID identifier) -> identifier)
getPolynomialSetIdentifier :: PolynomialSetWithIdentifier -> Identifier
-- returns the identifier of a PolynomialSet
getPolynomialSetIdentifier (PolynomialSetWithIdentifier subPolynomialSets identifier) = identifier
getOutputForOneCoefficient :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer
-- returns the output of the polynomial having coefficient coefficient for monomials from degree maxDegree to degree minDegree
-- and monomials of degree < minDegree having total value computedOutput for x value x
-- minDegree must be <= maxDegree
getOutputForOneCoefficient minDegree maxDegree coefficient x computedOutput
= List.foldl' (\total degree -> total + (coefficient * x ^ degree)) computedOutput [minDegree .. maxDegree]
getLowerBound :: Integer -> PolynomialConstraints -> Integer -> Integer
-- returns the lower bound for the polynomial having sum totalOutput for monomials of degree <= monomialDegree
-- and polynomial constraints (PolynomialConstraints x y bound maxPolynomialDegree)
getLowerBound totalOutput (PolynomialConstraints x y bound maxPolynomialDegree) monomialDegree
| x >= 0 = getOutputForOneCoefficient (monomialDegree + 1) maxPolynomialDegree (-bound) x totalOutput
| otherwise = List.foldl' (\total degree ->
if degree `mod` 2 == 0
then total + (-bound) * x ^ degree
else total + bound * x ^ degree) totalOutput [monomialDegree + 1 .. maxPolynomialDegree]
checkPolynomialSetPossible :: Integer -> PolynomialConstraints -> Integer -> Bool
-- returns False if it is impossible to produce y for PolynomialConstraints polynomialConstraints, Monomial monomial,
-- and total output computed so far Integer totalOutput
checkPolynomialSetPossible totalOutput (PolynomialConstraints x y bound maxPolynomialDegree) monomialDegree
| monomialDegree < maxPolynomialDegree =
let lowerBound = getLowerBound totalOutput (PolynomialConstraints x y bound maxPolynomialDegree) monomialDegree
upperBound = getOutputForOneCoefficient (monomialDegree + 1) maxPolynomialDegree bound x totalOutput in
lowerBound <= y && y <= upperBound
| otherwise = totalOutput == y
filterPolynomialsByDegree :: Map.Map Index PolynomialSetWithIdentifier -> Integer -> Map.Map Index PolynomialSetWithIdentifier
-- O(n)
-- returns Map Index PolynomialSetWithIdentifier in which all values have degree correctDegree
filterPolynomialsByDegree mapPolynomialSets correctDegree = Map.filterWithKey (\(Index degree output) polynomialSetID -> degree == correctDegree) mapPolynomialSets
mapValues :: Ord a => Map.Map k a -> Set.Set a
mapValues m = Map.foldlWithKey'(\accumulator key value -> Set.insert value accumulator) Set.empty m
addOneMonomialToPolySets :: Monomial -> PolynomialConstraints -> Map.Map Index PolynomialSetWithIdentifier -> Map.Map Index PolynomialSetWithIdentifier -> Map.Map Index PolynomialSetWithIdentifier
addOneMonomialToPolySets (Monomial coefficient degree) (PolynomialConstraints x y bound polynomialDegree) existingMapDegreeMinus1 existingAccumulatorMap =
let newMonomial = Monomial coefficient degree -- this does get bound way too early, but it's so small... probably something else?
