s CWchar c u it let rt ss tns is szs ns as ms es CUtsname ms bs us fs CUtimbuf hs os rs ts CUShort r t et nt c t y&t s-t y4t m;t bBt oIt lPt GeneralCategory lt oqt nxt gt CULong ot nt gt CULLong nt tt CUInt mt pt tt rt CUIntPtr au x u CUIntMax h#u a*u r1u CUChar eu iru mRu CTm sdu CTms myu eu CTime ru mu iu ou su CTermios cQw h,w isv sNv tu a8v ru iu nu g v CString lv e v n$v CStringLen t?v CStat iUv z\v ecv CSsize gv zv ev CSize av sv ev tv CSigset cv tv ov mv iv cv CSigAtomic tw i w ow nw CSigaction o3w r:w tAw CShort hXw a_w rfw CSChar aw iw tw rw dw iw fw fw CPtrdiff dw CPid sw sw ww dw CPasswd fy my nx iy ny sfx t%x r,x o3x l:x GeneralCategory cTx ConsoleEvent ox trx Const rx Constr rx ex px ConstrRep lx ex ex vx ex nx tx ConsoleEvent e y cy ty o y r&y p-y u4y n;y cBy tIy uPy aWy t^y iey oly nsy GeneralCategory ny dy ey xy ConIndex py ly ey xy Complex fy COff oy dz e z CMode c{ dl{ lG{ o2z c{ nz sCz eJz ConsoleEvent dz pfz umz ntz c{z tz uz az tz iz oz nz GeneralCategory hz az nz dz lz ez HandleType g{ CLong k{ t { i&{ c-{ k4{ ClockTick oN{ nU{ g\{ CLLong os{ uz{ b{ l{ e{ CLDouble o{ n{ v{ CLconv m{ p{ b{ u{ f{ CJmpBuf n| oc| t | CInt mD| p%| t,| r3| CIntPtr aK| xR| CIntMax CIno ax| n| r| Char #| Char# Chan r| o| u| p| CGroup iO} l} p| o| s| CFpos o} a8} c!} k(} CFLock t?} CFloat lV} e]} CFile e} i} o}} u} b} l} e} CDouble r} CDir e} n} t} CDirent v} CDev h)~ l~ o ~ c~ k~ CClock a0~ r7~ CChar tM~ cT~ h[~ Handler Char í l oD r u y~ t~ e~ a~ c~ o~ u~ n~ t~ ByteCount r~ r~ a~ y~ #~ ByteArray# f f e' r. Buffer l m~ sM tT a[ tb ei BufferState o d e BufferMode i s t BufferList c n i l BufferList o n s BufferList e$ a+ k2 ConsoleEvent o uP nW d^ ez sj Bounds d Bounded l Bool o c k b eȀ dπ i) oۀ n d e a d m v a r Exception n0 d7 e> fE iL nS iZ ta eh lo yv Exception u f f e r i n g BufferMode tԁ sہ Bits b c d lp n\ p r s s y n& c- e4 x; cB eI pP tW i^ oe nl AsyncException e r t i o n f a i lʂ eт d Exception g- iȄ r aH o w Arrow a c l m p` z8 e? rF oM ArrowZero lg un su ArrowPlus o n a d ArrowMonad o oƃ p̓ ArrowLoop h o i c e ArrowChoice p p& l- y4 ArrowApply yO Array # eh xo cv e} p t i o n ArrayException Array# tτ hք e݄ x c e p t i o n ArithException dg o9 r@ dG eN rU ArgOrder en su c| r ArgDescr p e l i c a tą i˅ v҅ eم Applicative n d h) m o d e IOMode a0 n7 d> lE eL HandleType yc Any g7 l* rӆ t e r n a t i v e Alternative eچ a d y e x i s t s IOErrorType All c^ rC eJ pQ DataRep oe nl ss tz r ConstrRep d r # Addr# y c lɇ iЇ cׇ sއ c c SCC s o l u t e s& e- e4 k; SeekMode :a ]U [] :h ]o [::] * + : :+: : :*: ) () Ȉ ޖ \ ԕ Δ z \ 0 w l k D Bool w t k c @ ? ; 3 + * ! Int u A 4 , IntSet x v l h V U a G B 5 - b IntSetBoolIntSet(,,)j IntIntArray IntSetInt(,)p IntSetIntSet(,) i ak(,)d akMap! e Q K J I " ak2Map bkMap ckMap ckMapa(,) Int[]IntArray aSeta(,)8 cIntMapa(,) Char[] q ^ ] \ T C < % Int[]r Intm aIntMap n m a P H aSeq z y o g W 6 0 / aSet | Z Y X S : 9 aTree aViewL{ 1 aViewR7 2 a[]R F = & am b bIntMap bSet kSet# k[]' vertexSCC [ vertex[]. akMapak(,)(,) akMapakMap(,) ckMapbkMap(,) akMapaMaybeakMap(,,) IntInt(,)[] IntSetInt(,)ms aInt(,)[] ak(,)[]$ akMapa(,)m) IntMaybekeykey[]keynode(,,)IntInt[]IntArray(,,)M key[]keynode(,,)IntInt[]IntArray(,)L aSeta(,)m> aSetBoolaSet(,,)~ akMapaMaybe(,) aIntMapaMaybeaIntMap(,,)` aIntMapaIntMap(,) _ aIntMapaMaybe(,) aSeqaSeq(,)f aSetaSet(,) } cIntMapbIntMap(,) VertexTree[] aTree[] D aTreem a[][]E nodeSCC[]O key[]keynode(,,)SCC[]N akMapak(,)(,)m( aIntMapaInt(,)(,)m Vertex[]Tree[] aTree[]m © Ψ T ם I $ ! X K I aaaInt aaak abaInt bbaInt bbak cbak ca(,)bInta ca(,)bka aMaybebaInt aMaybebak BoolaInt Boolak Boolba aaInt aaa aak aba baInt bak bbInt bba cba ca(,)ba cbEitheraInt cbEitherak Char[]ak aMaybeaInt aMaybeak aMaybeba bMaybeaInt bMaybeak BoolInt Boola IntInt aa ba k2k1 cbEithera b[]a(,)b aMaybea bMaybea b[]a(,)mb aMaybeaMaybe Bool ^ ^ ] ] \ \ Int! o n m l k j i h g f e d c b a ` _ 5 IntSet x x w w v u t s r q p l k j i ^ a ~ } | { z y o n m 7 6 b k - vertex IntInt(,) akMap@ e d - , + * ) ( ' & % $ # " ! ! ak1Map bkMap " Int[]IntArray Int[]U IntSet[]V aIntMap5 n c b a ` _ \ aSeq { z o g f 7 6 5 4 3 2 1 0 0 / aSet ~ } ] B A @ ? > = < ; ; : : 9 8 aTreeG F E D a[]Z Y X W bIntMap b[] vertexSCC. vertex[][ key[]keynode(,,)[]O N M L IntInt(,)[] aInt(,)[] H ak(,)[] K J I akMap[] Q Char[]TreeC StringTree[]T aIntMap[] P aSCC[]R aSet[]S aTree[] } r g \ Q 4 # ڻ g O D 0 Ӻ y j [ J 0 ٹ ι ù y n ] R G < 1 & Ѹ s \ Q @ 5 & ʷ ~ ^ K 8 - Զ ɶ n U C 4 % ֵ ˵ } n _ T E 3 ܴ ʹ y h S > , ٳ v e Z I > 3 ( ݲ β { l ] N ? 0 % ڱ ϱ u d U F 7 , ܰ ˰ y n c X A 6 + կ ʯ h Q @ 1 & Ю | k V K : / Ordk2 Ordk c : Ordk Ordk Ordk y Ordk l Eqk & Ordk Ordk Q Ordk Ordk String Ordk 6 Ordk , Ordk * 0 4 Ordk Monadm MonadmForest Forest Ordk a ` ^ Ordk 8 Ordk 7 OrdaOrdb Ordk2 Ordk Key" Ordk ! w Ordk j Eqk i v Key$ Ordk # Ordk Key- 1 KeyO Orda Orda N Ordk Ordk L Ordk ( Ordk ' Key. 2 Ordk _ b Key Key9 Key Key Key Keyk x Key% Key Key/ 3 KeyP Key Key Key5 Key+ Key Key M Ordk Ordk R Ordk Ordk MonadmOrdk MonadmOrdk " Ordk Ordk Ordk Z Ordk Y Key Forest Orda # Orda Orda Orda 4 + . S V Monadm B String% ( ) Key Key! = $ @ Key MonadmKey Key Key Key String ShowaString ShowaString u Orda h Eqa p t f n r ; ForestString Orda ] Ordk Ordkey Ordkey { OrdkeyGraphVertex| OrdkeyGraphVertexs Ordk g Eqk o e m q Key [ Forest< StringU X 8 Orda Monadm D ShowaString Orda 6 Orda - 0 ' * ? ~ > < \ Ordk 7 Ordk Monadm Monadm C ShowaShowkString 5 Ordk EqaOrdk Ordk , / T W & ) Key MonadmKeyA Key ShowaString Key 3 Eqa GraphVertex GraphVertex2 ForestGraphVertex : GraphVertex 1 ForestGraph ForestGraph? EdgeGraph} GraphTable Graph BoundsEdgeGraphF K J I H G E j Z J : * r ` H 0 d 6 n < b J 2 T : l > x J 0 R . Z $ X 4 p T 2 g M ! i G k G ) e J 8 ` > $ ~ ` J 6 r L p L * n > ¿ t S 2 " |>) |>? viewr< ViewR= viewr> viewl] ViewL; viewl< vertices vertices: vertex Vertex9 valid valid7 8 updatewithkeyԿ updateWithKey5 6 updateminwithkey updateMinWithKey3 4 updatemin* updateMin1 2 updatemaxwithkeyS updateMaxWithKey/ 0 updatemax| updateMax- . updatelookupwithkey updateLookupWithKey+ , updateat updateAt* update update' ( ) unionwithkey unionWithKey% & unionwith8 unionWith# $ unionswith[ unionsWith! " unions{ unions union union unfoldtreem_bf unfoldTreeM_BF unfoldtreem unfoldTreeM unfoldtree unfoldTree unfoldforestm_bf5 unfoldForestM_BF unfoldforestm^ unfoldForestM unfoldforest unfoldForest tree Tree transposeg transposeG topsort topSort tolist toList toasclist toAscList take? take tableT Table subforestn subForest stronglyconncompr stronglyConnCompR stronglyconncomp stronglyConnComp splitmember splitMember splitlookup splitLookup splitat0 splitAt splitH split sizei size singleton singleton showtreewith showTreeWith showtree showTree set Set sequence) Sequence seq@ Seq sccR SCC scc rootlabels rootLabel reverse reverse reachable reachable path path partitionwithkey partitionWithKey partition partition outdegree7 outdegree nullP null notmembery notMember node Node minviewwithkey minViewWithKey minview minView member member maxviewwithkey. maxViewWithKey maxviewS maxView mapwithkeyx mapWithKey mapmonotonic mapMonotonic mapmaybewithkey mapMaybeWithKey mapmaybe mapMaybe mapkeyswith mapKeysWith mapkeysmonotonic6 mapKeysMonotonic mapkeysY mapKeys mapeitherwithkey| mapEitherWithKey mapeither mapEither