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)
138 import qualified Data.IntSet as IntSet
143 import qualified Prelude
144 import Debug.QuickCheck
145 import List (nub,sort)
146 import qualified List
149 #if __GLASGOW_HASKELL__
150 import Data.Generics.Basics
151 import Data.Generics.Instances
154 #if __GLASGOW_HASKELL__ >= 503
156 import GHC.Exts ( Word(..), Int(..), shiftRL# )
157 #elif __GLASGOW_HASKELL__
159 import GlaExts ( Word(..), Int(..), shiftRL# )
164 infixl 9 \\{-This comment teaches CPP correct behaviour -}
166 -- A "Nat" is a natural machine word (an unsigned Int)
169 natFromInt :: Key -> Nat
170 natFromInt i = fromIntegral i
172 intFromNat :: Nat -> Key
173 intFromNat w = fromIntegral w
175 shiftRL :: Nat -> Key -> Nat
176 #if __GLASGOW_HASKELL__
177 {--------------------------------------------------------------------
178 GHC: use unboxing to get @shiftRL@ inlined.
179 --------------------------------------------------------------------}
180 shiftRL (W# x) (I# i)
183 shiftRL x i = shiftR x i
186 {--------------------------------------------------------------------
188 --------------------------------------------------------------------}
190 -- | /O(min(n,W))/. Find the value at a key.
191 -- 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 at 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 at 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 --------------------------------------------------------------------}
300 -- | /O(min(n,W))/. Insert a new key\/value pair in the map.
301 -- If the key is already present in the map, the associated value is
302 -- replaced with the supplied value, i.e. 'insert' is equivalent to
303 -- @'insertWith' 'const'@.
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 maps.
436 -- It prefers the first map when duplicate keys are encountered,
437 -- i.e. (@'union' == 'unionWith' 'const'@).
438 union :: IntMap a -> IntMap a -> IntMap a
439 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
440 | shorter m1 m2 = union1
441 | shorter m2 m1 = union2
442 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
443 | otherwise = join p1 t1 p2 t2
445 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
446 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
447 | otherwise = Bin p1 m1 l1 (union r1 t2)
449 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
450 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
451 | otherwise = Bin p2 m2 l2 (union t1 r2)
453 union (Tip k x) t = insert k x t
454 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
458 -- | /O(n+m)/. The union with a combining function.
459 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
461 = unionWithKey (\k x y -> f x y) m1 m2
463 -- | /O(n+m)/. The union with a combining function.
464 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
465 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
466 | shorter m1 m2 = union1
467 | shorter m2 m1 = union2
468 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
469 | otherwise = join p1 t1 p2 t2
471 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
472 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
473 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
475 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
476 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
477 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
479 unionWithKey f (Tip k x) t = insertWithKey f k x t
480 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
481 unionWithKey f Nil t = t
482 unionWithKey f t Nil = t
484 {--------------------------------------------------------------------
486 --------------------------------------------------------------------}
487 -- | /O(n+m)/. Difference between two maps (based on keys).
488 difference :: IntMap a -> IntMap b -> IntMap a
489 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
490 | shorter m1 m2 = difference1
491 | shorter m2 m1 = difference2
492 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
495 difference1 | nomatch p2 p1 m1 = t1
496 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
497 | otherwise = bin p1 m1 l1 (difference r1 t2)
499 difference2 | nomatch p1 p2 m2 = t1
500 | zero p1 m2 = difference t1 l2
501 | otherwise = difference t1 r2
503 difference t1@(Tip k x) t2
507 difference Nil t = Nil
508 difference t (Tip k x) = delete k t
511 -- | /O(n+m)/. Difference with a combining function.
512 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
513 differenceWith f m1 m2
514 = differenceWithKey (\k x y -> f x y) m1 m2
516 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
517 -- encountered, the combining function is applied to the key and both values.
518 -- If it returns 'Nothing', the element is discarded (proper set difference).
