# Ticket #3909: containers-pqueue.2.patch

File containers-pqueue.2.patch, 32.2 KB (added by LouisWasserman, 6 years ago) |
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1 | Thu Mar 4 11:22:34 CST 2010 wasserman.louis@gmail.com |

2 | * Data.PQueue with binomial heaps |

3 | |

4 | New patches: |

5 | |

6 | [Data.PQueue with binomial heaps |

7 | wasserman.louis@gmail.com**20100304172234 |

8 | Ignore-this: ff30638168b7add7d1fd1e5473289500 |

9 | ] { |

10 | adddir ./Data/PQueue |

11 | addfile ./Data/PQueue.hs |

12 | hunk ./Data/PQueue.hs 1 |

13 | + |

14 | +----------------------------------------------------------------------------- |

15 | +-- | |

16 | +-- Module : Data.MinQueue |

17 | +-- Copyright : (c) Louis Wasserman 2010 |

18 | +-- License : BSD-style |

19 | +-- Maintainer : libraries@haskell.org |

20 | +-- Stability : experimental |

21 | +-- Portability : portable |

22 | +-- |

23 | +-- General purpose priority queue, supporting extract-maximum operations. |

24 | +-- |

25 | +-- This module reexports "Data.PQueue.Min". If you need to use a max-queue, |

26 | +-- you should import "Data.PQueue.Max". |

27 | +--------------------------------------------------------------------------- |

28 | +module Data.PQueue ( |

29 | + PQueue, |

30 | + module Data.PQueue.Min) where |

31 | hunk ./Data/PQueue.hs 20 |

32 | +import Data.PQueue.Min |

33 | + |

34 | +type PQueue = MinQueue |

35 | addfile ./Data/PQueue/Max.hs |

36 | hunk ./Data/PQueue/Max.hs 1 |

37 | +{-# LANGUAGE CPP #-} |

38 | hunk ./Data/PQueue/Max.hs 3 |

39 | +----------------------------------------------------------------------------- |

40 | +-- | |

41 | +-- Module : Data.MinQueue.Max |

42 | +-- Copyright : (c) Louis Wasserman 2010 |

43 | +-- License : BSD-style |

44 | +-- Maintainer : libraries@haskell.org |

45 | +-- Stability : experimental |

46 | +-- Portability : portable |

47 | +-- |

48 | +-- General purpose priority queue, supporting extract-maximum operations. |

49 | +-- |

50 | +-- An amortized running time is given for each operation, with /n/ referring |

51 | +-- to the length of the sequence and /i/ being the integral index used by |

52 | +-- some operations. These bounds hold even in a persistent (shared) setting. |

53 | +-- |

54 | +-- This implementation is based on a binomial heap augmented with a global root. |

55 | +-- The spine of the heap is maintained strictly, ensuring that computations happen |

56 | +-- as they are performed. Note that this module is a small wrapper around |

57 | +-- "Data.PQueue.Min". |

58 | +-- |

59 | +-- /WARNING:/ 'toList' and 'toAscList' are /not/ equivalent, unlike for example |

60 | +-- "Data.Map". |

61 | +----------------------------------------------------------------------------- |

62 | +module Data.PQueue.Max( |

63 | + MaxQueue, |

64 | + -- * Basic operations |

65 | + empty, |

66 | + null, |

67 | + size, |

68 | + -- * Query operations |

69 | + ViewQ(..), |

70 | + top, |

71 | + delete, |

72 | + extract, |

73 | + -- * Construction operations |

74 | + singleton, |

75 | + insert, |

76 | + union, |

77 | + unions, |

78 | + intersection, |

79 | + difference, |

80 | + -- * Fold\/Functor\/Traversable variations |

81 | + mapMonotonic, |

82 | + foldrQueue, |

83 | + foldlQueue, |

84 | + traverseMonotonic, |

85 | + -- * List operations |

86 | + toList, |

87 | + toDescList, |

88 | + fromList, |

89 | + fromDescList) where |

90 | + |

91 | +import Control.Applicative (Applicative(..), (<$>)) |

92 | + |

93 | +import Data.Monoid |

94 | +import Data.Foldable hiding (toList) |

95 | +import Data.Traversable |

96 | + |

97 | +import qualified Data.PQueue.Min as Min |

98 | + |

99 | +import Prelude hiding (foldr, foldl, null) |

100 | + |

101 | +#ifdef __GLASGOW_HASKELL__ |

102 | +import GHC.Exts (build) |

103 | +import Text.Read (Lexeme(Ident), lexP, parens, prec, |

104 | + readPrec, readListPrec, readListPrecDefault) |

105 | +#endif |

106 | + |

107 | +-- | A priority queue implementation. Implemented as a wrapper around "Data.PQueue.Min". |

108 | +-- /Warning/: the 'Functor', 'Foldable', and 'Traversable' instances of this type /ignore ordering/. |

109 | +-- For 'Functor', it is guaranteed that if @f@ is a monotonic function, then @'fmap' f@ on a valid |

110 | +-- 'MaxQueue' will return a valid 'MaxQueue'. An analogous guarantee holds for 'traverse'. (Note: |

111 | +-- if passed constant-time operations, every function in 'Functor', 'Foldable', and 'Traversable' |

112 | +-- will run in /O(n)/.) |

113 | +-- |

114 | +-- If you wish to perform folds on a priority queue that respect order, use 'foldrQueue' or |

