1 {-# OPTIONS -cpp -fglasgow-exts #-}
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
57 , insertWith, insertWithKey, insertLookupWithKey
114 , fromDistinctAscList
126 , isSubmapOf, isSubmapOfBy
127 , isProperSubmapOf, isProperSubmapOfBy
135 import Prelude hiding (lookup,map,filter,foldr,foldl,null)
139 import qualified Data.IntSet as IntSet
144 import qualified Prelude
145 import Debug.QuickCheck
146 import List (nub,sort)
147 import qualified List
150 #if __GLASGOW_HASKELL__
151 import Data.Generics.Basics
152 import Data.Generics.Instances
155 #if __GLASGOW_HASKELL__ >= 503
157 import GHC.Exts ( Word(..), Int(..), shiftRL# )
158 #elif __GLASGOW_HASKELL__
160 import GlaExts ( Word(..), Int(..), shiftRL# )
165 infixl 9 \\{-This comment teaches CPP correct behaviour -}
167 -- A "Nat" is a natural machine word (an unsigned Int)
170 natFromInt :: Key -> Nat
171 natFromInt i = fromIntegral i
173 intFromNat :: Nat -> Key
174 intFromNat w = fromIntegral w
176 shiftRL :: Nat -> Key -> Nat
177 #if __GLASGOW_HASKELL__
178 {--------------------------------------------------------------------
179 GHC: use unboxing to get @shiftRL@ inlined.
180 --------------------------------------------------------------------}
181 shiftRL (W# x) (I# i)
184 shiftRL x i = shiftR x i
187 {--------------------------------------------------------------------
189 --------------------------------------------------------------------}
191 -- | /O(min(n,W))/. Find the value of a key. Calls 'error' when the element can not be found.
193 (!) :: IntMap a -> Key -> a
196 -- | /O(n+m)/. See 'difference'.
197 (\\) :: IntMap a -> IntMap b -> IntMap a
198 m1 \\ m2 = difference m1 m2
200 {--------------------------------------------------------------------
202 --------------------------------------------------------------------}
203 -- | A map of integers to values @a@.
205 | Tip {-# UNPACK #-} !Key a
206 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
212 #if __GLASGOW_HASKELL__
214 {--------------------------------------------------------------------
216 --------------------------------------------------------------------}
218 -- This instance preserves data abstraction at the cost of inefficiency.
219 -- We omit reflection services for the sake of data abstraction.
221 instance Data a => Data (IntMap a) where
222 gfoldl f z im = z fromList `f` (toList im)
223 toConstr _ = error "toConstr"
224 gunfold _ _ = error "gunfold"
225 dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
229 {--------------------------------------------------------------------
231 --------------------------------------------------------------------}
232 -- | /O(1)/. Is the map empty?
233 null :: IntMap a -> Bool
237 -- | /O(n)/. Number of elements in the map.
238 size :: IntMap a -> Int
241 Bin p m l r -> size l + size r
245 -- | /O(min(n,W))/. Is the key a member of the map?
246 member :: Key -> IntMap a -> Bool
252 -- | /O(min(n,W))/. Lookup the value of a key in the map.
253 lookup :: Key -> IntMap a -> Maybe a
255 = let nk = natFromInt k in seq nk (lookupN nk t)
257 lookupN :: Nat -> IntMap a -> Maybe a
261 | zeroN k (natFromInt m) -> lookupN k l
262 | otherwise -> lookupN k r
264 | (k == natFromInt kx) -> Just x
265 | otherwise -> Nothing
268 find' :: Key -> IntMap a -> a
271 Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
275 -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
276 -- returns the value of key @k@ or returns @def@ when the key is not an
277 -- element of the map.
278 findWithDefault :: a -> Key -> IntMap a -> a
279 findWithDefault def k m
284 {--------------------------------------------------------------------
286 --------------------------------------------------------------------}
287 -- | /O(1)/. The empty map.
292 -- | /O(1)/. A map of one element.
