1 {-# OPTIONS -cpp -fglasgow-exts -fno-bang-patterns #-}
2 -----------------------------------------------------------------------------
3 -- Module : Data.IntMap
4 -- Copyright : (c) Daan Leijen 2002
6 -- Maintainer : libraries@haskell.org
7 -- Stability : provisional
8 -- Portability : portable
10 -- An efficient implementation of maps from integer keys to values.
12 -- This module is intended to be imported @qualified@, to avoid name
13 -- clashes with "Prelude" functions. eg.
15 -- > import Data.IntMap as Map
17 -- The implementation is based on /big-endian patricia trees/. This data
18 -- structure performs especially well on binary operations like 'union'
19 -- and 'intersection'. However, my benchmarks show that it is also
20 -- (much) faster on insertions and deletions when compared to a generic
21 -- size-balanced map implementation (see "Data.Map" and "Data.FiniteMap").
23 -- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
24 -- Workshop on ML, September 1998, pages 77-86,
25 -- <http://www.cse.ogi.edu/~andy/pub/finite.htm>
27 -- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
28 -- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
29 -- October 1968, pages 514-534.
31 -- Many operations have a worst-case complexity of /O(min(n,W))/.
32 -- This means that the operation can become linear in the number of
33 -- elements with a maximum of /W/ -- the number of bits in an 'Int'
35 -----------------------------------------------------------------------------
39 IntMap, Key -- instance Eq,Show
58 , insertWith, insertWithKey, insertLookupWithKey
116 , fromDistinctAscList
128 , isSubmapOf, isSubmapOfBy
129 , isProperSubmapOf, isProperSubmapOfBy
137 import Prelude hiding (lookup,map,filter,foldr,foldl,null)
140 import qualified Data.IntSet as IntSet
141 import Data.Monoid (Monoid(..))
143 import Data.Foldable (Foldable(foldMap))
147 import qualified Prelude
148 import Debug.QuickCheck
149 import List (nub,sort)
150 import qualified List
153 #if __GLASGOW_HASKELL__
155 import Data.Generics.Basics
156 import Data.Generics.Instances
159 #if __GLASGOW_HASKELL__ >= 503
161 import GHC.Exts ( Word(..), Int(..), shiftRL# )
162 #elif __GLASGOW_HASKELL__
164 import GlaExts ( Word(..), Int(..), shiftRL# )
169 infixl 9 \\{-This comment teaches CPP correct behaviour -}
171 -- A "Nat" is a natural machine word (an unsigned Int)
174 natFromInt :: Key -> Nat
175 natFromInt i = fromIntegral i
177 intFromNat :: Nat -> Key
178 intFromNat w = fromIntegral w
180 shiftRL :: Nat -> Key -> Nat
181 #if __GLASGOW_HASKELL__
182 {--------------------------------------------------------------------
183 GHC: use unboxing to get @shiftRL@ inlined.
184 --------------------------------------------------------------------}
185 shiftRL (W# x) (I# i)
188 shiftRL x i = shiftR x i
191 {--------------------------------------------------------------------
193 --------------------------------------------------------------------}
195 -- | /O(min(n,W))/. Find the value at a key.
196 -- Calls 'error' when the element can not be found.
198 (!) :: IntMap a -> Key -> a
201 -- | /O(n+m)/. See 'difference'.
202 (\\) :: IntMap a -> IntMap b -> IntMap a
203 m1 \\ m2 = difference m1 m2
205 {--------------------------------------------------------------------
207 --------------------------------------------------------------------}
208 -- | A map of integers to values @a@.
210 | Tip {-# UNPACK #-} !Key a
211 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
217 instance Monoid (IntMap a) where
222 instance Foldable IntMap where
223 foldMap f Nil = mempty
224 foldMap f (Tip _k v) = f v
225 foldMap f (Bin _ _ l r) = foldMap f l `mappend` foldMap f r
227 #if __GLASGOW_HASKELL__
229 {--------------------------------------------------------------------
231 --------------------------------------------------------------------}
233 -- This instance preserves data abstraction at the cost of inefficiency.