115 | +-- 'foldlQueue'. |

116 | +newtype MaxQueue a = MaxQ {unMaxQ :: Min.MinQueue (Down a)} |

117 | +newtype Down a = Down a deriving (Eq) |

118 | + |

119 | +instance Ord a => Ord (Down a) where |

120 | + Down x `compare` Down y = compare y x |

121 | + Down x <= Down y = y <= x |

122 | + Down x < Down y = y < x |

123 | + Down x >= Down y = y >= x |

124 | + Down x > Down y = y > x |

125 | + |

126 | +instance Ord a => Eq (MaxQueue a) where |

127 | + q1 == q2 = toDescList q1 == toDescList q2 |

128 | + |

129 | +instance Ord a => Ord (MaxQueue a) where |

130 | + q1 `compare` q2 = toDescList q1 `compare` toDescList q2 |

131 | + |

132 | +instance (Ord a, Show a) => Show (MaxQueue a) where |

133 | + showsPrec p xs = showParen (p > 10) $ |

134 | + showString "fromDescList " . shows (toDescList xs) |

135 | + |

136 | +instance Read a => Read (MaxQueue a) where |

137 | +#ifdef __GLASGOW_HASKELL__ |

138 | + readPrec = parens $ prec 10 $ do |

139 | + Ident "fromDescList" <- lexP |

140 | + xs <- readPrec |

141 | + return (fromDescList xs) |

142 | + |

143 | + readListPrec = readListPrecDefault |

144 | +#else |

145 | + readsPrec p = readParen (p > 10) $ \ r -> do |

146 | + ("fromDescList",s) <- lex r |

147 | + (xs,t) <- reads s |

148 | + return (fromDescList xs,t) |

149 | +#endif |

150 | + |

151 | +instance Ord a => Monoid (MaxQueue a) where |

152 | + mempty = empty |

153 | + mappend = union |

154 | + |

155 | +-- | /O(1)/. The empty priority queue. |

156 | +empty :: MaxQueue a |

157 | +empty = MaxQ Min.empty |

158 | + |

159 | +-- | /O(1)/. Is this the empty priority queue? |

160 | +null :: MaxQueue a -> Bool |

161 | +null (MaxQ q) = Min.null q |

162 | + |

163 | +-- | /O(1)/. The number of elements in the queue. |

164 | +size :: MaxQueue a -> Int |

165 | +size (MaxQ q) = Min.size q |

166 | + |

167 | +data ViewQ a = EmptyQ -- ^ empty queue |

168 | + | a :^ MaxQueue a -- ^ the top (maximum) of the queue and the rest of the queue |

169 | + deriving (Eq, Ord, Read, Show) |

170 | + |

171 | +instance Functor ViewQ where |

172 | + fmap f (a :^ q) = f a :^ fmap f q |

173 | + fmap _ _ = EmptyQ |

174 | + |

175 | +instance Foldable ViewQ where |

176 | + foldr _ z EmptyQ = z |

177 | + foldr f z (a :^ q) = a `f` foldr f z q |

178 | + foldl _ z EmptyQ = z |

179 | + foldl f z (a :^ q) = foldl f (z `f` a) q |

180 | + |

181 | +instance Traversable ViewQ where |

182 | + traverse _ EmptyQ = pure EmptyQ |

183 | + traverse f (a :^ q) = (:^) <$> f a <*> traverse f q |

184 | + |

185 | +-- | /O(log n)/. The top (maximum) element of the queue, if there is one. |

186 | +top :: Ord a => MaxQueue a -> Maybe a |

187 | +top q = case extract q of |

188 | + EmptyQ -> Nothing |

189 | + x :^ _ -> Just x |

190 | + |

191 | +-- | /O(log n)/. Extract the top (maximum) element of the sequence, if there is one. |

192 | +extract :: Ord a => MaxQueue a -> ViewQ a |

193 | +extract (MaxQ q) = case Min.extract q of |

194 | + Min.EmptyQ -> EmptyQ |

195 | + (Min.:^) (Down a) q' |

196 | + -> a :^ MaxQ q' |

197 | + |

198 | +-- | /O(log n)/. Delete the top (maximum) element of the sequence, if there is one. |

199 | +delete :: Ord a => MaxQueue a -> Maybe (MaxQueue a) |

200 | +delete (MaxQ q) = MaxQ <$> Min.delete q |

201 | + |

202 | +-- | /O(1)/. Construct a priority queue with a single element. |

203 | +singleton :: a -> MaxQueue a |

204 | +singleton = MaxQ . Min.singleton . Down |

205 | + |

206 | +-- | /O(1)/. Insert an element into the priority queue. |

207 | +insert :: Ord a => a -> MaxQueue a -> MaxQueue a |

208 | +insert x (MaxQ q) = MaxQ (Min.insert (Down x) q) |

209 | + |

210 | +-- | /O(log (min(n,m)))/. Take the union of two priority queues. |

211 | +union :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a |

212 | +MaxQ q1 `union` MaxQ q2 = MaxQ (Min.union q1 q2) |

213 | + |

214 | +-- | Takes the union of a list of priority queues. Equivalent to @'foldl' 'union' 'empty'@. |

215 | +unions :: Ord a => [MaxQueue a] -> MaxQueue a |

216 | +unions = foldl union empty |

217 | + |

218 | +-- | /O(n log n + m log m)/. Take the intersection of two priority queues. |

219 | +intersection :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a |

220 | +MaxQ q1 `intersection` MaxQ q2 = MaxQ (Min.intersection q1 q2) |

221 | + |

222 | +-- | /O(n log n + m log m)/. Takes the difference of two priority queues. |

223 | +difference :: Ord a => MaxQueue a -> MaxQueue a -> MaxQueue a |

224 | +MaxQ q1 `difference` MaxQ q2 = MaxQ (Min.difference q1 q2) |

225 | + |

226 | +-- | /O(n)/. Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue, |

227 | +-- as in 'fmap'. If it is not, the result is undefined. |

228 | +mapMonotonic :: (a -> b) -> MaxQueue a -> MaxQueue b |

229 | +mapMonotonic = fmap |

230 | + |

231 | +-- | /O(n)/. Assumes that the function it is given is monotonic, in some sense, and performs the 'traverse' operation. |

232 | +-- If the function is not monotonic, the result is undefined. |

233 | +traverseMonotonic :: Applicative f => (a -> f b) -> MaxQueue a -> f (MaxQueue b) |