mapaccumwithkey mapAccumWithKey mapaccum mapAccum map Map map lookupindexB lookupIndex lookup_ lookup levels{ levels length length keysset keysSet keys keys key Key issubsetof isSubsetOf issubmapofby isSubmapOfBy issubmapofC isSubmapOf ispropersubsetofm isProperSubsetOf ispropersubmapofby isProperSubmapOfBy ispropersubmapof isProperSubmapOf intset IntSet intmap IntMap intersectionwithkey< intersectionWithKey intersectionwitho intersectionWith intersection intersection insertwithkey' insertWithKey' insertwithkey insertWithKey insertwith' insertWith' insertwith= insertWith insertlookupwithkeyj insertLookupWithKey insert insert index index~ indegree indegree} graphfromedges' graphFromEdges'| graphfromedges graphFromEdges{ graph: Graph z fromlistwithkey^ fromListWithKeyx y fromlistwith fromListWithv w fromlist fromListq r s t u fromdistinctasclist fromDistinctAscListm n o p fromasclistwithkey! fromAscListWithKeyk l fromasclistwithR fromAscListWithi j fromasclist| fromAscListe f g h forest Forestd foldwithkey foldWithKeyb c fold fold^ _ ` a flattensccs flattenSCCs] flattenscc) flattenSCC\ flattenF flatten[ findwithdefaulth findWithDefaultY Z findmin findMinV W X findmax findMaxS T U findindex findIndexR filterwithkey filterWithKeyP Q filter filterL M N O emptyr= EmptyRK emptylU EmptyLJ emptyl emptyE F G H I elems elemsA B C D elemat elemAt@ edges edges? edge Edge> drop drop= drawtree drawTree< drawforest+ drawForest; differencewithkeyR differenceWithKey9 : differencewith differenceWith7 8 difference difference3 4 5 6 dfs dfs2 dff dff1 deletemin deleteMin. / 0 deletemax deleteMax+ , - deletefindminH deleteFindMin( ) * deletefindmaxv deleteFindMax% & ' deleteat deleteAt$ delete delete ! " # cyclicscc CyclicSCC containers containers components components buildg; buildG boundsS Bounds bcch bcc assocs} assocs alter alter adjustwithkey adjustWithKey adjust adjust acyclicscc AcyclicSCC \\ \\ ><1 >< <|A <| :>Q :> : _> < < : $9 7 5 F5 4 4 3 T3 2 s2 +2 H1 0 / . , ?+ I' 8$ # ## " " ! ! % ] N 8 E B _ | A ! x > ! y 9 c ( ? E i 2 N ] 4 O h |> (|>) :: Seq a -> a -> Seq a Seqaa Seqa| O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end. viewrviewr :: Seq a -> ViewR a Seqa ViewRa2 O(1). Analyse the right end of a sequence. ViewR data ViewR a& % View of the right end of a sequence. viewlviewl :: Seq a -> ViewL a Seqa ViewLa1 O(1). Analyse the left end of a sequence. ViewL data ViewL a $ View of the left end of a sequence. verticesvertices :: Graph -> [Vertex] ~ Graph []Vertex All vertices of a graph. Vertex type Vertex = Int % Abstract representation of vertices. validvalid :: Ord a => Set a -> Boolv Y Orda SetaBool: O(n). Test if the internal set structure is valid. validvalid :: Ord k => Map k a -> Bool Ordk MapkaBool: O(n). Test if the internal map structure is valid. updateWithKey updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a% Ordkka Maybeak Mapka Mapka% O(log n). The expression (updateWithKey f k map) updates the value x at k (if it is in the map). If (f k x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y. updateWithKey updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a Keya MaybeaKey IntMapa IntMapa! O(min(n,W)). The expression (update f k map) updates the value x at k (if it is in the map). If (f k x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y. updateMinWithKeyupdateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a ka Maybea Mapka Mapka6 O(log n). Update the value at the minimal key. updateMinWithKeyupdateMinWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a Keyaa IntMapa IntMapa6 O(log n). Update the value at the minimal key. updateMin updateMin :: (a -> Maybe a) -> Map k a -> Map k a Z a Maybea Mapka Mapka6 O(log n). Update the value at the minimal key. updateMin updateMin :: (a -> a) -> IntMap a -> IntMap aJ % aa IntMapa IntMapa6 O(log n). Update the value at the minimal key. updateMaxWithKeyupdateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a/ ka Maybea Mapka Mapka6 O(log n). Update the value at the maximal key. updateMaxWithKeyupdateMaxWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a Keyaa IntMapa IntMapa6 O(log n). Update the value at the maximal key. updateMax updateMax :: (a -> Maybe a) -> Map k a -> Map k a a Maybea Mapka Mapka6 O(log n). Update the value at the maximal key. updateMax updateMax :: (a -> a) -> IntMap a -> IntMap a w aa IntMapa IntMapa6 O(log n). Update the value at the maximal key. updateLookupWithKey updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a) w Ordkka Maybeak Mapka (,) Maybea Mapka$ O(log n). Lookup and update. updateLookupWithKey updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a, IntMap a) Keya MaybeaKey IntMapa (,) Maybea IntMapa' O(min(n,W)). Lookup and update. updateAt updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a } ka MaybeaInt Mapka Mapkag O(log n). Update the element at index. Calls error when an invalid index is used. update update :: Int -> a -> Seq a -> Seq a } Inta Seqa SeqaI O(log(min(i,n-i))). Replace the element at the specified position update update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a ` Ordka Maybeak Mapka Mapka O(log n). The expression (update f k map) updates the value x at k (if it is in the map). If (f x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y. update update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a` - a MaybeaKey IntMapa IntMapa O(min(n,W)). The expression (update f k map) updates the value x at k (if it is in the map). If (f x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y. unionWithKey unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k aR Ordkkaaa Mapka Mapka Mapka O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm. Hedge-union is more efficient on (bigset union smallset). unionWithKey unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a Keyaaa IntMapa IntMapa IntMapa4 O(n+m). The union with a combining function. unionWith unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a Ordkaaa Mapka Mapka Mapkat O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm. unionWith unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a aaa IntMapa IntMapa IntMapa4 O(n+m). The union with a combining function. unionsWith unionsWith :: Ord k => (a -> a -> a) -> [Map k a] -> Map k a Ordkaaa [] Mapka Mapka The union of a list of maps, with a combining operation: (unionsWith f == Prelude.foldl (unionWith f) empty). unionsWith unionsWith :: (a -> a -> a) -> [IntMap a] -> IntMap a aaa [] IntMapa IntMapa8 The union of a list of maps, with a combining operation unionsunions :: Ord a => [Set a] -> Set a Orda [] Seta Setaa The union of a list of sets: (unions == foldl union empty). unionsunions :: Ord k => [Map k a] -> Map k a e Ordk [] Mapka Mapkab The union of a list of maps: (unions == Prelude.foldl union empty). unionsunions :: [IntSet] -> IntSetX ? []IntSetIntSet The union of a list of sets. unionsunions :: [IntMap a] -> IntMap a [] IntMapa IntMapa6 O(log n). The expression (alter f k map) alters the value x at k, or absence thereof. alter can be used to insert, delete, or update a value in a Map. In short : lookup k (alter f k m) = f (lookup k m) The union of a list of maps. unionunion :: Ord a => Set a -> Set a -> Set a | Orda Seta Seta Seta O(n+m). The union of two sets, preferring the first set when equal elements are encountered. The implementation uses the efficient hedge-union algorithm. Hedge-union is more efficient on (bigset union smallset). unionunion :: Ord k => Map k a -> Map k a -> Map k a) Ordk Mapka Mapka Mapkaw O(n+m). The expression (union t1 t2) takes the left-biased union of t1 and t2. It prefers t1 when duplicate keys are encountered, i.e. (union == unionWith const). The implementation uses the efficient hedge-union algorithm. Hedge-union is more efficient on (bigset union smallset) unionunion :: IntSet -> IntSet -> IntSet IntSetIntSetIntSet& O(n+m). The union of two sets. unionunion :: IntMap a -> IntMap a -> IntMap a IntMapa IntMapa IntMapa O(n+m). The (left-biased) union of two maps. It prefers the first map when duplicate keys are encountered, i.e. (union == unionWith const). unfoldTreeM_BFunfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)3 Monadmb m (,)a []bb m Treea Monadic tree builder, in breadth-first order, using an algorithm adapted from Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design, by Chris Okasaki, ICFP'00. unfoldTreeM unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a) p Monadmb m (,)a []bb m Treea+ Monadic tree builder, in depth-first order unfoldTree unfoldTree :: (b -> (a, [b])) -> b -> Tree aj A b (,)a []bb Treea Build a tree from a seed value unfoldForestM_BFunfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)X Monadmb m (,)a []b []b m Foresta Monadic forest builder, in breadth-first order, using an algorithm adapted from Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design, by Chris Okasaki, ICFP'00. unfoldForestM unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a) Monadmb m (,)a []b []b m Foresta- Monadic forest builder, in depth-first order unfoldForest unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a b (,)a []b []b Foresta* Build a forest from a list of seed values Tree data Tree a 2 Multi-way trees, also known as rose trees. transposeG transposeG :: Graph -> Graph GraphGraph+ The graph obtained by reversing all edges. topSorttopSort :: Graph -> [Vertex], Graph []Vertex A topological sort of the graph. The order is partially specified by the condition that a vertex i precedes j whenever j is reachable from i but not vice versa. toListtoList :: Set a -> [a]D . Seta []a4 O(n). Convert the set to a list of elements. toListtoList :: Map k a -> [(k, a)] Mapka [] (,)ka3 O(n). Convert to a list of key/value pairs. toListtoList :: IntSet -> [Int]x b IntSet []Int4 O(n). Convert the set to a list of elements. toListtoList :: IntMap a -> [(Key, a)] IntMapa [] (,)Keya; O(n). Convert the map to a list of key/value pairs. toAscList toAscList :: Set a -> [a] Seta []a? O(n). Convert the set to an ascending list of elements. toAscList toAscList :: Map k a -> [(k, a)]p M Mapka [] (,)ka+ O(n). Convert to an ascending list. toAscList toAscList :: IntSet -> [Int] IntSet []Int? O(n). Convert the set to an ascending list of elements. toAscList toAscList :: IntMap a -> [(Key, a)] IntMapa [] (,)Keyaa O(n). Convert the map to a list of key/value pairs where the keys are in ascending order. taketake :: Int -> Seq a -> Seq a k Int Seqa SeqaH O(log(min(i,n-i))). The first i elements of a sequence. Table type Table a = Array Vertex a / Table indexed by a contiguous set of vertices. subForest subForest :: Tree a -> Forest a Treea Foresta zero or more child trees stronglyConnCompRstronglyConnCompR :: Ord key => [(node, key, [key])] -> [SCC (node, key, [key])] P Ordkey [] (,,)nodekey []key [] SCC (,,)nodekey []keyT The strongly connected components of a directed graph, topologically sorted. The function is the same as stronglyConnComp, except that all the information about each node retained. This interface is used when you expect to apply SCC to (some of) the result of SCC, so you don't want to lose the dependency information. stronglyConnCompstronglyConnComp :: Ord key => [(node, key, [key])] -> [SCC node] | Ordkey [] (,,)nodekey []key [] SCCnodeM The strongly connected components of a directed graph, topologically sorted. splitMember splitMember :: Ord a => a -> Set a -> (Set a, Bool, Set a) Ordaa Seta (,,) SetaBool Setas O(log n). Performs a split but also returns whether the pivot element was found in the original set. splitMember splitMember :: Int -> IntSet -> (IntSet, Bool, IntSet) IntIntSet (,,)IntSetBoolIntSetv O(min(n,W)). Performs a split but also returns whether the pivot element was found in the original set. splitLookup splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a) Ordkk Mapka (,,) Mapka Maybea Mapka O(log n). The expression (splitLookup k map) splits a map just like split but also returns lookup k map. splitLookup splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a)i & Key IntMapa (,,) IntMapa Maybea IntMapao O(log n). Performs a split but also returns whether the pivot key was found in the original map. splitAtsplitAt :: Int -> Seq a -> (Seq a, Seq a)f 9 Int Seqa (,) Seqa SeqaA O(log(min(i,n-i))). Split a sequence at a given position. splitsplit :: Ord a => a -> Set a -> (Set a, Set a)@ Ordaa Seta (,) Seta Seta O(log n). The expression (split x set) is a pair (set1,set2) where all elements in set1 are lower than x and all elements in set2 larger than x. x is not found in neither set1 nor set2. splitsplit :: Ord k => k -> Map k a -> (Map k a, Map k a) Ordkk Mapka (,) Mapka Mapka O(log n). The expression (split k map) is a pair (map1,map2) where the keys in map1 are smaller than k and the keys in map2 larger than k. Any key equal to k is found in neither map1 nor map2. splitsplit :: Int -> IntSet -> (IntSet, IntSet) IntIntSet (,)IntSetIntSet$ O(min(n,W)). The expression (split x set) is a pair (set1,set2) where all elements in set1 are lower than x and all elements in set2 larger than x.
split 3 (fromList [1..5]) == (fromList [1,2], fromList [3,4])splitsplit :: Key -> IntMap a -> (IntMap a, IntMap a)h 2 Key IntMapa (,) IntMapa IntMapa O(log n). The expression (split k map) is a pair (map1,map2) where all keys in map1 are lower than k and all keys in map2 larger than k. Any key equal to k is found in neither map1 nor map2. sizesize :: Set a -> Int SetaInt0 O(1). The number of elements in the set. sizesize :: Map k a -> Inta L MapkaInt0 O(1). The number of elements in the map. sizesize :: IntSet -> Int IntSetInt% O(n). Cardinality of the set. sizesize :: IntMap a -> Inta! L! IntMapaInt, O(n). Number of elements in the map. singleton singleton :: a -> Set a! ! a Seta% O(1). Create a singleton set. singleton singleton :: a -> Seq ad" T" a Seqa# O(1). A singleton sequence. singleton singleton :: k -> a -> Map k a" " ka Mapka* O(1). A map with a single element. singleton singleton :: Int -> IntSet{# k# IntIntSet# O(1). A set of one element. singleton singleton :: Key -> a -> IntMap a$ # Keya IntMapa# O(1). A map of one element. showTreeWith showTreeWith :: Show a => Bool -> Bool -> Set a -> String$ $ ShowaBoolBool SetaStringg O(n). The expression (showTreeWith hang wide map) shows the tree that implements the set. If hang is True, a hanging tree is shown otherwise a rotated tree is shown. If wide is True, an extra wide version is shown.
Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5] 4 +--2 | +--1 | +--3 +--5 Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5] 4 | +--2 | | | +--1 | | | +--3 | +--5 Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5] +--5 | 4 | | +--3 | | +--2 | +--1showTreeWith showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String ( ' kaStringBoolBool MapkaString. O(n). The expression (showTreeWith showelem hang wide map) shows the tree that implements the map. Elements are shown using the showElem function. If hang is True, a hanging tree is shown otherwise a rotated tree is shown. If wide is True, an extra wide version is shown.
Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t (4,()) +--(2,()) | +--(1,()) | +--(3,()) +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t (4,()) | +--(2,()) | | | +--(1,()) | | | +--(3,()) | +--(5,()) Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t +--(5,()) | (4,()) | | +--(3,()) | | +--(2,()) | +--(1,())showTreeWith showTreeWith :: Bool -> Bool -> IntSet -> String+ + BoolBoolIntSetString O(n). The expression (showTreeWith hang wide map) shows the tree that implements the set. If hang is True, a hanging tree is shown otherwise a rotated tree is shown. If wide is True, an extra wide version is shown. showTreeWith showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String- e- ShowaBoolBool IntMapaString O(n). The expression (showTreeWith hang wide map) shows the tree that implements the map. If hang is True, a hanging tree is shown otherwise a rotated tree is shown. If wide is True, an extra wide version is shown. showTreeshowTree :: Show a => Set a -> String / . Showa SetaStringg O(n). Show the tree that implements the set. The tree is shown in a compressed, hanging format. showTreeshowTree :: (Show k, Show a) => Map k a -> String0 / Showk Showa MapkaStringg O(n). Show the tree that implements the map. The tree is shown in a compressed, hanging format. showTreeshowTree :: IntSet -> String0 0 IntSetStringg O(n). Show the tree that implements the set. The tree is shown in a compressed, hanging format. showTreeshowTree :: Show a => IntMap a -> String1 1 Showa IntMapaStringg O(n). Show the tree that implements the map. The tree is shown in a compressed, hanging format. Set data Set aS2 A set of values a. Seq data Seq a2 " General-purpose finite sequences. sccscc :: Graph -> Forest Vertex"3 3 Graph ForestVertex. The strongly connected components of a graph. SCC data SCC vertex3 Strongly connected component. rootLabel rootLabel :: Tree a -> a3 3 Treeaa label value reversereverse :: Seq a -> Seq af4 O4 Seqa Seqa( O(n). The reverse of a sequence. reachable reachable :: Graph -> Vertex -> [Vertex]5 4 GraphVertex []Vertex2 A list of vertices reachable from a given vertex. path path :: Graph -> Vertex -> Vertex -> Bool5 5 GraphVertexVertexBool/ Is the second vertex reachable from the first? partitionWithKeypartitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)6 6 OrdkkaBool Mapka (,) Mapka Mapka O(n). partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split. partitionWithKeypartitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)\8 8 KeyaBool IntMapa (,) IntMapa IntMapa O(n). partition the map according to some predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split. partition partition :: Ord a => (a -> Bool) -> Set a -> (Set a, Set a)9 9 OrdaaBool Seta (,) Seta Seta O(n). Partition the set into two sets, one with all elements that satisfy the predicate and one with all elements that don't satisfy the predicate. See also split. partition partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a, Map k a)G; ; OrdkaBool Mapka (,) Mapka Mapka O(n). partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split. partition partition :: (Int -> Bool) -> IntSet -> (IntSet, IntSet)< z< IntBoolIntSet (,)IntSetIntSet< O(n). partition the set according to some predicate. partition partition :: (a -> Bool) -> IntMap a -> (IntMap a, IntMap a)= [= aBool IntMapa (,) IntMapa IntMapa O(n). partition the map according to some predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split. outdegree outdegree :: Graph -> Table Int> > Graph TableInt. A table of the count of edges from each node. nullnull :: Set a -> BoolG? 4? SetaBool$ O(1). Is this the empty set? nullnull :: Seq a -> Bool? ? SeqaBool) O(1). Is this the empty sequence? nullnull :: Map k a -> BoolC@ -@ MapkaBool O(1). Is the map empty? nullnull :: IntSet -> Bool@ @ IntSetBool O(1). Is the set empty? nullnull :: IntMap a -> Bool0A A IntMapaBool O(1). Is the map empty? notMember notMember :: Ord a => a -> Set a -> BoolA A Ordaa SetaBool0 O(log n). Is the element not in the set? notMember notMember :: Ord k => k -> Map k a -> BoolB eB Ordkk MapkaBool5 O(log n). Is the key not a member of the map? notMember notMember :: Int -> IntSet -> Bool/C C IntIntSetBool3 O(min(n,W)). Is the element not in the set? notMember notMember :: Key -> IntMap a -> BoolC C Key IntMapaBool5 O(log n). Is the key not a member of the map? NodeNode :: a -> Forest a -> Tree aD dD a Foresta Treea minViewWithKeyminViewWithKey :: Monad m => Map k a -> m ((k, a), Map k a)6E D Monadm Mapka m (,) (,)ka Mapka O(log n). Retrieves the minimal (key,value) pair of the map, and the map stripped from that element fails (in the monad) when passed an empty map. minViewWithKeyminViewWithKey :: Monad m => IntMap a -> m ((Key, a), IntMap a)F OF Monadm IntMapa m (,) (,)Keya IntMapa O(log n). Retrieves the minimal (key,value) couple of the map, and the map stripped from that element. fails (in the monad) when passed an empty map. minViewminView :: Monad m => Set a -> m (a, Set a)G G Monadm Seta m (,)a Seta O(log n). Retrieves the minimal key of the set, and the set stripped from that element fails (in the monad) when passed an empty set. minViewminView :: Monad m => Map k a -> m (a, Map k a)H H Monadm Mapka m (,)a Mapka O(log n). Retrieves the minimal key's value of the map, and the map stripped from that element fails (in the monad) when passed an empty map. minViewminView :: Monad m => IntSet -> m (Int, IntSet) J I MonadmIntSet m (,)IntIntSet O(min(n,W)). Retrieves the minimal key of the set, and the set stripped from that element fails (in the monad) when passed an empty set. membermember :: Ord a => a -> Set a -> Bool5K K Ordaa SetaBool, O(log n). Is the element in the set? membermember :: Ord k => k -> Map k a -> BoolK K Ordkk MapkaBool1 O(log n). Is the key a member of the map? membermember :: Int -> IntSet -> BoolL iL IntIntSetBool6 O(min(n,W)). Is the value a member of the set? membermember :: Key -> IntMap a -> Bool(M M Key IntMapaBool4 O(min(n,W)). Is the key a member of the map? maxViewWithKeymaxViewWithKey :: Monad m => Map k a -> m ((k, a), Map k a)N M Monadm Mapka m (,) (,)ka Mapka O(log n). Retrieves the maximal (key,value) pair of the map, and the map stripped from that element fails (in the monad) when passed an empty map. maxViewWithKeymaxViewWithKey :: Monad m => IntMap a -> m ((Key, a), IntMap a)mO )O Monadm IntMapa m (,) (,)Keya IntMapa O(log n). Retrieves the maximal (key,value) couple of the map, and the map stripped from that element. fails (in the monad) when passed an empty map. maxViewmaxView :: Monad m => Set a -> m (a, Set a)P nP Monadm Seta m (,)a Seta O(log n). Retrieves the maximal key of the set, and the set stripped from that element fails (in the monad) when passed an empty set. maxViewmaxView :: Monad m => Map k a -> m (a, Map k a)Q Q Monadm Mapka m (,)a Mapka O(log n). Retrieves the maximal key's value of the map, and the map stripped from that element fails (in the monad) when passed an empty map. maxViewmaxView :: Monad m => IntSet -> m (Int, IntSet)R R MonadmIntSet m (,)IntIntSet O(min(n,W)). Retrieves the maximal key of the set, and the set stripped from that element fails (in the monad) when passed an empty set. mapWithKey mapWithKey :: (k -> a -> b) -> Map k a -> Map k b'T S kab Mapka Mapkb8 O(n). Map a function over all values in the map. mapWithKey mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap bT T Keyab IntMapa IntMapb8 O(n). Map a function over all values in the map. mapMonotonic mapMonotonic :: (a -> b) -> Set a -> Set bU U ab Seta SetbM O(n). The mapMonotonic f s == map f s, but works only when f is monotonic. The precondition is not checked. Semi-formally, we have:
and [x < y ==> f x < f y | x <- ls, y <- ls]
==> mapMonotonic f s == map f s
where ls = toList s
mapMaybeWithKeymapMaybeWithKey :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k bW W Ordkka Maybeb Mapka MapkbB O(n). Map keys/values and collect the Just results.
mapMaybeWithKeymapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap bX X Keya Maybeb IntMapa IntMapbB O(n). Map keys/values and collect the Just results.
mapMaybemapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k bY mY Ordka Maybeb Mapka Mapkb= O(n). Map values and collect the Just results.
mapMaybemapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b{Z MZ a Maybeb IntMapa IntMapb= O(n). Map values and collect the Just results.
mapKeysWith
mapKeysWith ::
Ord k2 =>
(a -> a -> a) ->
(k1 -> k2) -> Map k1 a -> Map k2 a[ H[ Ordk2aaak1k2 Mapk1a Mapk2a* O(n*log n). mapKeysWith c f s is the map
obtained by applying f to each key of s.
The size of the result may be smaller if f maps two or more
distinct keys to the same new key. In this case the associated values
will be combined using c.
mapKeysMonotonicmapKeysMonotonic ::
(k1 -> k2) -> Map k1 a -> Map k2 aQ] (] k1k2 Mapk1a Mapk2a_ O(n). mapKeysMonotonic f s == mapKeys f
s, but works only when f is strictly monotonic. The
precondition is not checked. Semi-formally, we have:
and [x < y ==> f x < f y | x <- ls, y <- ls]
==> mapKeysMonotonic f s == mapKeys f s
where ls = keys s
mapKeysmapKeys ::
Ord k2 =>
(k1 -> k2) -> Map k1 a -> Map k2 aS_ _ Ordk2k1k2 Mapk1a Mapk2a O(n*log n). mapKeys f s is the map obtained by
applying f to each key of s.
The size of the result may be smaller if f maps two or more
distinct keys to the same new key. In this case the value at the
smallest of these keys is retained.
mapEitherWithKeymapEitherWithKey :: Ord k => (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)[a a Ordkka Eitherbc Mapka (,) Mapkb MapkcT O(n). Map keys/values and separate the Left and
Right results.
mapEitherWithKeymapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)b @b Keya Eitherbc IntMapa (,) IntMapb IntMapcT O(n). Map keys/values and separate the Left and
Right results.
mapEither mapEither :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c)c ac Ordka Eitherbc Mapka (,) Mapkb MapkcO O(n). Map values and separate the Left and Right
results.
mapEither mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)d |d a Eitherbc IntMapa (,) IntMapb IntMapcO O(n). Map values and separate the Left and Right
results.
mapAccumWithKey
mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)e e akb (,)aca Mapkb (,)a Mapkc~ O(n). The function mapAccumWithKey threads an
accumulating argument through the map in ascending order of keys.
mapAccumWithKey
mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b ->
(a, IntMap c)=g f aKeyb (,)aca IntMapb (,)a IntMapc O(n). The function mapAccumWithKey threads an
accumulating argument through the map in ascending order of keys.
mapAccum
mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)h Ch ab (,)aca Mapkb (,)a Mapkcw O(n). The function mapAccum threads an accumulating
argument through the map in ascending order of keys.
mapAccum
mapAccum :: (a -> b -> (a, c)) -> a -> IntMap b ->
(a, IntMap c)i zi ab (,)aca IntMapb (,)a IntMapc O(n). The function mapAccum threads an
accumulating argument through the map in ascending order of keys.
mapmap :: (Ord a, Ord b) => (a -> b) -> Set a -> Set bj j Orda Ordbab Seta Setb O(n*log n). map f s is the set obtained by
applying f to each element of s.
It's worth noting that the size of the result may be smaller if, for
some (x,y), x /= y && f x == f y
mapmap :: (a -> b) -> Map k a -> Map k bGl "l ab Mapka Mapkb8 O(n). Map a function over all values in the map.
mapmap :: (Int -> Int) -> IntSet -> IntSetl l IntIntIntSetIntSet O(n*min(n,W)). map f s is the set obtained by
applying f to each element of s.
It's worth noting that the size of the result may be smaller if, for
some (x,y), x /= y && f x == f y
mapmap :: (a -> b) -> IntMap a -> IntMap brn Mn ab IntMapa IntMapb8 O(n). Map a function over all values in the map.
Map data Map k an 1 A Map from keys k to values a.
lookupIndex lookupIndex :: (Monad m, Ord k) => k -> Map k a -> m Into }o Monadm Ordkk Mapka mInt O(log n). Lookup the index of a key. The index is a
number from 0 up to, but not including, the size of the
map.
lookuplookup :: (Monad m, Ord k) => k -> Map k a -> m ap p Monadm Ordkk Mapka ma O(log n). Lookup the value at a key in the map.
The function will return the result in the monad or
fail in it the key isn't in the map. Often, the monad to use
is Maybe, so you get either (Just result) or
Nothing.
lookuplookup :: Monad m => Key -> IntMap a -> m ayr Pr MonadmKey IntMapa ma: O(min(n,W)). Lookup the value at a key in the map.
levelslevels :: Tree a -> [[a]]s r Treea [] []a* Lists of nodes at each level of the tree.
lengthlength :: Seq a -> Ints s SeqaInt5 O(1). The number of elements in the sequence.
keysSetkeysSet :: Map k a -> Set k3t t Mapka Setk- O(n). The set of all keys of the map.
keysSetkeysSet :: IntMap a -> IntSett t IntMapaIntSet6 O(n*min(n,W)). The set of all keys of the map.
keyskeys :: Map k a -> [k]Wu >u Mapka []k< O(n). Return all keys of the map in ascending order.
keyskeys :: IntMap a -> [Key]u u IntMapa []Key< O(n). Return all keys of the map in ascending order.
Key type Key = Intbv
isSubsetOf
isSubsetOf :: Ord a => Set a -> Set a -> Boolv v Orda Seta SetaBoolz O(n+m). Is this a subset? (s1 isSubsetOf s2)
tells whether s1 is a subset of s2.
isSubsetOf
isSubsetOf :: IntSet -> IntSet -> Boolw w IntSetIntSetBoolz O(n+m). Is this a subset? (s1 isSubsetOf s2)
tells whether s1 is a subset of s2.