234 -- We omit reflection services for the sake of data abstraction.
236 instance Data a => Data (IntMap a) where
237 gfoldl f z im = z fromList `f` (toList im)
238 toConstr _ = error "toConstr"
239 gunfold _ _ = error "gunfold"
240 dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
241 dataCast1 f = gcast1 f
245 {--------------------------------------------------------------------
247 --------------------------------------------------------------------}
248 -- | /O(1)/. Is the map empty?
249 null :: IntMap a -> Bool
253 -- | /O(n)/. Number of elements in the map.
254 size :: IntMap a -> Int
257 Bin p m l r -> size l + size r
261 -- | /O(min(n,W))/. Is the key a member of the map?
262 member :: Key -> IntMap a -> Bool
268 -- | /O(log n)/. Is the key not a member of the map?
269 notMember :: Key -> IntMap a -> Bool
270 notMember k m = not $ member k m
272 -- | /O(min(n,W))/. Lookup the value at a key in the map.
273 lookup :: (Monad m) => Key -> IntMap a -> m a
274 lookup k t = case lookup' k t of
276 Nothing -> fail "Data.IntMap.lookup: Key not found"
278 lookup' :: Key -> IntMap a -> Maybe a
280 = let nk = natFromInt k in seq nk (lookupN nk t)
282 lookupN :: Nat -> IntMap a -> Maybe a
286 | zeroN k (natFromInt m) -> lookupN k l
287 | otherwise -> lookupN k r
289 | (k == natFromInt kx) -> Just x
290 | otherwise -> Nothing
293 find' :: Key -> IntMap a -> a
296 Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
300 -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
301 -- returns the value at key @k@ or returns @def@ when the key is not an
302 -- element of the map.
303 findWithDefault :: a -> Key -> IntMap a -> a
304 findWithDefault def k m
309 {--------------------------------------------------------------------
311 --------------------------------------------------------------------}
312 -- | /O(1)/. The empty map.
317 -- | /O(1)/. A map of one element.
318 singleton :: Key -> a -> IntMap a
322 {--------------------------------------------------------------------
324 --------------------------------------------------------------------}
325 -- | /O(min(n,W))/. Insert a new key\/value pair in the map.
326 -- If the key is already present in the map, the associated value is
327 -- replaced with the supplied value, i.e. 'insert' is equivalent to
328 -- @'insertWith' 'const'@.
329 insert :: Key -> a -> IntMap a -> IntMap a
333 | nomatch k p m -> join k (Tip k x) p t
334 | zero k m -> Bin p m (insert k x l) r
335 | otherwise -> Bin p m l (insert k x r)
338 | otherwise -> join k (Tip k x) ky t
341 -- right-biased insertion, used by 'union'
342 -- | /O(min(n,W))/. Insert with a combining function.
343 -- @'insertWith' f key value mp@
344 -- will insert the pair (key, value) into @mp@ if key does
345 -- not exist in the map. If the key does exist, the function will
346 -- insert @f new_value old_value@.
347 insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
349 = insertWithKey (\k x y -> f x y) k x t
351 -- | /O(min(n,W))/. Insert with a combining function.
352 -- @'insertWithKey' f key value mp@
353 -- will insert the pair (key, value) into @mp@ if key does
354 -- not exist in the map. If the key does exist, the function will
355 -- insert @f key new_value old_value@.
356 insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
357 insertWithKey f k x t
360 | nomatch k p m -> join k (Tip k x) p t
361 | zero k m -> Bin p m (insertWithKey f k x l) r
362 | otherwise -> Bin p m l (insertWithKey f k x r)
364 | k==ky -> Tip k (f k x y)
365 | otherwise -> join k (Tip k x) ky t
369 -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
370 -- is a pair where the first element is equal to (@'lookup' k map@)
371 -- and the second element equal to (@'insertWithKey' f k x map@).
372 insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
373 insertLookupWithKey f k x t
376 | nomatch k p m -> (Nothing,join k (Tip k x) p t)
377 | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
378 | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
380 | k==ky -> (Just y,Tip k (f k x y))
381 | otherwise -> (Nothing,join k (Tip k x) ky t)
382 Nil -> (Nothing,Tip k x)
385 {--------------------------------------------------------------------
387 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
388 --------------------------------------------------------------------}
389 -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
390 -- a member of the map, the original map is returned.