234 | +traverseMonotonic = traverse |

235 | + |

236 | +instance Functor Down where |

237 | + fmap f (Down a) = Down (f a) |

238 | + |

239 | +instance Foldable Down where |

240 | + foldr f z (Down a) = a `f` z |

241 | + foldl f z (Down a) = z `f` a |

242 | + |

243 | +instance Traversable Down where |

244 | + traverse f (Down a) = Down <$> f a |

245 | + |

246 | +instance Functor MaxQueue where |

247 | + fmap f (MaxQ q) = MaxQ (fmap (fmap f) q) |

248 | + |

249 | +instance Foldable MaxQueue where |

250 | + foldr f z (MaxQ q) = foldr (flip (foldr f)) z q |

251 | + foldl f z (MaxQ q) = foldl (foldl f) z q |

252 | + |

253 | +instance Traversable MaxQueue where |

254 | + traverse f (MaxQ q) = MaxQ <$> traverse (traverse f) q |

255 | + |

256 | +foldrQueue :: Ord a => (a -> b -> b) -> b -> MaxQueue a -> b |

257 | +foldrQueue f z (MaxQ q) = Min.foldrQueue (flip (foldr f)) z q |

258 | + |

259 | +foldlQueue :: Ord a => (b -> a -> b) -> b -> MaxQueue a -> b |

260 | +foldlQueue f z (MaxQ q) = Min.foldlQueue (foldl f) z q |

261 | + |

262 | +{-# INLINE toDescList #-} |

263 | +-- | /O(n log n)/. Extracts the elements of the priority queue in descending order. |

264 | +toDescList :: Ord a => MaxQueue a -> [a] |

265 | +#ifdef __GLASGOW_HASKELL__ |

266 | +toDescList q = build (\ c nil -> foldrQueue c nil q) |

267 | +#else |

268 | +toDescList = foldrQueue (:) [] |

269 | +#endif |

270 | + |

271 | +{-# INLINE toList #-} |

272 | +-- | /O(n)/. Returns the elements of the priority queue in no particular order. |

273 | +toList :: MaxQueue a -> [a] |

274 | +#ifdef __GLASGOW_HASKELL__ |

275 | +toList q = build (\ c nil -> foldr c nil q) |

276 | +#else |

277 | +toList = foldr (:) [] |

278 | +#endif |

279 | + |

280 | +{-# INLINE fromDescList #-} |

281 | +-- | /O(n)/. Constructs a priority queue from an descending list. /Warning/: Does not check the precondition. |

282 | +fromDescList :: [a] -> MaxQueue a |

283 | +fromDescList = MaxQ . Min.fromAscList . map Down |

284 | + |

285 | +{-# INLINE fromList #-} |

286 | +-- | /O(n log n)/. Constructs a priority queue from an unordered list. |

287 | +fromList :: Ord a => [a] -> MaxQueue a |

288 | +fromList = foldr insert empty |

289 | addfile ./Data/PQueue/Min.hs |

290 | hunk ./Data/PQueue/Min.hs 1 |

291 | +{-# LANGUAGE CPP #-} |

292 | hunk ./Data/PQueue/Min.hs 3 |

293 | +----------------------------------------------------------------------------- |

294 | +-- | |

295 | +-- Module : Data.MinQueue.Min |

296 | +-- Copyright : (c) Louis Wasserman 2010 |

297 | +-- License : BSD-style |

298 | +-- Maintainer : libraries@haskell.org |

299 | +-- Stability : experimental |

300 | +-- Portability : portable |

301 | +-- |

302 | +-- General purpose priority queue, supporting extract-minimum operations. |

303 | +-- |

304 | +-- An amortized running time is given for each operation, with /n/ referring |

305 | +-- to the length of the sequence and /i/ being the integral index used by |

306 | +-- some operations. These bounds hold even in a persistent (shared) setting. |

307 | +-- |

308 | +-- This implementation is based on a binomial heap augmented with a global root. |

309 | +-- The spine of the heap is maintained strictly, ensuring that computations happen |

310 | +-- as they are performed. |

311 | +-- |

312 | +-- /WARNING:/ 'toList' and 'toAscList' are /not/ equivalent, unlike for example |

313 | +-- "Data.Map". |

314 | +----------------------------------------------------------------------------- |

315 | +module Data.PQueue.Min ( |

316 | + MinQueue, |

317 | + -- * Basic operations |

318 | + empty, |

319 | + null, |

320 | + size, |

321 | + -- * Query operations |

322 | + ViewQ(..), |

323 | + top, |

324 | + delete, |

325 | + extract, |

326 | + -- * Construction operations |

327 | + singleton, |

328 | + insert, |

329 | + union, |

330 | + unions, |

331 | + intersection, |

332 | + difference, |

333 | + -- * Fold\/Functor\/Traversable variations |

334 | + mapMonotonic, |

335 | + foldrQueue, |

336 | + foldlQueue, |

337 | + traverseMonotonic, |

338 | + -- * List operations |

339 | + toList, |

340 | + toAscList, |

341 | + fromList, |

342 | + fromAscList) where |

343 | + |

344 | +import Prelude hiding (null, foldr, foldl) |

345 | + |

346 | +import Control.Applicative (Applicative(..), (<$>)) |

347 | + |

348 | +import Data.Monoid |

349 | +import Data.Foldable hiding (toList) |

350 | +import Data.Traversable |

351 | + |

352 | +#ifdef __GLASGOW_HASKELL__ |

353 | +import GHC.Exts (build) |

354 | +import Text.Read (Lexeme(Ident), lexP, parens, prec, |

355 | + readPrec, readListPrec, readListPrecDefault) |

356 | +#endif |

357 | + |

358 | +-- | A priority queue implementation. Implemented as a find-min wrapper around a binomial heap. |

359 | +-- /Warning/: the 'Functor', 'Foldable', and 'Traversable' instances of this type /ignore ordering/. |

360 | +-- For 'Functor', it is guaranteed that if @f@ is a monotonic function, then @'fmap' f@ on a valid |

361 | +-- 'MinQueue' will return a valid 'MinQueue'. An analogous guarantee holds for 'traverse'. (Note: |

362 | +-- if passed constant-time operations, every function in 'Functor', 'Foldable', and 'Traversable' |

363 | +-- will run in /O(n)/.) |

364 | +-- |

365 | +-- If you wish to perform folds on a priority queue that respect order, use 'foldrQueue' or |