519 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
520 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
521 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
522 | shorter m1 m2 = difference1
523 | shorter m2 m1 = difference2
524 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
527 difference1 | nomatch p2 p1 m1 = t1
528 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
529 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
531 difference2 | nomatch p1 p2 m2 = t1
532 | zero p1 m2 = differenceWithKey f t1 l2
533 | otherwise = differenceWithKey f t1 r2
535 differenceWithKey f t1@(Tip k x) t2
536 = case lookup k t2 of
537 Just y -> case f k x y of
542 differenceWithKey f Nil t = Nil
543 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
544 differenceWithKey f t Nil = t
547 {--------------------------------------------------------------------
549 --------------------------------------------------------------------}
550 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
551 intersection :: IntMap a -> IntMap b -> IntMap a
552 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
553 | shorter m1 m2 = intersection1
554 | shorter m2 m1 = intersection2
555 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
558 intersection1 | nomatch p2 p1 m1 = Nil
559 | zero p2 m1 = intersection l1 t2
560 | otherwise = intersection r1 t2
562 intersection2 | nomatch p1 p2 m2 = Nil
563 | zero p1 m2 = intersection t1 l2
564 | otherwise = intersection t1 r2
566 intersection t1@(Tip k x) t2
569 intersection t (Tip k x)
573 intersection Nil t = Nil
574 intersection t Nil = Nil
576 -- | /O(n+m)/. The intersection with a combining function.
577 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
578 intersectionWith f m1 m2
579 = intersectionWithKey (\k x y -> f x y) m1 m2
581 -- | /O(n+m)/. The intersection with a combining function.
582 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
583 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
584 | shorter m1 m2 = intersection1
585 | shorter m2 m1 = intersection2
586 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
589 intersection1 | nomatch p2 p1 m1 = Nil
590 | zero p2 m1 = intersectionWithKey f l1 t2
591 | otherwise = intersectionWithKey f r1 t2
593 intersection2 | nomatch p1 p2 m2 = Nil
594 | zero p1 m2 = intersectionWithKey f t1 l2
595 | otherwise = intersectionWithKey f t1 r2
597 intersectionWithKey f t1@(Tip k x) t2
598 = case lookup k t2 of
599 Just y -> Tip k (f k x y)
601 intersectionWithKey f t1 (Tip k y)
602 = case lookup k t1 of
603 Just x -> Tip k (f k x y)
605 intersectionWithKey f Nil t = Nil
606 intersectionWithKey f t Nil = Nil
609 {--------------------------------------------------------------------
611 --------------------------------------------------------------------}
612 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
613 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
614 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
615 isProperSubmapOf m1 m2
616 = isProperSubmapOfBy (==) m1 m2
618 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
619 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
620 @m1@ and @m2@ are not equal,
621 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
622 applied to their respective values. For example, the following
623 expressions are all 'True':
625 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
626 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
628 But the following are all 'False':
630 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
631 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
632 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
634 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
635 isProperSubmapOfBy pred t1 t2
636 = case submapCmp pred t1 t2 of
640 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
642 | shorter m2 m1 = submapCmpLt
643 | p1 == p2 = submapCmpEq
644 | otherwise = GT -- disjoint
646 submapCmpLt | nomatch p1 p2 m2 = GT
647 | zero p1 m2 = submapCmp pred t1 l2
648 | otherwise = submapCmp pred t1 r2
649 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
655 submapCmp pred (Bin p m l r) t = GT
656 submapCmp pred (Tip kx x) (Tip ky y)
657 | (kx == ky) && pred x y = EQ
658 | otherwise = GT -- disjoint
659 submapCmp pred (Tip k x) t
661 Just y | pred x y -> LT
662 other -> GT -- disjoint
663 submapCmp pred Nil Nil = EQ
664 submapCmp pred Nil t = LT
666 -- | /O(n+m)/. Is this a submap?
667 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
668 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
670 = isSubmapOfBy (==) m1 m2
673 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
674 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
675 applied to their respective values. For example, the following
676 expressions are all 'True':
678 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
679 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
680 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
682 But the following are all 'False':
684 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
685 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
686 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
689 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
690 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
691 | shorter m1 m2 = False
692 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
693 else isSubmapOfBy pred t1 r2)
694 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
695 isSubmapOfBy pred (Bin p m l r) t = False
696 isSubmapOfBy pred (Tip k x) t = case lookup k t of
699 isSubmapOfBy pred Nil t = True
701 {--------------------------------------------------------------------
703 --------------------------------------------------------------------}
704 -- | /O(n)/. Map a function over all values in the map.
705 map :: (a -> b) -> IntMap a -> IntMap b
707 = mapWithKey (\k x -> f x) m
709 -- | /O(n)/. Map a function over all values in the map.
710 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
713 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
714 Tip k x -> Tip k (f k x)
717 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
718 -- argument through the map in ascending order of keys.