391 delete :: Key -> IntMap a -> IntMap a
396 | zero k m -> bin p m (delete k l) r
397 | otherwise -> bin p m l (delete k r)
403 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
404 -- a member of the map, the original map is returned.
405 adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
407 = adjustWithKey (\k x -> f x) k m
409 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
410 -- a member of the map, the original map is returned.
411 adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
413 = updateWithKey (\k x -> Just (f k x)) k m
415 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
416 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
417 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
418 update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
420 = updateWithKey (\k x -> f x) k m
422 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
423 -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
424 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
425 updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
430 | zero k m -> bin p m (updateWithKey f k l) r
431 | otherwise -> bin p m l (updateWithKey f k r)
433 | k==ky -> case (f k y) of
439 -- | /O(min(n,W))/. Lookup and update.
440 updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
441 updateLookupWithKey f k t
444 | nomatch k p m -> (Nothing,t)
445 | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
446 | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
448 | k==ky -> case (f k y) of
449 Just y' -> (Just y,Tip ky y')
450 Nothing -> (Just y,Nil)
451 | otherwise -> (Nothing,t)
456 -- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
457 -- 'alter' can be used to insert, delete, or update a value in a 'Map'.
458 -- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@
462 | nomatch k p m -> case f Nothing of
464 Just x -> join k (Tip k x) p t
465 | zero k m -> bin p m (alter f k l) r
466 | otherwise -> bin p m l (alter f k r)
468 | k==ky -> case f (Just y) of
471 | otherwise -> case f Nothing of
472 Just x -> join k (Tip k x) ky t
474 Nil -> case f Nothing of
479 {--------------------------------------------------------------------
481 --------------------------------------------------------------------}
482 -- | The union of a list of maps.
483 unions :: [IntMap a] -> IntMap a
485 = foldlStrict union empty xs
487 -- | The union of a list of maps, with a combining operation
488 unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
490 = foldlStrict (unionWith f) empty ts
492 -- | /O(n+m)/. The (left-biased) union of two maps.
493 -- It prefers the first map when duplicate keys are encountered,
494 -- i.e. (@'union' == 'unionWith' 'const'@).
495 union :: IntMap a -> IntMap a -> IntMap a
496 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
497 | shorter m1 m2 = union1
498 | shorter m2 m1 = union2
499 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
500 | otherwise = join p1 t1 p2 t2
502 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
503 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
504 | otherwise = Bin p1 m1 l1 (union r1 t2)
506 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
507 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
508 | otherwise = Bin p2 m2 l2 (union t1 r2)
510 union (Tip k x) t = insert k x t
511 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
515 -- | /O(n+m)/. The union with a combining function.
516 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
518 = unionWithKey (\k x y -> f x y) m1 m2
520 -- | /O(n+m)/. The union with a combining function.
521 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
522 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
523 | shorter m1 m2 = union1
524 | shorter m2 m1 = union2
525 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
526 | otherwise = join p1 t1 p2 t2
528 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
529 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
530 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
532 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
533 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
534 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
536 unionWithKey f (Tip k x) t = insertWithKey f k x t
537 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
538 unionWithKey f Nil t = t
539 unionWithKey f t Nil = t
541 {--------------------------------------------------------------------
543 --------------------------------------------------------------------}
544 -- | /O(n+m)/. Difference between two maps (based on keys).
545 difference :: IntMap a -> IntMap b -> IntMap a
546 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
547 | shorter m1 m2 = difference1
548 | shorter m2 m1 = difference2
549 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
552 difference1 | nomatch p2 p1 m1 = t1
553 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
554 | otherwise = bin p1 m1 l1 (difference r1 t2)
556 difference2 | nomatch p1 p2 m2 = t1
557 | zero p1 m2 = difference t1 l2
558 | otherwise = difference t1 r2
560 difference t1@(Tip k x) t2
564 difference Nil t = Nil
565 difference t (Tip k x) = delete k t
568 -- | /O(n+m)/. Difference with a combining function.