366 | +-- 'foldlQueue'. |

367 | +data MinQueue a = Empty | MinQueue {-# UNPACK #-} !Int a !(BinomHeap a) |

368 | +type BinomHeap a = BinomForest a Zero |

369 | + |

370 | +instance Ord a => Eq (MinQueue a) where |

371 | + q1 == q2 = toAscList q1 == toAscList q2 |

372 | + |

373 | +instance Ord a => Ord (MinQueue a) where |

374 | + compare q1 q2 = compare (toAscList q1) (toAscList q2) |

375 | + |

376 | +instance (Ord a, Show a) => Show (MinQueue a) where |

377 | + showsPrec p xs = showParen (p > 10) $ |

378 | + showString "fromAscList " . shows (toAscList xs) |

379 | + |

380 | +instance Read a => Read (MinQueue a) where |

381 | +#ifdef __GLASGOW_HASKELL__ |

382 | + readPrec = parens $ prec 10 $ do |

383 | + Ident "fromAscList" <- lexP |

384 | + xs <- readPrec |

385 | + return (fromAscList xs) |

386 | + |

387 | + readListPrec = readListPrecDefault |

388 | +#else |

389 | + readsPrec p = readParen (p > 10) $ \ r -> do |

390 | + ("fromAscList",s) <- lex r |

391 | + (xs,t) <- reads s |

392 | + return (fromAscList xs,t) |

393 | +#endif |

394 | + |

395 | +instance Ord a => Monoid (MinQueue a) where |

396 | + mempty = Empty |

397 | + mappend = union |

398 | + |

399 | +-- We implement tree ranks in the type system with a nicely elegant approach, as follows. |

400 | +-- |

401 | +-- A binomial tree of rank @0@ with elements of type @e@ has type @'BinomTree' e 'Zero'@. |

402 | +-- If a binomial tree of rank @k@ has type @BinomTree e k@, then a binomial tree of rank |

403 | +-- @k+1@ has type @'BinomTree' e ('Succ' e k)@. Therefore, we may justifiably label the |

404 | +-- second type argument as the /rank/ of the node. |

405 | +-- |

406 | +-- Consider the set-theoretic definition of the natural numbers, in which a number is specified |

407 | +-- to be the set of all numbers less than it, and 0 is the empty set. The ranks of binomial |

408 | +-- trees are similar: the children of a binomial tree of rank @k@ are a collection of a binomial |

409 | +-- tree of every rank less than @k@. We can then /define/ the type representing rank @k@ |

410 | +-- to be a sequence of a binomial tree of every rank less than @k@. In particular, |

411 | +-- @'Succ' e k@ is equivalent to @(BinomTree e k, k)@, since @k@ is a type representing a |

412 | +-- sequence of binomial trees of rank less than @k@. We may reasonably define the type |

413 | +-- corresponding to @0@ to be @()@, since it should be an unambiguous ``unit.'' This is |

414 | +-- nicely analogous to the construction of the natural numbers, where @succ(a) = {a} `union` a@. |

415 | +-- |

416 | +-- Now that we've defined rank types, we note that a binomial tree with a given rank @rk@, |

417 | +-- written as @'BinomTree' e rk@, has a root of type @e@ and a set of children of type @rk@. |

418 | +-- We may justifiably say, then, |

419 | +-- |

420 | +-- > data BinomTree e rk = BinomTree e rk |

421 | +-- |

422 | +-- Cute! |

423 | +-- |

424 | +-- To implement binomial heaps, in which we may have at most one root of each rank, we define |

425 | +-- @'BinomForest' e rk@ to be a binomial forest of roots of rank at least @rk@. Since there is only |

426 | +-- one root of each rank, we may either have a binomial forest of rank @rk@ or not, and then |

427 | +-- a @BinomForest e (Succ e rk)@ contains the rest of the forest. We also have a 'Nil' constructor, |

428 | +-- for when we have no more roots. We maintain the invariant that @Nil@ always follows a @Cons@, but |

429 | +-- don't implement that in the type system. |

430 | +data BinomForest e rk = Nil | Skip !(BinomForest' e rk) | Cons {-# UNPACK #-} !(BinomTree e rk) !(BinomForest' e rk) |

431 | +type BinomForest' e rk = BinomForest e (Succ e rk) |

432 | + |

433 | +instance Ord e => Monoid (BinomForest e rk) where |

434 | + mempty = Nil |

435 | + mappend = merge (<=) |

436 | + |

437 | +data BinomTree e rk = BinomTree e rk |

438 | +type BinomTree' e rk = BinomTree e (Succ e rk) |

439 | +data Succ e rk = Succ {-# UNPACK #-} !(BinomTree e rk) rk |

440 | +type Zero = () |

441 | + |

442 | +-- basics |

443 | + |

444 | +-- | /O(1)/. The empty priority queue. |

445 | +empty :: MinQueue a |

446 | +empty = Empty |

447 | + |

448 | +-- | /O(1)/. Is this the empty priority queue? |

449 | +null :: MinQueue a -> Bool |

450 | +null Empty = True |

451 | +null _ = False |

452 | + |

453 | +-- | /O(1)/. The number of elements in the queue. |

454 | +size :: MinQueue a -> Int |

455 | +size Empty = 0 |

456 | +size (MinQueue n _ _) = n |

457 | + |

458 | +-- queries |

459 | + |

460 | +-- | View of the top of a sequence. Note: the 'Functor', 'Foldable', and 'Traversable' instances |

461 | +-- have the same caveats as the instances for 'MinQueue'. |

462 | +data ViewQ a = EmptyQ -- ^ empty queue |

463 | + | a :^ MinQueue a -- ^ the top (minimum) of the queue and the rest of the queue |

464 | + deriving (Eq, Ord, Read, Show) |

465 | + |

466 | +instance Functor ViewQ where |

467 | + fmap f (a :^ q) = f a :^ fmap f q |

468 | + fmap _ _ = EmptyQ |

469 | + |

470 | +instance Foldable ViewQ where |

471 | + foldr _ z EmptyQ = z |

472 | + foldr f z (a :^ q) = a `f` foldr f z q |

473 | + foldl _ z EmptyQ = z |

474 | + foldl f z (a :^ q) = foldl f (z `f` a) q |

475 | + |

476 | +instance Traversable ViewQ where |

477 | + traverse _ EmptyQ = pure EmptyQ |

478 | + traverse f (a :^ q) = (:^) <$> f a <*> traverse f q |

479 | + |

480 | +-- | /O(1)/. View the top (minimum) element of the queue, if there is one. |