293 singleton :: Key -> a -> IntMap a
297 {--------------------------------------------------------------------
299 'insert' is the inlined version of 'insertWith (\k x y -> x)'
300 --------------------------------------------------------------------}
301 -- | /O(min(n,W))/. Insert a new key\/value pair in the map. When the key
302 -- is already an element of the set, its value is replaced by the new value,
303 -- ie. 'insert' is left-biased.
304 insert :: Key -> a -> IntMap a -> IntMap a
308 | nomatch k p m -> join k (Tip k x) p t
309 | zero k m -> Bin p m (insert k x l) r
310 | otherwise -> Bin p m l (insert k x r)
313 | otherwise -> join k (Tip k x) ky t
316 -- right-biased insertion, used by 'union'
317 -- | /O(min(n,W))/. Insert with a combining function.
318 insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
320 = insertWithKey (\k x y -> f x y) k x t
322 -- | /O(min(n,W))/. Insert with a combining function.
323 insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
324 insertWithKey f k x t
327 | nomatch k p m -> join k (Tip k x) p t
328 | zero k m -> Bin p m (insertWithKey f k x l) r
329 | otherwise -> Bin p m l (insertWithKey f k x r)
331 | k==ky -> Tip k (f k x y)
332 | otherwise -> join k (Tip k x) ky t
336 -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
337 -- is a pair where the first element is equal to (@'lookup' k map@)
338 -- and the second element equal to (@'insertWithKey' f k x map@).
339 insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
340 insertLookupWithKey f k x t
343 | nomatch k p m -> (Nothing,join k (Tip k x) p t)
344 | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
345 | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
347 | k==ky -> (Just y,Tip k (f k x y))
348 | otherwise -> (Nothing,join k (Tip k x) ky t)
349 Nil -> (Nothing,Tip k x)
352 {--------------------------------------------------------------------
354 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
355 --------------------------------------------------------------------}
356 -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
357 -- a member of the map, the original map is returned.
358 delete :: Key -> IntMap a -> IntMap a
363 | zero k m -> bin p m (delete k l) r
364 | otherwise -> bin p m l (delete k r)
370 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
371 -- a member of the map, the original map is returned.
372 adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
374 = adjustWithKey (\k x -> f x) k m
376 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
377 -- a member of the map, the original map is returned.
378 adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
380 = updateWithKey (\k x -> Just (f k x)) k m
382 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
383 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
384 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
385 update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
387 = updateWithKey (\k x -> f x) k m
389 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
390 -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
391 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
392 updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
397 | zero k m -> bin p m (updateWithKey f k l) r
398 | otherwise -> bin p m l (updateWithKey f k r)
400 | k==ky -> case (f k y) of
406 -- | /O(min(n,W))/. Lookup and update.
407 updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
408 updateLookupWithKey f k t
411 | nomatch k p m -> (Nothing,t)
412 | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
413 | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
415 | k==ky -> case (f k y) of
416 Just y' -> (Just y,Tip ky y')
417 Nothing -> (Just y,Nil)
418 | otherwise -> (Nothing,t)
422 {--------------------------------------------------------------------
424 --------------------------------------------------------------------}
425 -- | The union of a list of maps.
426 unions :: [IntMap a] -> IntMap a
428 = foldlStrict union empty xs
430 -- | The union of a list of maps, with a combining operation
431 unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
433 = foldlStrict (unionWith f) empty ts
435 -- | /O(n+m)/. The (left-biased) union of two sets.
436 union :: IntMap a -> IntMap a -> IntMap a
437 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
438 | shorter m1 m2 = union1
439 | shorter m2 m1 = union2
440 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
441 | otherwise = join p1 t1 p2 t2
443 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
444 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
445 | otherwise = Bin p1 m1 l1 (union r1 t2)
447 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
448 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
449 | otherwise = Bin p2 m2 l2 (union t1 r2)
451 union (Tip k x) t = insert k x t
452 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
456 -- | /O(n+m)/. The union with a combining function.
457 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
459 = unionWithKey (\k x y -> f x y) m1 m2
461 -- | /O(n+m)/. The union with a combining function.