569 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
570 differenceWith f m1 m2
571 = differenceWithKey (\k x y -> f x y) m1 m2
573 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
574 -- encountered, the combining function is applied to the key and both values.
575 -- If it returns 'Nothing', the element is discarded (proper set difference).
576 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
577 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
578 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
579 | shorter m1 m2 = difference1
580 | shorter m2 m1 = difference2
581 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
584 difference1 | nomatch p2 p1 m1 = t1
585 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
586 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
588 difference2 | nomatch p1 p2 m2 = t1
589 | zero p1 m2 = differenceWithKey f t1 l2
590 | otherwise = differenceWithKey f t1 r2
592 differenceWithKey f t1@(Tip k x) t2
593 = case lookup k t2 of
594 Just y -> case f k x y of
599 differenceWithKey f Nil t = Nil
600 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
601 differenceWithKey f t Nil = t
604 {--------------------------------------------------------------------
606 --------------------------------------------------------------------}
607 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
608 intersection :: IntMap a -> IntMap b -> IntMap a
609 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
610 | shorter m1 m2 = intersection1
611 | shorter m2 m1 = intersection2
612 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
615 intersection1 | nomatch p2 p1 m1 = Nil
616 | zero p2 m1 = intersection l1 t2
617 | otherwise = intersection r1 t2
619 intersection2 | nomatch p1 p2 m2 = Nil
620 | zero p1 m2 = intersection t1 l2
621 | otherwise = intersection t1 r2
623 intersection t1@(Tip k x) t2
626 intersection t (Tip k x)
630 intersection Nil t = Nil
631 intersection t Nil = Nil
633 -- | /O(n+m)/. The intersection with a combining function.
634 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
635 intersectionWith f m1 m2
636 = intersectionWithKey (\k x y -> f x y) m1 m2
638 -- | /O(n+m)/. The intersection with a combining function.
639 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
640 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
641 | shorter m1 m2 = intersection1
642 | shorter m2 m1 = intersection2
643 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
646 intersection1 | nomatch p2 p1 m1 = Nil
647 | zero p2 m1 = intersectionWithKey f l1 t2
648 | otherwise = intersectionWithKey f r1 t2
650 intersection2 | nomatch p1 p2 m2 = Nil
651 | zero p1 m2 = intersectionWithKey f t1 l2
652 | otherwise = intersectionWithKey f t1 r2
654 intersectionWithKey f t1@(Tip k x) t2
655 = case lookup k t2 of
656 Just y -> Tip k (f k x y)
658 intersectionWithKey f t1 (Tip k y)
659 = case lookup k t1 of
660 Just x -> Tip k (f k x y)
662 intersectionWithKey f Nil t = Nil
663 intersectionWithKey f t Nil = Nil
666 {--------------------------------------------------------------------
668 --------------------------------------------------------------------}
669 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
670 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
671 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
672 isProperSubmapOf m1 m2
673 = isProperSubmapOfBy (==) m1 m2
675 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
676 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
677 @m1@ and @m2@ are not equal,
678 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
679 applied to their respective values. For example, the following
680 expressions are all 'True':
682 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
683 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
685 But the following are all 'False':
687 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
688 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
689 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
691 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
692 isProperSubmapOfBy pred t1 t2
693 = case submapCmp pred t1 t2 of
697 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
699 | shorter m2 m1 = submapCmpLt
700 | p1 == p2 = submapCmpEq
701 | otherwise = GT -- disjoint
703 submapCmpLt | nomatch p1 p2 m2 = GT
704 | zero p1 m2 = submapCmp pred t1 l2
705 | otherwise = submapCmp pred t1 r2
706 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
712 submapCmp pred (Bin p m l r) t = GT
713 submapCmp pred (Tip kx x) (Tip ky y)
714 | (kx == ky) && pred x y = EQ
715 | otherwise = GT -- disjoint
716 submapCmp pred (Tip k x) t
718 Just y | pred x y -> LT
719 other -> GT -- disjoint
720 submapCmp pred Nil Nil = EQ
721 submapCmp pred Nil t = LT
723 -- | /O(n+m)/. Is this a submap?