481 | +top :: Ord a => MinQueue a -> Maybe a |

482 | +top q = case extract q of |

483 | + EmptyQ -> Nothing |

484 | + x :^ _ -> Just x |

485 | + |

486 | +-- | /O(log n)/. Extract the top (minimum) element of the sequence, if there is one. |

487 | +extract :: Ord a => MinQueue a -> ViewQ a |

488 | +extract Empty = EmptyQ |

489 | +extract (MinQueue n x f) = x :^ delete' n f |

490 | + |

491 | +-- | /O(log n)/. Delete the top element of the sequence, if there is one. |

492 | +delete :: Ord a => MinQueue a -> Maybe (MinQueue a) |

493 | +delete q = case extract q of |

494 | + EmptyQ -> Nothing |

495 | + _ :^ q' -> Just q' |

496 | + |

497 | +-- | Takes a size and a binomial forest and produces a priority queue with a distinguished global root. |

498 | +delete' :: Ord a => Int -> BinomHeap a -> MinQueue a |

499 | +delete' n f = n `seq` case extractBin (<=) f of |

500 | + NoExtract -> Empty |

501 | + YesExtract x' _ f' |

502 | + -> MinQueue (n-1) x' f' |

503 | + |

504 | +-- | A specialized type intended to organize the return of extract-min queries |

505 | +-- from a binomial forest. We walk all the way through the forest, and then |

506 | +-- walk backwards. @Extract e rk@ is the result type of an extract-min |

507 | +-- operation that has walked as far backwards of rank @rk@ -- that is, it |

508 | +-- has visited every root of rank @>= rk@. |

509 | +-- |

510 | +-- The interpretation of @YesExtract minKey children forest@ is |

511 | +-- |

512 | +-- * @minKey@ is the key of the minimum root visited so far. It may have |

513 | +-- any rank @>= rk@. We will denote the root corresponding to |

514 | +-- @minKey@ as @minRoot@. |

515 | +-- |

516 | +-- * @children@ is those children of @minRoot@ which have not yet been |

517 | +-- merged with the rest of the forest. Specifically, these are |

518 | +-- the children with rank @< rk@. |

519 | +-- |

520 | +-- * @forest@ is a partial reconstruction of the binomial forest without |

521 | +-- @minRoot@. It is the union of all old roots with rank @>= rk@ |

522 | +-- (except @minRoot@), with the set of all children of @minRoot@ |

523 | +-- with rank @>= rk@. Note that @forest@ is lazy, so if we discover |

524 | +-- a smaller key than @minKey@ later, we haven't wasted significant |

525 | +-- work. |

526 | +data Extract e rk = NoExtract | YesExtract e rk (BinomForest e rk) |

527 | + |

528 | +-- | Walks backward from the biggest key in the forest, as far as rank @rk@. |

529 | +-- Returns its progress. Each successive application of @extractBin@ takes |

530 | +-- amortized /O(1)/ time, so applying it from the beginning takes /O(log n)/ time. |

531 | +extractBin :: (e -> e -> Bool) -> BinomForest e rk -> Extract e rk |

532 | +extractBin _ Nil = NoExtract |

533 | +extractBin (<=) (Skip f) = case extractBin (<=) f of |

534 | + NoExtract -> NoExtract |

535 | + YesExtract minKey (Succ kChild kChildren) f' -> |

536 | + YesExtract minKey kChildren (Cons kChild f') |

537 | +extractBin (<=) (Cons t@(BinomTree x ts) f) = case extractBin (<=) f of |

538 | + YesExtract minKey (Succ kChild kChildren) f' |

539 | + | minKey <= x -> YesExtract minKey kChildren (Skip (carry1 (<=) (t `cat` kChild) f')) |

540 | + _ -> YesExtract x ts (Skip f) |

541 | + where cat = joinBin (<=) |

542 | + |

543 | +-- | /O(1)/. Construct a priority queue with a single element. |

544 | +singleton :: a -> MinQueue a |

545 | +singleton x = MinQueue 1 x Nil |

546 | + |

547 | +-- | /O(1)/. Insert an element into the priority queue. |

548 | +insert :: Ord a => a -> MinQueue a -> MinQueue a |

549 | +insert x' (MinQueue n x f) |

550 | + | x' <= x = MinQueue (n+1) x' (insertBin x f) |

551 | + | otherwise = MinQueue (n+1) x (insertBin x' f) |

552 | + where insertBin = carry1 (<=) . tip |

553 | +insert x Empty = singleton x |

554 | + |

555 | +-- | /O(log (min(n,m)))/. Take the union of two priority queues. |

556 | +union :: Ord a => MinQueue a -> MinQueue a -> MinQueue a |

557 | +Empty `union` q = q |

558 | +q `union` Empty = q |

559 | +MinQueue n1 x1 f1 `union` MinQueue n2 x2 f2 |

560 | + | x1 <= x2 = MinQueue (n1 + n2) x1 (carry (<=) (tip x2) f1 f2) |

561 | + | otherwise = MinQueue (n1 + n2) x2 (carry (<=) (tip x1) f1 f2) |

562 | + |

563 | +-- | Takes the union of a list of priority queues. Equivalent to @'foldl' 'union' 'empty'@. |

564 | +unions :: Ord a => [MinQueue a] -> MinQueue a |

565 | +unions = foldl union Empty |

566 | + |

567 | +-- | /O(n log n + m log m)/. Take the intersection of two priority queues. |

568 | +intersection :: Ord a => MinQueue a -> MinQueue a -> MinQueue a |

569 | +Empty `intersection` _ = Empty |

570 | +_ `intersection` Empty = Empty |

571 | +MinQueue _ x1 f1 `intersection` MinQueue _ x2 f2 = intersectBin (<=) compare x1 f1 x2 f2 |

572 | + |

573 | +-- Takes the intersection of two binomial heaps. Essentially, this is just the algorithm |

574 | +-- for intersecting two sorted lists, except unconsing is replaced by dequeueing. |

575 | +-- Not particularly necessary, but interesting to have just for grins. |

576 | +intersectBin :: (a -> a -> Bool) -> (a -> a -> Ordering) -> a -> BinomHeap a -> a -> BinomHeap a -> MinQueue a |

577 | +intersectBin (<=) cmp = intersect where |

578 | + intersect x1 f1 x2 f2 = case (cmp x1 x2, extractBin (<=) f1, extractBin (<=) f2) of |