719 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
721 = mapAccumWithKey (\a k x -> f a x) a m
723 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
724 -- argument through the map in ascending order of keys.
725 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
726 mapAccumWithKey f a t
729 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
730 -- argument through the map in ascending order of keys.
731 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
734 Bin p m l r -> let (a1,l') = mapAccumL f a l
735 (a2,r') = mapAccumL f a1 r
736 in (a2,Bin p m l' r')
737 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
741 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
742 -- argument throught the map in descending order of keys.
743 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
746 Bin p m l r -> let (a1,r') = mapAccumR f a r
747 (a2,l') = mapAccumR f a1 l
748 in (a2,Bin p m l' r')
749 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
752 {--------------------------------------------------------------------
754 --------------------------------------------------------------------}
755 -- | /O(n)/. Filter all values that satisfy some predicate.
756 filter :: (a -> Bool) -> IntMap a -> IntMap a
758 = filterWithKey (\k x -> p x) m
760 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
761 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
765 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
771 -- | /O(n)/. partition the map according to some predicate. The first
772 -- map contains all elements that satisfy the predicate, the second all
773 -- elements that fail the predicate. See also 'split'.
774 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
776 = partitionWithKey (\k x -> p x) m
778 -- | /O(n)/. partition the map according to some predicate. The first
779 -- map contains all elements that satisfy the predicate, the second all
780 -- elements that fail the predicate. See also 'split'.
781 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
782 partitionWithKey pred t
785 -> let (l1,l2) = partitionWithKey pred l
786 (r1,r2) = partitionWithKey pred r
787 in (bin p m l1 r1, bin p m l2 r2)
789 | pred k x -> (t,Nil)
790 | otherwise -> (Nil,t)
794 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
795 -- where all keys in @map1@ are lower than @k@ and all keys in
796 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
797 split :: Key -> IntMap a -> (IntMap a,IntMap a)
801 | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
802 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
803 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
807 | otherwise -> (Nil,Nil)
810 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
811 -- key was found in the original map.
812 splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
816 | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
817 | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
818 | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
820 | k>ky -> (t,Nothing,Nil)
821 | k<ky -> (Nil,Nothing,t)
822 | otherwise -> (Nil,Just y,Nil)
823 Nil -> (Nil,Nothing,Nil)
825 {--------------------------------------------------------------------
827 --------------------------------------------------------------------}
828 -- | /O(n)/. Fold the values in the map, such that
829 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
832 -- > elems map = fold (:) [] map
834 fold :: (a -> b -> b) -> b -> IntMap a -> b
836 = foldWithKey (\k x y -> f x y) z t
838 -- | /O(n)/. Fold the keys and values in the map, such that
839 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
842 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
844 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
848 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
851 Bin p m l r -> foldr f (foldr f z r) l
855 {--------------------------------------------------------------------
857 --------------------------------------------------------------------}
859 -- Return all elements of the map in the ascending order of their keys.
860 elems :: IntMap a -> [a]
862 = foldWithKey (\k x xs -> x:xs) [] m
864 -- | /O(n)/. Return all keys of the map in ascending order.
865 keys :: IntMap a -> [Key]
867 = foldWithKey (\k x ks -> k:ks) [] m
869 -- | /O(n*min(n,W))/. The set of all keys of the map.
870 keysSet :: IntMap a -> IntSet.IntSet
871 keysSet m = IntSet.fromDistinctAscList (keys m)
874 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
875 assocs :: IntMap a -> [(Key,a)]
880 {--------------------------------------------------------------------
882 --------------------------------------------------------------------}
883 -- | /O(n)/. Convert the map to a list of key\/value pairs.
884 toList :: IntMap a -> [(Key,a)]
886 = foldWithKey (\k x xs -> (k,x):xs) [] t
888 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
889 -- keys are in ascending order.
890 toAscList :: IntMap a -> [(Key,a)]
892 = -- NOTE: the following algorithm only works for big-endian trees
893 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
895 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
896 fromList :: [(Key,a)] -> IntMap a
898 = foldlStrict ins empty xs
900 ins t (k,x) = insert k x t
902 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
903 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
905 = fromListWithKey (\k x y -> f x y) xs
907 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
908 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
910 = foldlStrict ins empty xs
912 ins t (k,x) = insertWithKey f k x t
914 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
915 -- the keys are in ascending order.