462 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
463 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
464 | shorter m1 m2 = union1
465 | shorter m2 m1 = union2
466 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
467 | otherwise = join p1 t1 p2 t2
469 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
470 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
471 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
473 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
474 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
475 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
477 unionWithKey f (Tip k x) t = insertWithKey f k x t
478 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
479 unionWithKey f Nil t = t
480 unionWithKey f t Nil = t
482 {--------------------------------------------------------------------
484 --------------------------------------------------------------------}
485 -- | /O(n+m)/. Difference between two maps (based on keys).
486 difference :: IntMap a -> IntMap b -> IntMap a
487 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
488 | shorter m1 m2 = difference1
489 | shorter m2 m1 = difference2
490 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
493 difference1 | nomatch p2 p1 m1 = t1
494 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
495 | otherwise = bin p1 m1 l1 (difference r1 t2)
497 difference2 | nomatch p1 p2 m2 = t1
498 | zero p1 m2 = difference t1 l2
499 | otherwise = difference t1 r2
501 difference t1@(Tip k x) t2
505 difference Nil t = Nil
506 difference t (Tip k x) = delete k t
509 -- | /O(n+m)/. Difference with a combining function.
510 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
511 differenceWith f m1 m2
512 = differenceWithKey (\k x y -> f x y) m1 m2
514 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
515 -- encountered, the combining function is applied to the key and both values.
516 -- If it returns 'Nothing', the element is discarded (proper set difference).
517 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
518 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
519 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
520 | shorter m1 m2 = difference1
521 | shorter m2 m1 = difference2
522 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
525 difference1 | nomatch p2 p1 m1 = t1
526 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
527 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
529 difference2 | nomatch p1 p2 m2 = t1
530 | zero p1 m2 = differenceWithKey f t1 l2
531 | otherwise = differenceWithKey f t1 r2
533 differenceWithKey f t1@(Tip k x) t2
534 = case lookup k t2 of
535 Just y -> case f k x y of
540 differenceWithKey f Nil t = Nil
541 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
542 differenceWithKey f t Nil = t
545 {--------------------------------------------------------------------
547 --------------------------------------------------------------------}
548 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
549 intersection :: IntMap a -> IntMap b -> IntMap a
550 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
551 | shorter m1 m2 = intersection1
552 | shorter m2 m1 = intersection2
553 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
556 intersection1 | nomatch p2 p1 m1 = Nil
557 | zero p2 m1 = intersection l1 t2
558 | otherwise = intersection r1 t2
560 intersection2 | nomatch p1 p2 m2 = Nil
561 | zero p1 m2 = intersection t1 l2
562 | otherwise = intersection t1 r2
564 intersection t1@(Tip k x) t2
567 intersection t (Tip k x)
571 intersection Nil t = Nil
572 intersection t Nil = Nil
574 -- | /O(n+m)/. The intersection with a combining function.
575 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
576 intersectionWith f m1 m2
577 = intersectionWithKey (\k x y -> f x y) m1 m2
579 -- | /O(n+m)/. The intersection with a combining function.