579 | + (LT, YesExtract x1' _ f1', _) |

580 | + -> intersect x1' f1' x2 f2 |

581 | + (EQ, YesExtract x1' _ f1', YesExtract x2' _ f2') |

582 | + -> x1 `insertMinQ` intersect x1' f1' x2' f2' |

583 | + (EQ, _, _) |

584 | + -> singleton x1 |

585 | + (GT, _, YesExtract x2' _ f2') |

586 | + -> intersect x1 f1 x2' f2' |

587 | + _ -> Empty |

588 | + |

589 | +-- | /O(n log n + m log m)/. Takes the difference of two priority queues. |

590 | +difference :: Ord a => MinQueue a -> MinQueue a -> MinQueue a |

591 | +queue `difference` Empty |

592 | + = queue |

593 | +Empty `difference` _ |

594 | + = Empty |

595 | +MinQueue n1 x1 f1 `difference` MinQueue _ x2 f2 |

596 | + = differenceBin (<=) compare n1 x1 f1 x2 f2 |

597 | + |

598 | +-- Takes the difference of two binomial heaps. Essentially, this is just the algorithm |

599 | +-- for the difference of two sorted lists, except unconsing is replaced by dequeueing. |

600 | +-- Not particularly necessary, but interesting to have just for grins. |

601 | +differenceBin :: (a -> a -> Bool) -> (a -> a -> Ordering) -> Int -> a -> BinomHeap a -> a -> BinomHeap a -> MinQueue a |

602 | +differenceBin (<=) cmp = diffBin where |

603 | + diffBin n x1 f1 x2 f2 = n `seq` case (cmp x1 x2, extractBin (<=) f1, extractBin (<=) f2) of |

604 | + (LT, YesExtract x1' _ f1', _) |

605 | + -> x1 `insertMinQ` diffBin (n-1) x1' f1' x2 f2 |

606 | + (LT, _, _) |

607 | + -> singleton x1 |

608 | + (EQ, YesExtract x1' _ f1', YesExtract x2' _ f2') |

609 | + -> diffBin (n-1) x1' f1' x2' f2' |

610 | + (EQ, YesExtract x1' _ f1', _) |

611 | + -> MinQueue n x1' f1' |

612 | + (EQ, _, _) |

613 | + -> Empty |

614 | + (GT, _, YesExtract x2' _ f2') |

615 | + -> diffBin n x1 f1 x2' f2' |

616 | + (GT, _, _) |

617 | + -> MinQueue n x1 f1 |

618 | + |

619 | +{-# INLINE tip #-} |

620 | +-- | Constructs a binomial tree of rank 0. |

621 | +tip :: e -> BinomTree e () |

622 | +tip x = BinomTree x () |

623 | + |

624 | +-- | Given two binomial forests starting at rank @rk@, takes their union. |

625 | +-- Each successive application of this function costs /O(1)/, so applying it |

626 | +-- from the beginning costs /O(log n)/. |

627 | +merge :: (e -> e -> Bool) -> BinomForest e rk -> BinomForest e rk -> BinomForest e rk |

628 | +merge (<=) f1 f2 = case (f1, f2) of |

629 | + (Nil, _) -> f2 |

630 | + (_, Nil) -> f1 |

631 | + (Skip f1', Skip f2') |

632 | + -> Skip (merge (<=) f1' f2') |

633 | + (Skip f1', Cons t2 f2') |

634 | + -> Cons t2 (merge (<=) f1' f2') |

635 | + (Cons t1 f1', Skip f2') |

636 | + -> Cons t1 (merge (<=) f1' f2') |

637 | + (Cons t1 f1', Cons t2 f2') |

638 | + -> Skip (carry (<=) (t1 `cat` t2) f1' f2') |

639 | + where cat = joinBin (<=) |

640 | + |

641 | +-- | Merges two binomial forests with another tree. If we are thinking of the trees |

642 | +-- in the binomial forest as binary digits, this corresponds to a carry operation. |

643 | +-- Each call to this function takes /O(1)/ time, so in total, it costs /O(log n)/. |

644 | +carry :: (e -> e -> Bool) -> BinomTree e rk -> BinomForest e rk -> BinomForest e rk -> BinomForest e rk |

645 | +carry (<=) t0 f1 f2 = t0 `seq` case (f1, f2) of |

646 | + (Nil, Nil) -> Cons t0 Nil |

647 | + (Nil, Skip f2') -> Cons t0 f2' |

648 | + (Skip f1', Nil) -> Cons t0 f1' |

649 | + (Nil, Cons t2 f2') -> Skip (carry1 (<=) (t0 `cat` t2) f2') |

650 | + (Cons t1 f1', Nil) -> Skip (carry1 (<=) (t0 `cat` t1) f1') |

651 | + (Skip f1', Skip f2') -> Cons t0 (merge (<=) f1' f2') |

652 | + (Skip f1', Cons t2 f2') -> Skip (carry (<=) (t0 `cat` t2) f1' f2') |

653 | + (Cons t1 f1', Skip f2') -> Skip (carry (<=) (t0 `cat` t1) f1' f2') |

654 | + (Cons t1 f1', Cons t2 f2') |

655 | + -> Cons t0 (carry (<=) (t1 `cat` t2) f1' f2') |

656 | + where cat = joinBin (<=) |

657 | + |

658 | +-- | Merges a binomial tree into a binomial forest. If we are thinking |

659 | +-- of the trees in the binomial forest as binary digits, this corresponds |

660 | +-- to adding a power of 2. This costs amortized /O(1)/ time. |

661 | +carry1 :: (e -> e -> Bool) -> BinomTree e rk -> BinomForest e rk -> BinomForest e rk |

662 | +carry1 (<=) t f = t `seq` case f of |

663 | + Nil -> Cons t Nil |

664 | + Skip f -> Cons t f |

665 | + Cons t' f' -> Skip (carry1 (<=) (t `cat` t') f') |

666 | + where cat = joinBin (<=) |

667 | + |

668 | +-- | The carrying operation: takes two binomial heaps of the same rank @k@ |

669 | +-- and returns one of rank @k+1@. Takes /O(1)/ time. |

670 | +joinBin :: (e -> e -> Bool) -> BinomTree e rk -> BinomTree e rk -> BinomTree' e rk |