isSubmapOfBy
isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool&y x OrdkabBool Mapka MapkbBool O(n+m). The expression (isSubmapOfBy f t1 t2)
returns True if all keys in t1 are in tree
t2, and when f returns True when applied to
their respective values. For example, the following expressions are
all True:
isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
But the following are all False:
isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
isSubmapOfBy
isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool| | abBool IntMapa IntMapbBool O(n+m). The expression (isSubmapOfBy f m1 m2)
returns True if all keys in m1 are in m2, and
when f returns True when applied to their respective
values. For example, the following expressions are all True:
isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])But the following are all False:
isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)]) isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])isSubmapOf isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Boold . Ordk Eqa Mapka MapkaBoold O(n+m). This function is defined as (isSubmapOf = isSubmapOfBy (==)). isSubmapOf isSubmapOf :: Eq a => IntMap a -> IntMap a -> Boola 5 Eqa IntMapa IntMapaBoole O(n+m). Is this a submap? Defined as (isSubmapOf = isSubmapOfBy (==)). isProperSubsetOfisProperSubsetOf :: Ord a => Set a -> Set a -> Boola : Orda Seta SetaBoolF O(n+m). Is this a proper subset? (ie. a subset but not equal). isProperSubsetOfisProperSubsetOf :: IntSet -> IntSet -> Bool- IntSetIntSetBoolF O(n+m). Is this a proper subset? (ie. a subset but not equal). isProperSubmapOfBy isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> BoolF OrdkabBool Mapka MapkbBool* O(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when m1 and m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True:
isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])But the following are all False:
isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])isProperSubmapOfBy isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool2 abBool IntMapa IntMapbBool* O(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when m1 and m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True:
isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])But the following are all False:
isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])isProperSubmapOfisProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool ܋ Ordk Eqa Mapka MapkaBool O(n+m). Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)). isProperSubmapOfisProperSubmapOf :: Eq a => IntMap a -> IntMap a -> BoolM ! Eqa IntMapa IntMapaBool O(log n). Retrieves the maximal key of the map, and the map stripped from that element. fails (in the monad) when passed an empty map. O(log n). Retrieves the minimal key of the map, and the map stripped from that element. fails (in the monad) when passed an empty map. O(log n). Delete and find the maximal element. O(log n). Delete and find the minimal element. O(log n). The minimal key of the map. O(log n). The maximal key of the map. O(log n). Delete the minimal key. O(log n). Delete the maximal key. O(n+m). Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)). IntSet data IntSet a A set of integers. IntMap data IntMap a ( A map of integers to values a. intersectionWithKey intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c m Ordkkabc Mapka Mapkb Mapkcy O(n+m). Intersection with a combining function. Intersection is more efficient on (bigset intersection smallset) intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c intersectionWithKey f Tip t = Tip intersectionWithKey f t Tip = Tip intersectionWithKey f t1 t2 = intersectWithKey f t1 t2 intersectWithKey f Tip t = Tip intersectWithKey f t Tip = Tip intersectWithKey f t (Bin _ kx x l r) = case found of Nothing -> merge tl tr Just y -> join kx (f kx y x) tl tr where (lt,found,gt) = splitLookup kx t tl = intersectWithKey f lt l tr = intersectWithKey f gt r intersectionWithKey intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a Ô Keyaba IntMapa IntMapb IntMapa; O(n+m). The intersection with a combining function. intersectionWith intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c ̕ Ordkabc Mapka Mapkb Mapkc7 O(n+m). Intersection with a combining function. intersectionWith intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a Ж aba IntMapa IntMapb IntMapa; O(n+m). The intersection with a combining function. intersection intersection :: Ord a => Set a -> Set a -> Set aؗ Orda Seta Seta Seta O(n+m). The intersection of two sets. Elements of the result come from the first set, so for example
import qualified Data.Set as S
data AB = A | B deriving Show
instance Ord AB where compare _ _ = EQ
instance Eq AB where _ == _ = True
main = print (S.singleton A `S.intersection` S.singleton B,
S.singleton B `S.intersection` S.singleton A)
prints (fromList [A],fromList [B]).
intersection intersection :: Ord k => Map k a -> Map k b -> Map k a& Ordk Mapka Mapkb Mapka O(n+m). Intersection of two maps. The values in the first map
are returned, i.e. (intersection m1 m2 ==
intersectionWith const m1 m2).
intersection intersection :: IntSet -> IntSet -> IntSetT 9 IntSetIntSetIntSet- O(n+m). The intersection of two sets.
intersection intersection :: IntMap a -> IntMap b -> IntMap a IntMapa IntMapb IntMapaK O(n+m). The (left-biased) intersection of two maps (based on
keys).
insertWithKey' insertWithKey' :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a: Ordkkaaaka Mapka MapkaN Same as insertWithKey, but the combining function is applied
strictly.
insertWithKey
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a] " Ordkkaaaka Mapka Mapkaf O(log n). Insert with a combining function.
insertWithKey f key value mp will insert the pair
(key, value) into mp if key does not exist in the map. If the
key does exist, the function will insert the pair (key,f key
new_value old_value). Note that the key passed to f is the same
key passed to insertWithKey.
insertWithKey
insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a Z KeyaaaKeya IntMapa IntMapa O(min(n,W)). Insert with a combining function.
insertWithKey f key value mp will insert the pair
(key, value) into mp if key does not exist in the map. If the
key does exist, the function will insert f key new_value
old_value.
insertWith' insertWith' :: Ord k =>
(a -> a -> a) -> k -> a -> Map k a -> Map k ad , Ordkaaaka Mapka MapkaK Same as insertWith, but the combining function is applied
strictly.
insertWith
insertWith :: Ord k =>
(a -> a -> a) -> k -> a -> Map k a -> Map k av > Ordkaaaka Mapka Mapka O(log n). Insert with a combining function.
insertWith f key value mp will insert the pair (key,
value) into mp if key does not exist in the map. If the key
does exist, the function will insert the pair (key, f new_value
old_value).
insertWith
insertWith ::
(a -> a -> a) -> Key -> a -> IntMap a -> IntMap aB aaaKeya IntMapa IntMapa O(min(n,W)). Insert with a combining function.
insertWith f key value mp will insert the pair (key,
value) into mp if key does not exist in the map. If the key
does exist, the function will insert f new_value old_value.
insertLookupWithKey insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)F Ordkkaaaka Mapka (,) Maybea Mapka O(log n). The expression (insertLookupWithKey f k x
map) is a pair where the first element is equal to
(lookup k map) and the second element equal to
(insertWithKey f k x map).
insertLookupWithKey insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)$ ܨ KeyaaaKeya IntMapa (,) Maybea IntMapa O(min(n,W)). The expression (insertLookupWithKey f k
x map) is a pair where the first element is equal to
(lookup k map) and the second element equal to
(insertWithKey f k x map).
insertinsert :: Ord a => a -> Set a -> Set a l Ordaa Seta Seta O(log n). Insert an element in a set. If the set already
contains an element equal to the given value, it is replaced with the
new value.
insert
insert :: Ord k => k -> a -> Map k a -> Map k a Ordkka Mapka Mapka O(log n). Insert a new key and value in the map. If the key is
already present in the map, the associated value is replaced with the
supplied value, i.e. insert is equivalent to
insertWith const.
insertinsert :: Int -> IntSet -> IntSet IntIntSetIntSet O(min(n,W)). Add a value to the set. When the value is already
an element of the set, it is replaced by the new one, ie.
insert is left-biased.
insert
insert :: Key -> a -> IntMap a -> IntMap aA Keya IntMapa IntMapa O(min(n,W)). Insert a new key/value pair in the map. If the key
is already present in the map, the associated value is replaced with
the supplied value, i.e. insert is equivalent to
insertWith const.
indexindex :: Seq a -> Int -> a ~ SeqaIntaA O(log(min(i,n-i))). The element at the specified position
indegreeindegree :: Graph -> Table Int; # Graph TableInt. A table of the count of edges into each node.
graphFromEdges'graphFromEdges' :: Ord key => [(node, key, [key])] -> %(Graph, Vertex -> (node, key, [key]))e Ordkey [] (,,)nodekey []key (,)GraphVertex (,,)nodekey []key Identical to graphFromEdges, except that the return value does
not include the function which maps keys to vertices. This version of
graphFromEdges is for backwards compatibility.
graphFromEdgesgraphFromEdges :: Ord key => [(node, key, [key])] -> :(Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)O Ͳ Ordkey [] (,,)nodekey []key (,,)GraphVertex (,,)nodekey []keykey MaybeVertex Build a graph from a list of nodes uniquely identified by keys, with a
list of keys of nodes this node should have edges to. The out-list may
contain keys that don't correspond to nodes of the graph; they are
ignored.
Graph type Graph = Table [Vertex]j Y Adjacency list representation of a graph, mapping each vertex to its
list of successors.
fromListWithKeyfromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a H Ordkkaaa [] (,)ka Mapka} O(n*log n). Build a map from a list of key/value pairs with a
combining function. See also fromAscListWithKey.
fromListWithKeyfromListWithKey :: (Key -> a -> a -> a) ->
[(Key, a)] -> IntMap a Keyaaa [] (,)Keya IntMapaz O(n*min(n,W)). Build a map from a list of key/value pairs with
a combining function. See also fromAscListWithKey'.
fromListWith fromListWith :: Ord k =>
(a -> a -> a) -> [(k, a)] -> Map k a Ordkaaa [] (,)ka Mapkaz O(n*log n). Build a map from a list of key/value pairs with a
combining function. See also fromAscListWith.
fromListWith fromListWith ::
(a -> a -> a) ->
[(Key, a)] -> IntMap a и aaa [] (,)Keya IntMapa~ O(n*min(n,W)). Create a map from a list of key/value pairs with
a combining function. See also fromAscListWith.
fromListfromList :: Ord a => [a] -> Set a й Orda []a Seta9 O(n*log n). Create a set from a list of elements.
fromListfromList :: [a] -> Seq a r []a Seqa O(n). Create a sequence from a finite list of elements. There
is a function toList in the opposite direction for all
instances of the Foldable class, including Seq.
fromListfromList :: Ord k => [(k, a)] -> Map k aϻ Ordk [] (,)ka Mapka\ O(n*log n). Build a map from a list of key/value pairs. See
also fromAscList.