724 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
725 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
727 = isSubmapOfBy (==) m1 m2
730 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
731 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
732 applied to their respective values. For example, the following
733 expressions are all 'True':
735 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
736 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
737 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
739 But the following are all 'False':
741 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
742 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
743 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
746 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
747 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
748 | shorter m1 m2 = False
749 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
750 else isSubmapOfBy pred t1 r2)
751 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
752 isSubmapOfBy pred (Bin p m l r) t = False
753 isSubmapOfBy pred (Tip k x) t = case lookup k t of
756 isSubmapOfBy pred Nil t = True
758 {--------------------------------------------------------------------
760 --------------------------------------------------------------------}
761 -- | /O(n)/. Map a function over all values in the map.
762 map :: (a -> b) -> IntMap a -> IntMap b
764 = mapWithKey (\k x -> f x) m
766 -- | /O(n)/. Map a function over all values in the map.
767 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
770 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
771 Tip k x -> Tip k (f k x)
774 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
775 -- argument through the map in ascending order of keys.
776 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
778 = mapAccumWithKey (\a k x -> f a x) a m
780 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
781 -- argument through the map in ascending order of keys.
782 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
783 mapAccumWithKey f a t
786 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
787 -- argument through the map in ascending order of keys.
788 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
791 Bin p m l r -> let (a1,l') = mapAccumL f a l
792 (a2,r') = mapAccumL f a1 r
793 in (a2,Bin p m l' r')
794 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
798 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
799 -- argument throught the map in descending order of keys.
800 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
803 Bin p m l r -> let (a1,r') = mapAccumR f a r
804 (a2,l') = mapAccumR f a1 l
805 in (a2,Bin p m l' r')
806 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
809 {--------------------------------------------------------------------
811 --------------------------------------------------------------------}
812 -- | /O(n)/. Filter all values that satisfy some predicate.
813 filter :: (a -> Bool) -> IntMap a -> IntMap a
815 = filterWithKey (\k x -> p x) m
817 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
818 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
822 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
828 -- | /O(n)/. partition the map according to some predicate. The first
829 -- map contains all elements that satisfy the predicate, the second all
830 -- elements that fail the predicate. See also 'split'.
831 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
833 = partitionWithKey (\k x -> p x) m
835 -- | /O(n)/. partition the map according to some predicate. The first
836 -- map contains all elements that satisfy the predicate, the second all
837 -- elements that fail the predicate. See also 'split'.
838 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
839 partitionWithKey pred t
842 -> let (l1,l2) = partitionWithKey pred l
843 (r1,r2) = partitionWithKey pred r
844 in (bin p m l1 r1, bin p m l2 r2)
846 | pred k x -> (t,Nil)
847 | otherwise -> (Nil,t)
851 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
852 -- where all keys in @map1@ are lower than @k@ and all keys in
853 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
854 split :: Key -> IntMap a -> (IntMap a,IntMap a)
858 | m < 0 -> (if k >= 0 -- handle negative numbers.
859 then let (lt,gt) = split' k l in (union r lt, gt)
860 else let (lt,gt) = split' k r in (lt, union gt l))
861 | otherwise -> split' k t
865 | otherwise -> (Nil,Nil)
868 split' :: Key -> IntMap a -> (IntMap a,IntMap a)
872 | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
873 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
874 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
878 | otherwise -> (Nil,Nil)
881 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
882 -- key was found in the original map.
883 splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
887 | m < 0 -> (if k >= 0 -- handle negative numbers.