580 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
581 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
582 | shorter m1 m2 = intersection1
583 | shorter m2 m1 = intersection2
584 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
587 intersection1 | nomatch p2 p1 m1 = Nil
588 | zero p2 m1 = intersectionWithKey f l1 t2
589 | otherwise = intersectionWithKey f r1 t2
591 intersection2 | nomatch p1 p2 m2 = Nil
592 | zero p1 m2 = intersectionWithKey f t1 l2
593 | otherwise = intersectionWithKey f t1 r2
595 intersectionWithKey f t1@(Tip k x) t2
596 = case lookup k t2 of
597 Just y -> Tip k (f k x y)
599 intersectionWithKey f t1 (Tip k y)
600 = case lookup k t1 of
601 Just x -> Tip k (f k x y)
603 intersectionWithKey f Nil t = Nil
604 intersectionWithKey f t Nil = Nil
607 {--------------------------------------------------------------------
609 --------------------------------------------------------------------}
610 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
611 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
612 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
613 isProperSubmapOf m1 m2
614 = isProperSubmapOfBy (==) m1 m2
616 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
617 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
618 @m1@ and @m2@ are not equal,
619 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
620 applied to their respective values. For example, the following
621 expressions are all 'True':
623 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
624 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
626 But the following are all 'False':
628 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
629 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
630 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
632 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
633 isProperSubmapOfBy pred t1 t2
634 = case submapCmp pred t1 t2 of
638 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
640 | shorter m2 m1 = submapCmpLt
641 | p1 == p2 = submapCmpEq
642 | otherwise = GT -- disjoint
644 submapCmpLt | nomatch p1 p2 m2 = GT
645 | zero p1 m2 = submapCmp pred t1 l2
646 | otherwise = submapCmp pred t1 r2
647 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
653 submapCmp pred (Bin p m l r) t = GT
654 submapCmp pred (Tip kx x) (Tip ky y)
655 | (kx == ky) && pred x y = EQ
656 | otherwise = GT -- disjoint
657 submapCmp pred (Tip k x) t
659 Just y | pred x y -> LT
660 other -> GT -- disjoint
661 submapCmp pred Nil Nil = EQ
662 submapCmp pred Nil t = LT
664 -- | /O(n+m)/. Is this a submap?
665 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
666 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
668 = isSubmapOfBy (==) m1 m2
671 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
672 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
673 applied to their respective values. For example, the following
674 expressions are all 'True':
676 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
677 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
678 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
680 But the following are all 'False':
682 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
683 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
684 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
687 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
688 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
689 | shorter m1 m2 = False
690 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
691 else isSubmapOfBy pred t1 r2)
692 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
693 isSubmapOfBy pred (Bin p m l r) t = False
694 isSubmapOfBy pred (Tip k x) t = case lookup k t of
697 isSubmapOfBy pred Nil t = True
699 {--------------------------------------------------------------------
701 --------------------------------------------------------------------}
702 -- | /O(n)/. Map a function over all values in the map.
703 map :: (a -> b) -> IntMap a -> IntMap b
705 = mapWithKey (\k x -> f x) m
707 -- | /O(n)/. Map a function over all values in the map.
708 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
711 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
712 Tip k x -> Tip k (f k x)
715 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
716 -- argument through the map in an unspecified order.
717 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
719 = mapAccumWithKey (\a k x -> f a x) a m
721 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
722 -- argument through the map in an unspecified order.
723 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
724 mapAccumWithKey f a t
727 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
728 -- argument through the map in pre-order.
729 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
732 Bin p m l r -> let (a1,l') = mapAccumL f a l
733 (a2,r') = mapAccumL f a1 r
734 in (a2,Bin p m l' r')
735 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
739 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
740 -- argument throught the map in post-order.
741 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
744 Bin p m l r -> let (a1,r') = mapAccumR f a r
745 (a2,l') = mapAccumR f a1 l
746 in (a2,Bin p m l' r')
747 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
750 {--------------------------------------------------------------------
752 --------------------------------------------------------------------}
753 -- | /O(n)/. Filter all values that satisfy some predicate.
754 filter :: (a -> Bool) -> IntMap a -> IntMap a
756 = filterWithKey (\k x -> p x) m
758 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
759 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
763 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
769 -- | /O(n)/. partition the map according to some predicate. The first
770 -- map contains all elements that satisfy the predicate, the second all
771 -- elements that fail the predicate. See also 'split'.
772 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
774 = partitionWithKey (\k x -> p x) m
776 -- | /O(n)/. partition the map according to some predicate. The first
777 -- map contains all elements that satisfy the predicate, the second all
778 -- elements that fail the predicate. See also 'split'.