fromListfromList :: [Int] -> IntSet w []IntIntSet< O(n*min(n,W)). Create a set from a list of integers.
fromListfromList ::
[(Key, a)] -> IntMap aA [] (,)Keya IntMapaC O(n*min(n,W)). Create a map from a list of key/value pairs.
fromDistinctAscListfromDistinctAscList :: [a] -> Set a []a Seta O(n). Build a set from an ascending list of distinct elements
in linear time. The precondition (input list is strictly ascending)
is not checked.
fromDistinctAscListfromDistinctAscList :: [(k, a)] -> Map k a" [] (,)ka Mapka} O(n). Build a map from an ascending list of distinct elements
in linear time. The precondition is not checked.
fromDistinctAscListfromDistinctAscList :: [Int] -> IntSet []IntIntSetO O(n*min(n,W)). Build a set from an ascending list of distinct
elements.
fromDistinctAscListfromDistinctAscList ::
[(Key, a)] -> IntMap a [] (,)Keya IntMapay O(n*min(n,W)). Build a map from a list of key/value pairs where
the keys are in ascending order and all distinct.
fromAscListWithKeyfromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a1 Eqkkaaa [] (,)ka Mapka O(n). Build a map from an ascending list in linear time with a
combining function for equal keys. The precondition (input list is
ascending) is not checked.
fromAscListWithKeyfromAscListWithKey :: (Key -> a -> a -> a) ->
[(Key, a)] -> IntMap a c Keyaaa [] (,)Keya IntMapa O(n*min(n,W)). Build a map from a list of key/value pairs where
the keys are in ascending order, with a combining function on equal
keys.
fromAscListWithfromAscListWith :: Eq k =>
(a -> a -> a) -> [(k, a)] -> Map k a Eqkaaa [] (,)ka Mapka O(n). Build a map from an ascending list in linear time with a
combining function for equal keys. The precondition (input list is
ascending) is not checked.
fromAscListWithfromAscListWith ::
(a -> a -> a) ->
[(Key, a)] -> IntMap a4 aaa [] (,)Keya IntMapa O(n*min(n,W)). Build a map from a list of key/value pairs where
the keys are in ascending order, with a combining function on equal
keys.
fromAscList fromAscList :: Eq a => [a] -> Set a; Eqa []a Seta O(n). Build a set from an ascending list in linear time. The
precondition (input list is ascending) is not checked.
fromAscList fromAscList :: Eq k => [(k, a)] -> Map k aG Eqk [] (,)ka Mapka O(n). Build a map from an ascending list in linear time. The
precondition (input list is ascending) is not checked.
fromAscList fromAscList :: [Int] -> IntSet1 []IntIntSetF O(n*min(n,W)). Build a set from an ascending list of elements.
fromAscList fromAscList ::
[(Key, a)] -> IntMap a [] (,)Keya IntMapah O(n*min(n,W)). Build a map from a list of key/value pairs where
the keys are in ascending order.
Forest type Forest a = [Tree a] foldWithKey
foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b: kabbb Mapkab O(n). Fold the keys and values in the map, such that
foldWithKey f z == Prelude.foldr (uncurry f) z .
toAscList. For example,
keys map = foldWithKey (\k x ks -> k:ks) [] mapfoldWithKey foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b Keyabbb IntMapab O(n). Fold the keys and values in the map, such that foldWithKey f z == Prelude.foldr (uncurry f) z . toAscList. For example,
keys map = foldWithKey (\k x ks -> k:ks) [] mapfold fold :: (a -> b -> b) -> b -> Set a -> b( abbb SetabF O(n). Fold over the elements of a set in an unspecified order. fold fold :: (a -> b -> b) -> b -> Map k a -> b abbb Mapkab O(n). Fold the values in the map, such that fold f z == Prelude.foldr f z . elems. For example,
elems map = fold (:) [] mapfold fold :: (Int -> b -> b) -> b -> IntSet -> b$ IntbbbIntSetb O(n). Fold over the elements of a set in an unspecified order.
sum set == fold (+) 0 set elems set == fold (:) [] setfold fold :: (a -> b -> b) -> b -> IntMap a -> b: abbb IntMapab O(n). Fold the values in the map, such that fold f z == Prelude.foldr f z . elems. For example,
elems map = fold (:) [] mapflattenSCCs flattenSCCs :: [SCC a] -> [a]O 3 [] SCCa []a9 The vertices of a list of strongly connected components. flattenSCC flattenSCC :: SCC vertex -> [vertex] SCCvertex []vertex0 The vertices of a strongly connected component. flattenflatten :: Tree a -> [a] w Treea []a% The elements of a tree in pre-order. findWithDefault findWithDefault :: Ord k => a -> k -> Map k a -> aP - Ordkak Mapkaa O(log n). The expression (findWithDefault def k map) returns the value at key k or returns def when the key is not in the map. findWithDefault findWithDefault :: a -> Key -> IntMap a -> a l aKey IntMapaa O(min(n,W)). The expression (findWithDefault def k map) returns the value at key k or returns def when the key is not an element of the map. findMinfindMin :: Set a -> a Setaa/ O(log n). The minimal element of a set. findMinfindMin :: Map k a -> (k, a)* Mapka (,)ka- O(log n). The minimal key of the map. findMinfindMin :: IntSet -> Int IntSetInt2 O(min(n,W)). The minimal element of a set. findMaxfindMax :: Set a -> a6 & Setaa/ O(log n). The maximal element of a set. findMaxfindMax :: Map k a -> (k, a) Mapka (,)ka- O(log n). The maximal key of the map. findMaxfindMax :: IntSet -> IntS C IntSetInt2 O(min(n,W)). The maximal element of a set. findIndex findIndex :: Ord k => k -> Map k a -> Int Ordkk MapkaInt O(log n). Return the index of a key. The index is a number from 0 up to, but not including, the size of the map. Calls error when the key is not a member of the map. filterWithKey filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a X OrdkkaBool Mapka Mapka@ O(n). Filter all keys/values that satisfy the predicate. filterWithKey filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap as F KeyaBool IntMapa IntMapaA O(n). Filter all keys/values that satisfy some predicate. filterfilter :: Ord a => (a -> Bool) -> Set a -> Set aG OrdaaBool Seta Seta= O(n). Filter all elements that satisfy the predicate. filterfilter :: Ord k => (a -> Bool) -> Map k a -> Map k a! OrdkaBool Mapka Mapka; O(n). Filter all values that satisfy the predicate. filterfilter :: (Int -> Bool) -> IntSet -> IntSet IntBoolIntSetIntSet> O(n). Filter all elements that satisfy some predicate. filterfilter :: (a -> Bool) -> IntMap a -> IntMap a aBool IntMapa IntMapa< O(n). Filter all values that satisfy some predicate. EmptyREmptyR :: ViewR a) ViewRa empty sequence EmptyLEmptyL :: ViewL a} p ViewLa empty sequence emptyempty :: Set a Seta O(1). The empty set. emptyempty :: Seq a& Seqa! O(1). The empty sequence. emptyempty :: Map k a } Mapka O(1). The empty map. emptyempty :: IntSet IntSet O(1). The empty set. emptyempty :: IntMap aF 8 IntMapa O(1). The empty map. elemselems :: Set a -> [a] Seta []a$ O(n). The elements of a set. elemselems :: Map k a -> [a]= $ Mapka []aR O(n). Return all elements of the map in the ascending order of their keys. elemselems :: IntSet -> [Int] IntSet []IntM O(n). The elements of a set. (For sets, this is equivalent to toList) elemselems :: IntMap a -> [a] ~ IntMapa []aR O(n). Return all elements of the map in the ascending order of their keys. elemAtelemAt :: Int -> Map k a -> (k, a)d B Int Mapka (,)kah O(log n). Retrieve an element by index. Calls error when an invalid index is used. edgesedges :: Graph -> [Edge]( Graph []Edge All edges of a graph. Edge type Edge = (Vertex, Vertex) - An edge from the first vertex to the second. dropdrop :: Int -> Seq a -> Seq a Int Seqa SeqaN O(log(min(i,n-i))). Elements of a sequence after the first i. drawTreedrawTree :: Tree String -> String TreeStringString& Neat 2-dimensional drawing of a tree. drawForest drawForest :: Forest String -> Stringp S ForestStringString( Neat 2-dimensional drawing of a forest. differenceWithKey differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a 9 Ordkkab Maybea Mapka Mapkb Mapka O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the key and both values. If it returns Nothing, the element is discarded (proper set difference). If it returns (Just y), the element is updated with a new value y. The implementation uses an efficient hedge algorithm comparable with hedge-union. differenceWithKey differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a Keyab Maybea IntMapa IntMapb IntMapaD O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the key and both values. If it returns Nothing, the element is discarded (proper set difference). If it returns (Just y), the element is updated with a new value y. differenceWith differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a* Ordkab Maybea Mapka Mapkb Mapka O(n+m). Difference with a combining function. The implementation uses an efficient hedge algorithm comparable with hedge-union. differenceWith differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a O ab Maybea IntMapa IntMapb IntMapa5 O(n+m). Difference with a combining function. difference difference :: Ord a => Set a -> Set a -> Set aV + Orda Seta Seta Seta O(n+m). Difference of two sets. The implementation uses an efficient hedge algorithm comparable with hedge-union. difference difference :: Ord k => Map k a -> Map k b -> Map k a L Ordk Mapka Mapkb Mapka O(n+m). Difference of two maps. The implementation uses an efficient hedge algorithm comparable with hedge-union. difference difference :: IntSet -> IntSet -> IntSet j IntSetIntSetIntSet, O(n+m). Difference between two sets. difference difference :: IntMap a -> IntMap b -> IntMap aD IntMapa IntMapb IntMapa< O(n+m). Difference between two maps (based on keys). dfsdfs :: Graph -> [Vertex] -> Forest Vertex Graph []Vertex ForestVertex A spanning forest of the part of the graph reachable from the listed vertices, obtained from a depth-first search of the graph starting at each of the listed vertices in order. dffdff :: Graph -> Forest Vertex Graph ForestVertex A spanning forest of the graph, obtained from a depth-first search of the graph starting from each vertex in an unspecified order. deleteMin deleteMin :: Set a -> Set a Seta Seta- O(log n). Delete the minimal element. deleteMin deleteMin :: Map k a -> Map k a Mapka Mapka) O(log n). Delete the minimal key. deleteMin deleteMin :: IntSet -> IntSet* IntSetIntSet0 O(min(n,W)). Delete the minimal element. deleteMax deleteMax :: Set a -> Set a Seta Seta- O(log n). Delete the maximal element. deleteMax deleteMax :: Map k a -> Map k aY < Mapka Mapka) O(log n). Delete the maximal key. deleteMax deleteMax :: IntSet -> IntSet IntSetIntSet0 O(min(n,W)). Delete the maximal element. deleteFindMin deleteFindMin :: Set a -> (a, Set a) n Seta (,)a Setau O(log n). Delete and find the minimal element.