888 then let (lt,found,gt) = splitLookup' k l in (union r lt,found, gt)
889 else let (lt,found,gt) = splitLookup' k r in (lt,found, union gt l))
890 | otherwise -> splitLookup' k t
892 | k>ky -> (t,Nothing,Nil)
893 | k<ky -> (Nil,Nothing,t)
894 | otherwise -> (Nil,Just y,Nil)
895 Nil -> (Nil,Nothing,Nil)
897 splitLookup' :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
901 | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
902 | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
903 | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
905 | k>ky -> (t,Nothing,Nil)
906 | k<ky -> (Nil,Nothing,t)
907 | otherwise -> (Nil,Just y,Nil)
908 Nil -> (Nil,Nothing,Nil)
910 {--------------------------------------------------------------------
912 --------------------------------------------------------------------}
913 -- | /O(n)/. Fold the values in the map, such that
914 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
917 -- > elems map = fold (:) [] map
919 fold :: (a -> b -> b) -> b -> IntMap a -> b
921 = foldWithKey (\k x y -> f x y) z t
923 -- | /O(n)/. Fold the keys and values in the map, such that
924 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
927 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
929 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
933 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
936 Bin 0 m l r | m < 0 -> foldr' f (foldr' f z l) r -- put negative numbers before.
937 Bin _ _ _ _ -> foldr' f z t
941 foldr' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
944 Bin p m l r -> foldr' f (foldr' f z r) l
950 {--------------------------------------------------------------------
952 --------------------------------------------------------------------}
954 -- Return all elements of the map in the ascending order of their keys.
955 elems :: IntMap a -> [a]
957 = foldWithKey (\k x xs -> x:xs) [] m
959 -- | /O(n)/. Return all keys of the map in ascending order.
960 keys :: IntMap a -> [Key]
962 = foldWithKey (\k x ks -> k:ks) [] m
964 -- | /O(n*min(n,W))/. The set of all keys of the map.
965 keysSet :: IntMap a -> IntSet.IntSet
966 keysSet m = IntSet.fromDistinctAscList (keys m)
969 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
970 assocs :: IntMap a -> [(Key,a)]
975 {--------------------------------------------------------------------
977 --------------------------------------------------------------------}
978 -- | /O(n)/. Convert the map to a list of key\/value pairs.
979 toList :: IntMap a -> [(Key,a)]
981 = foldWithKey (\k x xs -> (k,x):xs) [] t
983 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
984 -- keys are in ascending order.
985 toAscList :: IntMap a -> [(Key,a)]
987 = -- NOTE: the following algorithm only works for big-endian trees
988 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
990 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
991 fromList :: [(Key,a)] -> IntMap a
993 = foldlStrict ins empty xs
995 ins t (k,x) = insert k x t
997 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
998 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
1000 = fromListWithKey (\k x y -> f x y) xs
1002 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
1003 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
1004 fromListWithKey f xs
1005 = foldlStrict ins empty xs
1007 ins t (k,x) = insertWithKey f k x t
1009 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
1010 -- the keys are in ascending order.
1011 fromAscList :: [(Key,a)] -> IntMap a
1015 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
1016 -- the keys are in ascending order, with a combining function on equal keys.
1017 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
1018 fromAscListWith f xs
1021 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
1022 -- the keys are in ascending order, with a combining function on equal keys.
1023 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
1024 fromAscListWithKey f xs
1025 = fromListWithKey f xs
1027 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
1028 -- the keys are in ascending order and all distinct.