779 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
780 partitionWithKey pred t
783 -> let (l1,l2) = partitionWithKey pred l
784 (r1,r2) = partitionWithKey pred r
785 in (bin p m l1 r1, bin p m l2 r2)
787 | pred k x -> (t,Nil)
788 | otherwise -> (Nil,t)
792 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
793 -- where all keys in @map1@ are lower than @k@ and all keys in
794 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
795 split :: Key -> IntMap a -> (IntMap a,IntMap a)
799 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
800 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
804 | otherwise -> (Nil,Nil)
807 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
808 -- key was found in the original map.
809 splitLookup :: Key -> IntMap a -> (Maybe a,IntMap a,IntMap a)
813 | zero k m -> let (found,lt,gt) = splitLookup k l in (found,lt,union gt r)
814 | otherwise -> let (found,lt,gt) = splitLookup k r in (found,union l lt,gt)
816 | k>ky -> (Nothing,t,Nil)
817 | k<ky -> (Nothing,Nil,t)
818 | otherwise -> (Just y,Nil,Nil)
819 Nil -> (Nothing,Nil,Nil)
821 {--------------------------------------------------------------------
823 --------------------------------------------------------------------}
824 -- | /O(n)/. Fold over the elements of a map in an unspecified order.
826 -- > sum map = fold (+) 0 map
827 -- > elems map = fold (:) [] map
828 fold :: (a -> b -> b) -> b -> IntMap a -> b
830 = foldWithKey (\k x y -> f x y) z t
832 -- | /O(n)/. Fold over the elements of a map in an unspecified order.
834 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
835 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
839 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
842 Bin p m l r -> foldr f (foldr f z r) l
846 {--------------------------------------------------------------------
848 --------------------------------------------------------------------}
849 -- | /O(n)/. Return all elements of the map.
850 elems :: IntMap a -> [a]
852 = foldWithKey (\k x xs -> x:xs) [] m
854 -- | /O(n)/. Return all keys of the map.
855 keys :: IntMap a -> [Key]
857 = foldWithKey (\k x ks -> k:ks) [] m
859 -- | /O(n*min(n,W))/. The set of all keys of the map.
860 keysSet :: IntMap a -> IntSet.IntSet
861 keysSet m = IntSet.fromDistinctAscList (keys m)
864 -- | /O(n)/. Return all key\/value pairs in the map.
865 assocs :: IntMap a -> [(Key,a)]
870 {--------------------------------------------------------------------
872 --------------------------------------------------------------------}
873 -- | /O(n)/. Convert the map to a list of key\/value pairs.
874 toList :: IntMap a -> [(Key,a)]
876 = foldWithKey (\k x xs -> (k,x):xs) [] t
878 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
879 -- keys are in ascending order.
880 toAscList :: IntMap a -> [(Key,a)]
882 = -- NOTE: the following algorithm only works for big-endian trees
883 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
885 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
886 fromList :: [(Key,a)] -> IntMap a
888 = foldlStrict ins empty xs
890 ins t (k,x) = insert k x t
892 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
893 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
895 = fromListWithKey (\k x y -> f x y) xs
897 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
898 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
900 = foldlStrict ins empty xs
902 ins t (k,x) = insertWithKey f k x t
904 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
905 -- the keys are in ascending order.
906 fromAscList :: [(Key,a)] -> IntMap a
910 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
911 -- the keys are in ascending order, with a combining function on equal keys.
912 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
916 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
917 -- the keys are in ascending order, with a combining function on equal keys.
918 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
919 fromAscListWithKey f xs
920 = fromListWithKey f xs
922 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
923 -- the keys are in ascending order and all distinct.