916 fromAscList :: [(Key,a)] -> IntMap a
920 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
921 -- the keys are in ascending order, with a combining function on equal keys.
922 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
926 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
927 -- the keys are in ascending order, with a combining function on equal keys.
928 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
929 fromAscListWithKey f xs
930 = fromListWithKey f xs
932 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
933 -- the keys are in ascending order and all distinct.
934 fromDistinctAscList :: [(Key,a)] -> IntMap a
935 fromDistinctAscList xs
939 {--------------------------------------------------------------------
941 --------------------------------------------------------------------}
942 instance Eq a => Eq (IntMap a) where
943 t1 == t2 = equal t1 t2
944 t1 /= t2 = nequal t1 t2
946 equal :: Eq a => IntMap a -> IntMap a -> Bool
947 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
948 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
949 equal (Tip kx x) (Tip ky y)
950 = (kx == ky) && (x==y)
954 nequal :: Eq a => IntMap a -> IntMap a -> Bool
955 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
956 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
957 nequal (Tip kx x) (Tip ky y)
958 = (kx /= ky) || (x/=y)
959 nequal Nil Nil = False
962 {--------------------------------------------------------------------
964 --------------------------------------------------------------------}
966 instance Ord a => Ord (IntMap a) where
967 compare m1 m2 = compare (toList m1) (toList m2)
969 {--------------------------------------------------------------------
971 --------------------------------------------------------------------}
973 instance Functor IntMap where
976 {--------------------------------------------------------------------
978 --------------------------------------------------------------------}
980 instance Show a => Show (IntMap a) where
981 showsPrec d t = showMap (toList t)
984 showMap :: (Show a) => [(Key,a)] -> ShowS
988 = showChar '{' . showElem x . showTail xs
990 showTail [] = showChar '}'
991 showTail (x:xs) = showChar ',' . showElem x . showTail xs
993 showElem (k,x) = shows k . showString ":=" . shows x
995 {--------------------------------------------------------------------
997 --------------------------------------------------------------------}
999 #include "Typeable.h"
1000 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1002 {--------------------------------------------------------------------
1004 --------------------------------------------------------------------}
1005 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1006 -- in a compressed, hanging format.
1007 showTree :: Show a => IntMap a -> String
1009 = showTreeWith True False s
1012 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1013 the tree that implements the map. If @hang@ is
1014 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1015 @wide@ is 'True', an extra wide version is shown.
1017 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1018 showTreeWith hang wide t
1019 | hang = (showsTreeHang wide [] t) ""
1020 | otherwise = (showsTree wide [] [] t) ""
1022 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1023 showsTree wide lbars rbars t
1026 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1027 showWide wide rbars .
1028 showsBars lbars . showString (showBin p m) . showString "\n" .
1029 showWide wide lbars .
1030 showsTree wide (withEmpty lbars) (withBar lbars) l
1032 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1033 Nil -> showsBars lbars . showString "|\n"
1035 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1036 showsTreeHang wide bars t
1039 -> showsBars bars . showString (showBin p m) . showString "\n" .
1040 showWide wide bars .
1041 showsTreeHang wide (withBar bars) l .
1042 showWide wide bars .
1043 showsTreeHang wide (withEmpty bars) r
1045 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1046 Nil -> showsBars bars . showString "|\n"
1049 = "*" -- ++ show (p,m)
1052 | wide = showString (concat (reverse bars)) . showString "|\n"
1055 showsBars :: [String] -> ShowS
1059 _ -> showString (concat (reverse (tail bars))) . showString node
1062 withBar bars = "| ":bars
1063 withEmpty bars = " ":bars
1066 {--------------------------------------------------------------------
1068 --------------------------------------------------------------------}
1069 {--------------------------------------------------------------------
1071 --------------------------------------------------------------------}
1072 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1074 | zero p1 m = Bin p m t1 t2
1075 | otherwise = Bin p m t2 t1
1077 m = branchMask p1 p2
1080 {--------------------------------------------------------------------
1081 @bin@ assures that we never have empty trees within a tree.