1029 fromDistinctAscList :: [(Key,a)] -> IntMap a
1030 fromDistinctAscList xs
1034 {--------------------------------------------------------------------
1036 --------------------------------------------------------------------}
1037 instance Eq a => Eq (IntMap a) where
1038 t1 == t2 = equal t1 t2
1039 t1 /= t2 = nequal t1 t2
1041 equal :: Eq a => IntMap a -> IntMap a -> Bool
1042 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
1043 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
1044 equal (Tip kx x) (Tip ky y)
1045 = (kx == ky) && (x==y)
1046 equal Nil Nil = True
1049 nequal :: Eq a => IntMap a -> IntMap a -> Bool
1050 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
1051 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
1052 nequal (Tip kx x) (Tip ky y)
1053 = (kx /= ky) || (x/=y)
1054 nequal Nil Nil = False
1057 {--------------------------------------------------------------------
1059 --------------------------------------------------------------------}
1061 instance Ord a => Ord (IntMap a) where
1062 compare m1 m2 = compare (toList m1) (toList m2)
1064 {--------------------------------------------------------------------
1066 --------------------------------------------------------------------}
1068 instance Functor IntMap where
1071 {--------------------------------------------------------------------
1073 --------------------------------------------------------------------}
1075 instance Show a => Show (IntMap a) where
1076 showsPrec d m = showParen (d > 10) $
1077 showString "fromList " . shows (toList m)
1079 showMap :: (Show a) => [(Key,a)] -> ShowS
1083 = showChar '{' . showElem x . showTail xs
1085 showTail [] = showChar '}'
1086 showTail (x:xs) = showChar ',' . showElem x . showTail xs
1088 showElem (k,x) = shows k . showString ":=" . shows x
1090 {--------------------------------------------------------------------
1092 --------------------------------------------------------------------}
1093 instance (Read e) => Read (IntMap e) where
1094 #ifdef __GLASGOW_HASKELL__
1095 readPrec = parens $ prec 10 $ do
1096 Ident "fromList" <- lexP
1098 return (fromList xs)
1100 readListPrec = readListPrecDefault
1102 readsPrec p = readParen (p > 10) $ \ r -> do
1103 ("fromList",s) <- lex r
1105 return (fromList xs,t)
1108 {--------------------------------------------------------------------
1110 --------------------------------------------------------------------}
1112 #include "Typeable.h"
1113 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1115 {--------------------------------------------------------------------
1117 --------------------------------------------------------------------}
1118 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1119 -- in a compressed, hanging format.
1120 showTree :: Show a => IntMap a -> String
1122 = showTreeWith True False s
1125 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1126 the tree that implements the map. If @hang@ is
1127 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1128 @wide@ is 'True', an extra wide version is shown.
1130 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1131 showTreeWith hang wide t
1132 | hang = (showsTreeHang wide [] t) ""
1133 | otherwise = (showsTree wide [] [] t) ""
1135 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1136 showsTree wide lbars rbars t
1139 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1140 showWide wide rbars .
1141 showsBars lbars . showString (showBin p m) . showString "\n" .
1142 showWide wide lbars .
1143 showsTree wide (withEmpty lbars) (withBar lbars) l
1145 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1146 Nil -> showsBars lbars . showString "|\n"
1148 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1149 showsTreeHang wide bars t
1152 -> showsBars bars . showString (showBin p m) . showString "\n" .
1153 showWide wide bars .
1154 showsTreeHang wide (withBar bars) l .
1155 showWide wide bars .
1156 showsTreeHang wide (withEmpty bars) r
1158 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1159 Nil -> showsBars bars . showString "|\n"
1162 = "*" -- ++ show (p,m)
1165 | wide = showString (concat (reverse bars)) . showString "|\n"
1168 showsBars :: [String] -> ShowS
1172 _ -> showString (concat (reverse (tail bars))) . showString node
1175 withBar bars = "| ":bars
1176 withEmpty bars = " ":bars
1179 {--------------------------------------------------------------------
1181 --------------------------------------------------------------------}
1182 {--------------------------------------------------------------------
1184 --------------------------------------------------------------------}
1185 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1187 | zero p1 m = Bin p m t1 t2
1188 | otherwise = Bin p m t2 t1
1190 m = branchMask p1 p2
1193 {--------------------------------------------------------------------
1194 @bin@ assures that we never have empty trees within a tree.