deleteFindMin set = (findMin set, deleteMin set)deleteFindMin deleteFindMin :: Map k a -> ((k, a), Map k a) g Mapka (,) (,)ka Mapka6 O(log n). Delete and find the minimal element. deleteFindMin deleteFindMin :: IntSet -> (Int, IntSet)K , IntSet (,)IntIntSetx O(min(n,W)). Delete and find the minimal element.
deleteFindMin set = (findMin set, deleteMin set)deleteFindMax deleteFindMax :: Set a -> (a, Set a)> Seta (,)a Setau O(log n). Delete and find the maximal element.
deleteFindMax set = (findMax set, deleteMax set)deleteFindMax deleteFindMax :: Map k a -> ((k, a), Map k a)G Mapka (,) (,)ka Mapka6 O(log n). Delete and find the maximal element. deleteFindMax deleteFindMax :: IntSet -> (Int, IntSet) IntSet (,)IntIntSetx O(min(n,W)). Delete and find the maximal element.
deleteFindMax set = (findMax set, deleteMax set)deleteAtdeleteAt :: Int -> Map k a -> Map k a Int Mapka Mapka O(log n). Delete the element at index. Defined as (deleteAt i map = updateAt (k x -> Nothing) i map). deletedelete :: Ord a => a -> Set a -> Set a Ordaa Seta Seta/ O(log n). Delete an element from a set. deletedelete :: Ord k => k -> Map k a -> Map k a Ordkk Mapka Mapka O(log n). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned. deletedelete :: Int -> IntSet -> IntSet IntIntSetIntSeth O(min(n,W)). Delete a value in the set. Returns the original set when the value was not present. deletedelete :: Key -> IntMap a -> IntMap a w Key IntMapa IntMapa O(min(n,W)). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned. CyclicSCC CyclicSCC :: [vertex] -> SCC vertex r []vertex SCCvertex. A maximal set of mutually reachable vertices. components components :: Graph -> Forest Vertex3 Graph ForestVertex The connected components of a graph. Two vertices are connected if there is a path between them, traversing edges in either direction. buildGbuildG :: Bounds -> [Edge] -> Graph2 Bounds []EdgeGraph$ Build a graph from a list of edges. Bounds type Bounds = (Vertex, Vertex) The bounds of a Table. bccbcc :: Graph -> Forest [Vertex]& Graph Forest []Vertex} The biconnected components of a graph. An undirected graph is biconnected if the deletion of any vertex leaves it connected. assocsassocs :: Map k a -> [(k, a)] Mapka [] (,)kaK O(n). Return all key/value pairs in the map in ascending key order. assocsassocs :: IntMap a -> [(Key, a)] IntMapa [] (,)KeyaK O(n). Return all key/value pairs in the map in ascending key order. alter alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a Ordk Maybea Maybeak Mapka Mapka O(log n). The expression (alter f k map) alters the value x at k, or absence thereof. alter can be used to insert, delete, or update a value in a Map. In short : lookup k (alter f k m) = f (lookup k m) adjustWithKey adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a Ordkkaak Mapka Mapkaz O(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned. adjustWithKey adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a KeyaaKey IntMapa IntMapa} O(min(n,W)). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned. adjust adjust :: (a -> a) -> Int -> Seq a -> Seq a aaInt Seqa SeqaH O(log(min(i,n-i))). Update the element at the specified position adjust adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a Ordkaak Mapka Mapkaz O(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned. adjust adjust :: (a -> a) -> Key -> IntMap a -> IntMap a aaKey IntMapa IntMapa} O(min(n,W)). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned. AcyclicSCC AcyclicSCC :: vertex -> SCC vertex vertex SCCvertex* A single vertex that is not in any cycle. \\ (\\) :: Ord a => Set a -> Set a -> Set a l Orda Seta Seta Seta& O(n+m). See difference. \\ (\\) :: Ord k => Map k a -> Map k b -> Map k aV " Ordk Mapka Mapkb Mapka& O(n+m). See difference. \\ (\\) :: IntSet -> IntSet -> IntSet IntSetIntSetIntSet& O(n+m). See difference. \\ (\\) :: IntMap a -> IntMap b -> IntMap a u IntMapa IntMapb IntMapa& O(n+m). See difference. >< (><) :: Seq a -> Seq a -> Seq a< Seqa Seqa Seqa6 O(log(min(n1,n2))). Concatenate two sequences. <| (<|) :: a -> Seq a -> Seq a a Seqa Seqa{ O(1). Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end. :> (:>) :: Seq a -> a -> ViewR a Seqaa ViewRaD the sequence minus the rightmost element, and the rightmost element :< (:<) :: a -> Seq a -> ViewL a} a a Seqa ViewLa. leftmost element and the rest of the sequence ! (!) :: Ord k => Map k a -> k -> a" Ordk Mapkaka` O(log n). Find the value at a key. Calls error when the element can not be found. ! (!) :: IntMap a -> Key -> a IntMapaKeyac O(min(n,W)). Find the value at a key. Calls error when the element can not be found. Tree module Data.Tree } 5 Multi-way trees (aka rose trees) and forests. Set module Data.Set An efficient implementation of sets. Since many function names (but not the type name) clash with Prelude names, this module is usually imported qualified, e.g.
import Data.Set (Set) import qualified Data.Set as SetThe implementation of Set is based on size balanced binary trees (or trees of bounded balance) as described by:
import Data.Map (Map) import qualified Data.Map as MapThe implementation of Map is based on size balanced binary trees (or trees of bounded balance) as described by:
import Data.IntSet (IntSet) import qualified Data.IntSet as IntSetThe implementation is based on big-endian patricia trees. This data structure performs especially well on binary operations like union and intersection. However, my benchmarks show that it is also (much) faster on insertions and deletions when compared to a generic size-balanced set implementation (see Data.Set).
import Data.IntMap (IntMap) import qualified Data.IntMap as IntMapThe implementation is based on big-endian patricia trees. This data structure performs especially well on binary operations like union and intersection. However, my benchmarks show that it is also (much) faster on insertions and deletions when compared to a generic size-balanced map implementation (see Data.Map).