924 fromDistinctAscList :: [(Key,a)] -> IntMap a
925 fromDistinctAscList xs
929 {--------------------------------------------------------------------
931 --------------------------------------------------------------------}
932 instance Eq a => Eq (IntMap a) where
933 t1 == t2 = equal t1 t2
934 t1 /= t2 = nequal t1 t2
936 equal :: Eq a => IntMap a -> IntMap a -> Bool
937 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
938 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
939 equal (Tip kx x) (Tip ky y)
940 = (kx == ky) && (x==y)
944 nequal :: Eq a => IntMap a -> IntMap a -> Bool
945 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
946 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
947 nequal (Tip kx x) (Tip ky y)
948 = (kx /= ky) || (x/=y)
949 nequal Nil Nil = False
952 {--------------------------------------------------------------------
954 --------------------------------------------------------------------}
956 instance Ord a => Ord (IntMap a) where
957 compare m1 m2 = compare (toList m1) (toList m2)
959 {--------------------------------------------------------------------
961 --------------------------------------------------------------------}
963 instance Functor IntMap where
966 {--------------------------------------------------------------------
968 --------------------------------------------------------------------}
970 instance Ord a => Monoid (IntMap a) where
975 {--------------------------------------------------------------------
977 --------------------------------------------------------------------}
979 instance Show a => Show (IntMap a) where
980 showsPrec d t = showMap (toList t)
983 showMap :: (Show a) => [(Key,a)] -> ShowS
987 = showChar '{' . showElem x . showTail xs
989 showTail [] = showChar '}'
990 showTail (x:xs) = showChar ',' . showElem x . showTail xs
992 showElem (k,x) = shows k . showString ":=" . shows x
994 {--------------------------------------------------------------------
996 --------------------------------------------------------------------}
998 #include "Typeable.h"
999 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1001 {--------------------------------------------------------------------
1003 --------------------------------------------------------------------}
1004 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1005 -- in a compressed, hanging format.
1006 showTree :: Show a => IntMap a -> String
1008 = showTreeWith True False s
1011 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1012 the tree that implements the map. If @hang@ is
1013 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1014 @wide@ is 'True', an extra wide version is shown.
1016 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1017 showTreeWith hang wide t
1018 | hang = (showsTreeHang wide [] t) ""
1019 | otherwise = (showsTree wide [] [] t) ""
1021 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1022 showsTree wide lbars rbars t
1025 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1026 showWide wide rbars .
1027 showsBars lbars . showString (showBin p m) . showString "\n" .
1028 showWide wide lbars .
1029 showsTree wide (withEmpty lbars) (withBar lbars) l
1031 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1032 Nil -> showsBars lbars . showString "|\n"
1034 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1035 showsTreeHang wide bars t
1038 -> showsBars bars . showString (showBin p m) . showString "\n" .
1039 showWide wide bars .
1040 showsTreeHang wide (withBar bars) l .
1041 showWide wide bars .
1042 showsTreeHang wide (withEmpty bars) r
1044 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1045 Nil -> showsBars bars . showString "|\n"
1048 = "*" -- ++ show (p,m)
1051 | wide = showString (concat (reverse bars)) . showString "|\n"
1054 showsBars :: [String] -> ShowS
1058 _ -> showString (concat (reverse (tail bars))) . showString node
1061 withBar bars = "| ":bars
1062 withEmpty bars = " ":bars
1065 {--------------------------------------------------------------------
1067 --------------------------------------------------------------------}
1068 {--------------------------------------------------------------------
1070 --------------------------------------------------------------------}
1071 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1073 | zero p1 m = Bin p m t1 t2
1074 | otherwise = Bin p m t2 t1
1076 m = branchMask p1 p2
1079 {--------------------------------------------------------------------
1080 @bin@ assures that we never have empty trees within a tree.
1081 --------------------------------------------------------------------}
1082 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1085 bin p m l r = Bin p m l r
1088 {--------------------------------------------------------------------
1089 Endian independent bit twiddling
1090 --------------------------------------------------------------------}
1091 zero :: Key -> Mask -> Bool
1093 = (natFromInt i) .&. (natFromInt m) == 0
1095 nomatch,match :: Key -> Prefix -> Mask -> Bool
1102 mask :: Key -> Mask -> Prefix
1104 = maskW (natFromInt i) (natFromInt m)
1107 zeroN :: Nat -> Nat -> Bool
1108 zeroN i m = (i .&. m) == 0
1110 {--------------------------------------------------------------------
1111 Big endian operations
1112 --------------------------------------------------------------------}
1113 maskW :: Nat -> Nat -> Prefix
1115 = intFromNat (i .&. (complement (m-1) `xor` m))
1117 shorter :: Mask -> Mask -> Bool
1119 = (natFromInt m1) > (natFromInt m2)
1121 branchMask :: Prefix -> Prefix -> Mask
1123 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1125 {----------------------------------------------------------------------
1126 Finding the highest bit (mask) in a word [x] can be done efficiently in
1128 * convert to a floating point value and the mantissa tells us the
1129 [log2(x)] that corresponds with the highest bit position. The mantissa
1130 is retrieved either via the standard C function [frexp] or by some bit
1131 twiddling on IEEE compatible numbers (float). Note that one needs to
1132 use at least [double] precision for an accurate mantissa of 32 bit
1134 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1135 * use processor specific assembler instruction (asm).