1082 --------------------------------------------------------------------}
1083 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1086 bin p m l r = Bin p m l r
1089 {--------------------------------------------------------------------
1090 Endian independent bit twiddling
1091 --------------------------------------------------------------------}
1092 zero :: Key -> Mask -> Bool
1094 = (natFromInt i) .&. (natFromInt m) == 0
1096 nomatch,match :: Key -> Prefix -> Mask -> Bool
1103 mask :: Key -> Mask -> Prefix
1105 = maskW (natFromInt i) (natFromInt m)
1108 zeroN :: Nat -> Nat -> Bool
1109 zeroN i m = (i .&. m) == 0
1111 {--------------------------------------------------------------------
1112 Big endian operations
1113 --------------------------------------------------------------------}
1114 maskW :: Nat -> Nat -> Prefix
1116 = intFromNat (i .&. (complement (m-1) `xor` m))
1118 shorter :: Mask -> Mask -> Bool
1120 = (natFromInt m1) > (natFromInt m2)
1122 branchMask :: Prefix -> Prefix -> Mask
1124 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1126 {----------------------------------------------------------------------
1127 Finding the highest bit (mask) in a word [x] can be done efficiently in
1129 * convert to a floating point value and the mantissa tells us the
1130 [log2(x)] that corresponds with the highest bit position. The mantissa
1131 is retrieved either via the standard C function [frexp] or by some bit
1132 twiddling on IEEE compatible numbers (float). Note that one needs to
1133 use at least [double] precision for an accurate mantissa of 32 bit
1135 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1136 * use processor specific assembler instruction (asm).
1138 The most portable way would be [bit], but is it efficient enough?
1139 I have measured the cycle counts of the different methods on an AMD
1140 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1142 highestBitMask: method cycles
1149 highestBit: method cycles
1156 Wow, the bit twiddling is on today's RISC like machines even faster
1157 than a single CISC instruction (BSR)!
1158 ----------------------------------------------------------------------}
1160 {----------------------------------------------------------------------
1161 [highestBitMask] returns a word where only the highest bit is set.
1162 It is found by first setting all bits in lower positions than the
1163 highest bit and than taking an exclusive or with the original value.
1164 Allthough the function may look expensive, GHC compiles this into
1165 excellent C code that subsequently compiled into highly efficient
1166 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1167 ----------------------------------------------------------------------}
1168 highestBitMask :: Nat -> Nat
1170 = case (x .|. shiftRL x 1) of
1171 x -> case (x .|. shiftRL x 2) of
1172 x -> case (x .|. shiftRL x 4) of
1173 x -> case (x .|. shiftRL x 8) of
1174 x -> case (x .|. shiftRL x 16) of
1175 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1176 x -> (x `xor` (shiftRL x 1))
1179 {--------------------------------------------------------------------
1181 --------------------------------------------------------------------}
1185 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1188 {--------------------------------------------------------------------
1190 --------------------------------------------------------------------}
1191 testTree :: [Int] -> IntMap Int
1192 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1193 test1 = testTree [1..20]
1194 test2 = testTree [30,29..10]
1195 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1197 {--------------------------------------------------------------------
1199 --------------------------------------------------------------------}
1204 { configMaxTest = 500
1205 , configMaxFail = 5000
1206 , configSize = \n -> (div n 2 + 3)
1207 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1211 {--------------------------------------------------------------------
1212 Arbitrary, reasonably balanced trees
1213 --------------------------------------------------------------------}
1214 instance Arbitrary a => Arbitrary (IntMap a) where
1215 arbitrary = do{ ks <- arbitrary
1216 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1217 ; return (fromList xs)
1221 {--------------------------------------------------------------------
1222 Single, Insert, Delete
1223 --------------------------------------------------------------------}
1224 prop_Single :: Key -> Int -> Bool
1226 = (insert k x empty == singleton k x)
1228 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1229 prop_InsertDelete k x t
1230 = not (member k t) ==> delete k (insert k x t) == t
1232 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1233 prop_UpdateDelete k t
1234 = update (const Nothing) k t == delete k t
1237 {--------------------------------------------------------------------
1239 --------------------------------------------------------------------}
1240 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1241 prop_UnionInsert k x t
1242 = union (singleton k x) t == insert k x t
1244 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1245 prop_UnionAssoc t1 t2 t3
1246 = union t1 (union t2 t3) == union (union t1 t2) t3
1248 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1249 prop_UnionComm t1 t2
1250 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1253 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1255 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1256 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1258 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1260 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1261 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1263 {--------------------------------------------------------------------
1265 --------------------------------------------------------------------}
1267 = forAll (choose (5,100)) $ \n ->
1268 let xs = [(x,()) | x <- [0..n::Int]]
1269 in fromAscList xs == fromList xs
1271 prop_List :: [Key] -> Bool
1273 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])