671 | +joinBin (<=) t1@(BinomTree x1 ts1) t2@(BinomTree x2 ts2) |

672 | + | x1 <= x2 = BinomTree x1 (Succ t2 ts1) |

673 | + | otherwise = BinomTree x2 (Succ t1 ts2) |

674 | + |

675 | +-- folding |

676 | + |

677 | +-- | /O(n)/. Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue, |

678 | +-- as in 'fmap'. If it is not, the result is undefined. |

679 | +mapMonotonic :: (a -> b) -> MinQueue a -> MinQueue b |

680 | +mapMonotonic = fmap |

681 | + |

682 | +-- | /O(n)/. Assumes that the function it is given is monotonic, in some sense, and performs the 'traverse' operation. |

683 | +-- If the function is not monotonic, the result is undefined. |

684 | +traverseMonotonic :: Applicative f => (a -> f b) -> MinQueue a -> f (MinQueue b) |

685 | +traverseMonotonic = traverse |

686 | + |

687 | +instance Functor MinQueue where |

688 | + fmap _ Empty = Empty |

689 | + fmap f (MinQueue n x forest) = MinQueue n (f x) (mapForest f (const ()) forest) |

690 | + |

691 | +mapForest :: (a -> b) -> (rk -> rk') -> BinomForest a rk -> BinomForest b rk' |

692 | +mapForest f fCh forest = case forest of |

693 | + Nil -> Nil |

694 | + Skip forest' |

695 | + -> Skip (fF' forest') |

696 | + Cons t forest' |

697 | + -> Cons (fT t) (fF' forest') |

698 | + where fT (BinomTree x ts) = BinomTree (f x) (fCh ts) |

699 | + fCh' (Succ t ts) = Succ (fT t) (fCh ts) |

700 | + fF' = mapForest f fCh' |

701 | + |

702 | +instance Foldable MinQueue where |

703 | + foldr _ n Empty = n |

704 | + foldr c n (MinQueue _ x f) = x `c` foldrUnord c n (const id) f |

705 | + foldMap _ Empty = mempty |

706 | + foldMap f (MinQueue _ x forest) = f x `mappend` foldMap0 mappend mempty f forest |

707 | + |

708 | +-- | The initial level of 'foldMap'. Avoids unnecessary @'mappend' 'mempty'@ computations. |

709 | +foldMap0 :: (m -> m -> m) -> m -> (a -> m) -> BinomHeap a -> m |

710 | +foldMap0 (><) zero f forest = case forest of |

711 | + Nil -> zero |

712 | + Skip forest' |

713 | + -> fF' forest' |

714 | + Cons (BinomTree x _) forest' |

715 | + -> f x >< fF' forest' |

716 | + where fF' = foldMapUnord (><) zero f (\ (Succ (BinomTree x _) _) -> f x) |

717 | + |

718 | +-- | A recursive implementation of 'foldMap' capable of working up to trees of arbitrary rank. |

719 | +-- Does not respect ordering of the elements. |

720 | +foldMapUnord :: (m -> m -> m) -> m -> (a -> m) -> (rk -> m) -> BinomForest a rk -> m |

721 | +foldMapUnord (><) zero f fCh forest = case forest of |

722 | + Nil -> zero |

723 | + Skip forest' -> fF' forest' |

724 | + Cons t forest' -> fT t >< fF' forest' |

725 | + where fT (BinomTree x ts) = f x >< fCh ts |

726 | + fCh' (Succ t tss) = fT t >< fCh tss |

727 | + fF' = foldMapUnord (><) zero f fCh' |

728 | + |

729 | +-- | 'foldr' implementation on the binomial forest. Does not respect ordering of the elements. |

730 | +foldrUnord :: (a -> b -> b) -> b -> (rk -> b -> b) -> BinomForest a rk -> b |

731 | +foldrUnord c n cCh forest = case forest of |

732 | + Nil -> n |

733 | + Skip f' -> cF' f' |

734 | + Cons t f' -> t `cT` cF' f' |

735 | + where cT (BinomTree x ts) = c x . cCh ts |

736 | + cCh' (Succ t tss) = cT t . cCh tss |

737 | + cF' = foldrUnord c n cCh' |

738 | + |

739 | +instance Traversable MinQueue where |

740 | + traverse _ Empty = pure Empty |

741 | + traverse f (MinQueue n x forest) |

742 | + = MinQueue n <$> f x <*> traverseBin f (const (pure ())) forest |

743 | + |

744 | +traverseBin :: Applicative f => (a -> f b) -> (rk -> f rk') -> BinomForest a rk -> f (BinomForest b rk') |

745 | +traverseBin f fCh forest = case forest of |

746 | + Nil -> pure Nil |

747 | + Skip forest' |

748 | + -> Skip <$> fF' forest' |

749 | + Cons t forest' |

750 | + -> Cons <$> fT t <*> fF' forest' |

751 | + where fF' = traverseBin f fCh' |

752 | + fT (BinomTree x ts) = BinomTree <$> f x <*> fCh ts |

753 | + fCh' (Succ t tss) = Succ <$> fT t <*> fCh tss |

754 | + |

755 | +{-# INLINE toAscList #-} |

756 | +-- | /O(n log n)/. Extracts the elements of the priority queue in ascending order. |

757 | +toAscList :: Ord a => MinQueue a -> [a] |

758 | +#ifdef __GLASGOW_HASKELL__ |

759 | +toAscList q = build (\ c nil -> foldrQueue c nil q) |

760 | +#else |

761 | +toAscList = foldrQueue (:) [] |

762 | +#endif |

763 | + |

764 | +{-# INLINE toList #-} |

765 | +-- | /O(n)/. Returns the elements of the priority queue in no particular order. |

766 | +toList :: MinQueue a -> [a] |

767 | +#ifdef __GLASGOW_HASKELL__ |

768 | +toList q = build (\ c nil -> foldr c nil q) |

769 | +#else |

770 | +toList = foldr (:) [] |

771 | +#endif |

772 | + |

773 | +-- | /O(n log n)/. Performs a right-fold on the elements of a priority queue in ascending order. |