1195 --------------------------------------------------------------------}
1196 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1199 bin p m l r = Bin p m l r
1202 {--------------------------------------------------------------------
1203 Endian independent bit twiddling
1204 --------------------------------------------------------------------}
1205 zero :: Key -> Mask -> Bool
1207 = (natFromInt i) .&. (natFromInt m) == 0
1209 nomatch,match :: Key -> Prefix -> Mask -> Bool
1216 mask :: Key -> Mask -> Prefix
1218 = maskW (natFromInt i) (natFromInt m)
1221 zeroN :: Nat -> Nat -> Bool
1222 zeroN i m = (i .&. m) == 0
1224 {--------------------------------------------------------------------
1225 Big endian operations
1226 --------------------------------------------------------------------}
1227 maskW :: Nat -> Nat -> Prefix
1229 = intFromNat (i .&. (complement (m-1) `xor` m))
1231 shorter :: Mask -> Mask -> Bool
1233 = (natFromInt m1) > (natFromInt m2)
1235 branchMask :: Prefix -> Prefix -> Mask
1237 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1239 {----------------------------------------------------------------------
1240 Finding the highest bit (mask) in a word [x] can be done efficiently in
1242 * convert to a floating point value and the mantissa tells us the
1243 [log2(x)] that corresponds with the highest bit position. The mantissa
1244 is retrieved either via the standard C function [frexp] or by some bit
1245 twiddling on IEEE compatible numbers (float). Note that one needs to
1246 use at least [double] precision for an accurate mantissa of 32 bit
1248 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1249 * use processor specific assembler instruction (asm).
1251 The most portable way would be [bit], but is it efficient enough?
1252 I have measured the cycle counts of the different methods on an AMD
1253 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1255 highestBitMask: method cycles
1262 highestBit: method cycles
1269 Wow, the bit twiddling is on today's RISC like machines even faster
1270 than a single CISC instruction (BSR)!
1271 ----------------------------------------------------------------------}
1273 {----------------------------------------------------------------------
1274 [highestBitMask] returns a word where only the highest bit is set.
1275 It is found by first setting all bits in lower positions than the
1276 highest bit and than taking an exclusive or with the original value.
1277 Allthough the function may look expensive, GHC compiles this into
1278 excellent C code that subsequently compiled into highly efficient
1279 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1280 ----------------------------------------------------------------------}
1281 highestBitMask :: Nat -> Nat
1283 = case (x .|. shiftRL x 1) of
1284 x -> case (x .|. shiftRL x 2) of
1285 x -> case (x .|. shiftRL x 4) of
1286 x -> case (x .|. shiftRL x 8) of
1287 x -> case (x .|. shiftRL x 16) of
1288 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1289 x -> (x `xor` (shiftRL x 1))
1292 {--------------------------------------------------------------------
1294 --------------------------------------------------------------------}
1298 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1301 {--------------------------------------------------------------------
1303 --------------------------------------------------------------------}
1304 testTree :: [Int] -> IntMap Int
1305 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1306 test1 = testTree [1..20]
1307 test2 = testTree [30,29..10]
1308 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1310 {--------------------------------------------------------------------
1312 --------------------------------------------------------------------}
1317 { configMaxTest = 500
1318 , configMaxFail = 5000
1319 , configSize = \n -> (div n 2 + 3)
1320 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1324 {--------------------------------------------------------------------
1325 Arbitrary, reasonably balanced trees
1326 --------------------------------------------------------------------}
1327 instance Arbitrary a => Arbitrary (IntMap a) where
1328 arbitrary = do{ ks <- arbitrary
1329 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1330 ; return (fromList xs)
1334 {--------------------------------------------------------------------
1335 Single, Insert, Delete
1336 --------------------------------------------------------------------}
1337 prop_Single :: Key -> Int -> Bool
1339 = (insert k x empty == singleton k x)
1341 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1342 prop_InsertDelete k x t
1343 = not (member k t) ==> delete k (insert k x t) == t
1345 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1346 prop_UpdateDelete k t
1347 = update (const Nothing) k t == delete k t
1350 {--------------------------------------------------------------------
1352 --------------------------------------------------------------------}
1353 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1354 prop_UnionInsert k x t
1355 = union (singleton k x) t == insert k x t
1357 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1358 prop_UnionAssoc t1 t2 t3
1359 = union t1 (union t2 t3) == union (union t1 t2) t3
1361 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1362 prop_UnionComm t1 t2
1363 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1366 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1368 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1369 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1371 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1373 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1374 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1376 {--------------------------------------------------------------------
1378 --------------------------------------------------------------------}
1380 = forAll (choose (5,100)) $ \n ->
1381 let xs = [(x,()) | x <- [0..n::Int]]
1382 in fromAscList xs == fromList xs
1384 prop_List :: [Key] -> Bool
1386 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])