newMonomialOutput = coefficient * x ^ degree in
Map.foldlWithKey' (\accumulator (Index existingDegree existingOutput) !existingPolynomialSetWithID ->
let !totalOutput = newMonomialOutput + existingOutput in
if checkPolynomialSetPossible totalOutput (PolynomialConstraints x y bound polynomialDegree) degree
then
case Map.lookup (Index degree totalOutput) accumulator of
Just (PolynomialSetWithIdentifier !subPolynomialSets _) ->
let !newSubPolynomialSetWithID = SubPolynomialSetWithIdentifier newMonomial existingPolynomialSetWithID (Identifier $ hash (newMonomial, getPolynomialSetIdentifier existingPolynomialSetWithID)) in
let !newSubPolynomialSets = List.insert newSubPolynomialSetWithID subPolynomialSets in
let !newPolynomialSetWithID = PolynomialSetWithIdentifier newSubPolynomialSets (Identifier $ hash $ getSubPolynomialSetsIdentifiers newSubPolynomialSets) in
insert (Index degree totalOutput) newPolynomialSetWithID accumulator
Nothing ->
let !newSubPolynomialSetWithID = SubPolynomialSetWithIdentifier newMonomial existingPolynomialSetWithID (Identifier $ hash (newMonomial, getPolynomialSetIdentifier existingPolynomialSetWithID)) in
let !newPolynomialSetWithID = PolynomialSetWithIdentifier [newSubPolynomialSetWithID] (Identifier $ hash $ getSubPolynomialSetsIdentifiers [newSubPolynomialSetWithID]) in
insert (Index degree totalOutput) newPolynomialSetWithID accumulator
else accumulator
) existingAccumulatorMap existingMapDegreeMinus1
makePolynomialSetsFast :: PolynomialConstraints -> PolynomialsSolutions ()
makePolynomialSetsFast (PolynomialConstraints x y bound degree) =
makePolynomialSetsForMaxDegree (PolynomialConstraints x y bound 0) degree
makePolynomialSetsFastDegreeZero :: PolynomialConstraints -> Integer -> PolynomialsSolutions ()
makePolynomialSetsFastDegreeZero (PolynomialConstraints x y bound degree) maxDegree =
let newMap = (List.foldl' (\accumulator coefficient ->
let newMonomial = (Monomial coefficient degree)
newSubPolynomialSet = SubPolynomialSetWithIdentifier newMonomial emptyPolynomialSetWithID (Identifier $ hash (newMonomial, getPolynomialSetIdentifier emptyPolynomialSetWithID))
newPolynomialSet = PolynomialSetWithIdentifier [newSubPolynomialSet] (Identifier $ hash $ getSubPolynomialSetsIdentifiers [newSubPolynomialSet]) in
Map.insert (Index degree coefficient) newPolynomialSet accumulator) Map.empty [-bound .. bound]) in
modify' (const newMap)
makePolynomialSetsForMaxDegree :: PolynomialConstraints -> Integer -> PolynomialsSolutions ()
makePolynomialSetsForMaxDegree (PolynomialConstraints x y bound degree) maxDegree
| degree == maxDegree =
if degree == 0
then makePolynomialSetsFastDegreeZero (PolynomialConstraints x y bound degree) maxDegree
else do -- base case
!existingPolysets <- get only need highest level.
let finalMap = (List.foldl' (\accumulator coefficient ->
let newMonomial = (Monomial coefficient degree) in
Map.union (addOneMonomialToPolySets newMonomial (PolynomialConstraints x y bound maxDegree) existingPolysets accumulator) accumulator) Map.empty [-bound .. bound])
($!!) modify' (const finalMap) -- definitely needs to be deep-seq'ed
| degree == 0 = do
makePolynomialSetsFastDegreeZero (PolynomialConstraints x y bound degree) maxDegree
makePolynomialSetsForMaxDegree (PolynomialConstraints x y bound (degree +1)) maxDegree
| otherwise = do
!existingPolysets <- get
let newMap = (List.foldl' (\accumulator coefficient ->
let newMonomial = (Monomial coefficient degree)
innerMap = addOneMonomialToPolySets newMonomial (PolynomialConstraints x y bound maxDegree) existingPolysets accumulator in
Map.union innerMap accumulator) Map.empty [-bound..bound])
($!!) modify' (const newMap)
makePolynomialSetsForMaxDegree (PolynomialConstraints x y bound (degree +1)) maxDegree
Как я могу исправить эту утечку памяти?