774 | +foldrQueue :: Ord a => (a -> b -> b) -> b -> MinQueue a -> b |

775 | +foldrQueue c n (MinQueue _ x f) = x `c` foldrOrd (<=) c n f |

776 | +foldrQueue _ n _ = n |

777 | + |

778 | +-- | /O(n log n)/. Performs a left-fold on the elements of a priority queue in ascending order. |

779 | +foldlQueue :: Ord a => (b -> a -> b) -> b -> MinQueue a -> b |

780 | +foldlQueue f z (MinQueue _ x forest) = foldlOrd (<=) f (z `f` x) forest |

781 | +foldlQueue _ z _ = z |

782 | + |

783 | +-- | Right fold on a binomial forest. Respects order. |

784 | +foldrOrd :: (a -> a -> Bool) -> (a -> b -> b) -> b -> BinomHeap a -> b |

785 | +foldrOrd (<=) c n = foldQ0 where |

786 | + foldQ0 = foldQ1 . extractBin (<=) |

787 | + foldQ1 NoExtract = n |

788 | + foldQ1 (YesExtract x _ f) |

789 | + = x `c` foldQ0 f |

790 | + |

791 | +-- | Left fold on a binomial forest. Respects order. |

792 | +foldlOrd :: (a -> a -> Bool) -> (b -> a -> b) -> b -> BinomHeap a -> b |

793 | +foldlOrd (<=) f z = foldlQ0 z where |

794 | + foldlQ0 z = foldlQ1 z . extractBin (<=) |

795 | + foldlQ1 z NoExtract = z |

796 | + foldlQ1 z (YesExtract x _ f') |

797 | + = foldlQ0 (z `f` x) f' |

798 | + |

799 | + |

800 | +{-# INLINE fromAscList #-} |

801 | +-- | /O(n)/. Constructs a priority queue from an ascending list. /Warning/: Does not check the precondition. |

802 | +fromAscList :: [a] -> MinQueue a |

803 | +fromAscList = foldr insertMinQ Empty |

804 | + |

805 | +insertMinQ :: a -> MinQueue a -> MinQueue a |

806 | +insertMinQ x Empty = singleton x |

807 | +insertMinQ x (MinQueue n x' f) = MinQueue (n+1) x (insertMin (tip x') f) |

808 | + |

809 | +-- | @insertMin t f@ assumes that the root of @t@ compares as less than |

810 | +-- every other root in @f@, and merges accordingly. |

811 | +insertMin :: BinomTree e rk -> BinomForest e rk -> BinomForest e rk |

812 | +insertMin t Nil = Cons t Nil |

813 | +insertMin t (Skip f) = Cons t f |

814 | +insertMin (BinomTree x ts) (Cons t' f) = Skip (insertMin (BinomTree x (Succ t' ts)) f) |

815 | + |

816 | +{-# INLINE fromList #-} |

817 | +-- | /O(n log n)/. Constructs a priority queue from an unordered list. |

818 | +fromList :: Ord a => [a] -> MinQueue a |

819 | +fromList = foldr insert Empty |

820 | hunk ./containers.cabal 36 |

821 | Data.Graph |

822 | Data.Sequence |

823 | Data.Tree |

824 | + Data.PQueue |

825 | + Data.PQueue.Min |

826 | + Data.PQueue.Max |

827 | } |

828 | if impl(ghc) { |

829 | extensions: DeriveDataTypeable, MagicHash, Rank2Types |

830 | } |

831 | |

832 | Context: |

833 | |

834 | [Tweak layout to work with the alternative layout rule |

835 | Ian Lynagh <igloo@earth.li>**20091129154519] |

836 | [Disable building Data.Sequence (and dependents) for nhc98. |

837 | Malcolm.Wallace@cs.york.ac.uk**20091124025653 |

838 | There is some subtlety of polymorphically recursive datatypes and |

839 | type-class defaulting that nhc98's type system barfs over. |

840 | ] |

841 | [Fix another instance of non-ghc breakage. |

842 | Malcolm.Wallace@cs.york.ac.uk**20091123092637] |

843 | [Add #ifdef around ghc-only (<$) as member of Functor class. |

844 | Malcolm.Wallace@cs.york.ac.uk**20091123085155] |

845 | [Fix broken code in non-GHC branch of an ifdef. |

846 | Malcolm.Wallace@cs.york.ac.uk**20091123084824] |

847 | [doc bugfix: correct description of index argument |

848 | Ross Paterson <ross@soi.city.ac.uk>**20091028105532 |

849 | Ignore-this: 9790e7bf422c4cb528722c03cfa4fed9 |

850 | |

851 | As noted by iaefai on the libraries list. |

852 | |

853 | Please merge to STABLE. |

854 | ] |

855 | [Bump version to 0.3.0.0 |

856 | Ian Lynagh <igloo@earth.li>**20090920141847] |

857 | [update base dependency |

858 | Ross Paterson <ross@soi.city.ac.uk>**20090916073125 |

859 | Ignore-this: ad382ffc6c6a18c15364e6c072f19edb |

860 | |

861 | The package uses mkNoRepType and Data.Functor, which were not in the |

862 | stable branch of base-4. |

863 | ] |

864 | [add fast version of <$ for Seq |

865 | Ross Paterson <ross@soi.city.ac.uk>**20090916072812 |

866 | Ignore-this: 5a39a7d31d39760ed589790b1118d240 |

867 | ] |

868 | [new methods for Data.Sequence (proposal #3271) |

869 | Ross Paterson <ross@soi.city.ac.uk>**20090915173324 |

870 | Ignore-this: cf17bedd709a6ab3448fd718dcdf62e7 |

871 | |

872 | Adds a lot of new methods to Data.Sequence, mostly paralleling those |

873 | in Data.List. Several of these are significantly faster than versions |

874 | implemented with the previous public interface. In particular, replicate |

875 | takes O(log n) time and space instead of O(n). |

876 | (by Louis Wasserman) |

877 | ] |

878 | [Fix "Cabal check" warnings |

879 | Ian Lynagh <igloo@earth.li>**20090811215900] |

880 | [TAG 2009-06-25 |

881 | Ian Lynagh <igloo@earth.li>**20090625160202] |

882 | Patch bundle hash: |

883 | 7b157605a4dbb34b789009b9de1873b5ae0a190f |