1137 The most portable way would be [bit], but is it efficient enough?
1138 I have measured the cycle counts of the different methods on an AMD
1139 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1141 highestBitMask: method cycles
1148 highestBit: method cycles
1155 Wow, the bit twiddling is on today's RISC like machines even faster
1156 than a single CISC instruction (BSR)!
1157 ----------------------------------------------------------------------}
1159 {----------------------------------------------------------------------
1160 [highestBitMask] returns a word where only the highest bit is set.
1161 It is found by first setting all bits in lower positions than the
1162 highest bit and than taking an exclusive or with the original value.
1163 Allthough the function may look expensive, GHC compiles this into
1164 excellent C code that subsequently compiled into highly efficient
1165 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1166 ----------------------------------------------------------------------}
1167 highestBitMask :: Nat -> Nat
1169 = case (x .|. shiftRL x 1) of
1170 x -> case (x .|. shiftRL x 2) of
1171 x -> case (x .|. shiftRL x 4) of
1172 x -> case (x .|. shiftRL x 8) of
1173 x -> case (x .|. shiftRL x 16) of
1174 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1175 x -> (x `xor` (shiftRL x 1))
1178 {--------------------------------------------------------------------
1180 --------------------------------------------------------------------}
1184 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1187 {--------------------------------------------------------------------
1189 --------------------------------------------------------------------}
1190 testTree :: [Int] -> IntMap Int
1191 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1192 test1 = testTree [1..20]
1193 test2 = testTree [30,29..10]
1194 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1196 {--------------------------------------------------------------------
1198 --------------------------------------------------------------------}
1203 { configMaxTest = 500
1204 , configMaxFail = 5000
1205 , configSize = \n -> (div n 2 + 3)
1206 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1210 {--------------------------------------------------------------------
1211 Arbitrary, reasonably balanced trees
1212 --------------------------------------------------------------------}
1213 instance Arbitrary a => Arbitrary (IntMap a) where
1214 arbitrary = do{ ks <- arbitrary
1215 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1216 ; return (fromList xs)
1220 {--------------------------------------------------------------------
1221 Single, Insert, Delete
1222 --------------------------------------------------------------------}
1223 prop_Single :: Key -> Int -> Bool
1225 = (insert k x empty == singleton k x)
1227 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1228 prop_InsertDelete k x t
1229 = not (member k t) ==> delete k (insert k x t) == t
1231 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1232 prop_UpdateDelete k t
1233 = update (const Nothing) k t == delete k t
1236 {--------------------------------------------------------------------
1238 --------------------------------------------------------------------}
1239 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1240 prop_UnionInsert k x t
1241 = union (singleton k x) t == insert k x t
1243 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1244 prop_UnionAssoc t1 t2 t3
1245 = union t1 (union t2 t3) == union (union t1 t2) t3
1247 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1248 prop_UnionComm t1 t2
1249 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1252 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1254 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1255 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1257 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1259 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1260 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1262 {--------------------------------------------------------------------
1264 --------------------------------------------------------------------}
1266 = forAll (choose (5,100)) $ \n ->
1267 let xs = [(x,()) | x <- [0..n::Int]]
1268 in fromAscList xs == fromList xs
1270 prop_List :: [Key] -> Bool
1272 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])