diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,11 @@ +# Changelog + +`treap` uses [PVP Versioning][1]. +The changelog is available [on GitHub][2]. + +## 0.0.0.0 — Apr 29, 2019 + +* Initially created. + +[1]: https://pvp.haskell.org +[2]: https://github.com/chshersh/treap/releases diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,373 @@ +Mozilla Public License Version 2.0 +================================== + +1. Definitions +-------------- + +1.1. "Contributor" + means each individual or legal entity that creates, contributes to + the creation of, or owns Covered Software. + +1.2. "Contributor Version" + means the combination of the Contributions of others (if any) used + by a Contributor and that particular Contributor's Contribution. + +1.3. "Contribution" + means Covered Software of a particular Contributor. + +1.4. "Covered Software" + means Source Code Form to which the initial Contributor has attached + the notice in Exhibit A, the Executable Form of such Source Code + Form, and Modifications of such Source Code Form, in each case + including portions thereof. + +1.5. "Incompatible With Secondary Licenses" + means + + (a) that the initial Contributor has attached the notice described + in Exhibit B to the Covered Software; or + + (b) that the Covered Software was made available under the terms of + version 1.1 or earlier of the License, but not also under the + terms of a Secondary License. + +1.6. "Executable Form" + means any form of the work other than Source Code Form. + +1.7. "Larger Work" + means a work that combines Covered Software with other material, in + a separate file or files, that is not Covered Software. + +1.8. "License" + means this document. + +1.9. "Licensable" + means having the right to grant, to the maximum extent possible, + whether at the time of the initial grant or subsequently, any and + all of the rights conveyed by this License. + +1.10. "Modifications" + means any of the following: + + (a) any file in Source Code Form that results from an addition to, + deletion from, or modification of the contents of Covered + Software; or + + (b) any new file in Source Code Form that contains any Covered + Software. + +1.11. "Patent Claims" of a Contributor + means any patent claim(s), including without limitation, method, + process, and apparatus claims, in any patent Licensable by such + Contributor that would be infringed, but for the grant of the + License, by the making, using, selling, offering for sale, having + made, import, or transfer of either its Contributions or its + Contributor Version. + +1.12. "Secondary License" + means either the GNU General Public License, Version 2.0, the GNU + Lesser General Public License, Version 2.1, the GNU Affero General + Public License, Version 3.0, or any later versions of those + licenses. + +1.13. "Source Code Form" + means the form of the work preferred for making modifications. + +1.14. "You" (or "Your") + means an individual or a legal entity exercising rights under this + License. For legal entities, "You" includes any entity that + controls, is controlled by, or is under common control with You. For + purposes of this definition, "control" means (a) the power, direct + or indirect, to cause the direction or management of such entity, + whether by contract or otherwise, or (b) ownership of more than + fifty percent (50%) of the outstanding shares or beneficial + ownership of such entity. + +2. License Grants and Conditions +-------------------------------- + +2.1. Grants + +Each Contributor hereby grants You a world-wide, royalty-free, +non-exclusive license: + +(a) under intellectual property rights (other than patent or trademark) + Licensable by such Contributor to use, reproduce, make available, + modify, display, perform, distribute, and otherwise exploit its + Contributions, either on an unmodified basis, with Modifications, or + as part of a Larger Work; and + +(b) under Patent Claims of such Contributor to make, use, sell, offer + for sale, have made, import, and otherwise transfer either its + Contributions or its Contributor Version. + +2.2. Effective Date + +The licenses granted in Section 2.1 with respect to any Contribution +become effective for each Contribution on the date the Contributor first +distributes such Contribution. + +2.3. Limitations on Grant Scope + +The licenses granted in this Section 2 are the only rights granted under +this License. No additional rights or licenses will be implied from the +distribution or licensing of Covered Software under this License. +Notwithstanding Section 2.1(b) above, no patent license is granted by a +Contributor: + +(a) for any code that a Contributor has removed from Covered Software; + or + +(b) for infringements caused by: (i) Your and any other third party's + modifications of Covered Software, or (ii) the combination of its + Contributions with other software (except as part of its Contributor + Version); or + +(c) under Patent Claims infringed by Covered Software in the absence of + its Contributions. + +This License does not grant any rights in the trademarks, service marks, +or logos of any Contributor (except as may be necessary to comply with +the notice requirements in Section 3.4). + +2.4. Subsequent Licenses + +No Contributor makes additional grants as a result of Your choice to +distribute the Covered Software under a subsequent version of this +License (see Section 10.2) or under the terms of a Secondary License (if +permitted under the terms of Section 3.3). + +2.5. Representation + +Each Contributor represents that the Contributor believes its +Contributions are its original creation(s) or it has sufficient rights +to grant the rights to its Contributions conveyed by this License. + +2.6. Fair Use + +This License is not intended to limit any rights You have under +applicable copyright doctrines of fair use, fair dealing, or other +equivalents. + +2.7. Conditions + +Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted +in Section 2.1. + +3. Responsibilities +------------------- + +3.1. Distribution of Source Form + +All distribution of Covered Software in Source Code Form, including any +Modifications that You create or to which You contribute, must be under +the terms of this License. You must inform recipients that the Source +Code Form of the Covered Software is governed by the terms of this +License, and how they can obtain a copy of this License. You may not +attempt to alter or restrict the recipients' rights in the Source Code +Form. + +3.2. Distribution of Executable Form + +If You distribute Covered Software in Executable Form then: + +(a) such Covered Software must also be made available in Source Code + Form, as described in Section 3.1, and You must inform recipients of + the Executable Form how they can obtain a copy of such Source Code + Form by reasonable means in a timely manner, at a charge no more + than the cost of distribution to the recipient; and + +(b) You may distribute such Executable Form under the terms of this + License, or sublicense it under different terms, provided that the + license for the Executable Form does not attempt to limit or alter + the recipients' rights in the Source Code Form under this License. + +3.3. Distribution of a Larger Work + +You may create and distribute a Larger Work under terms of Your choice, +provided that You also comply with the requirements of this License for +the Covered Software. If the Larger Work is a combination of Covered +Software with a work governed by one or more Secondary Licenses, and the +Covered Software is not Incompatible With Secondary Licenses, this +License permits You to additionally distribute such Covered Software +under the terms of such Secondary License(s), so that the recipient of +the Larger Work may, at their option, further distribute the Covered +Software under the terms of either this License or such Secondary +License(s). + +3.4. Notices + +You may not remove or alter the substance of any license notices +(including copyright notices, patent notices, disclaimers of warranty, +or limitations of liability) contained within the Source Code Form of +the Covered Software, except that You may alter any license notices to +the extent required to remedy known factual inaccuracies. + +3.5. Application of Additional Terms + +You may choose to offer, and to charge a fee for, warranty, support, +indemnity or liability obligations to one or more recipients of Covered +Software. However, You may do so only on Your own behalf, and not on +behalf of any Contributor. You must make it absolutely clear that any +such warranty, support, indemnity, or liability obligation is offered by +You alone, and You hereby agree to indemnify every Contributor for any +liability incurred by such Contributor as a result of warranty, support, +indemnity or liability terms You offer. You may include additional +disclaimers of warranty and limitations of liability specific to any +jurisdiction. + +4. Inability to Comply Due to Statute or Regulation +--------------------------------------------------- + +If it is impossible for You to comply with any of the terms of this +License with respect to some or all of the Covered Software due to +statute, judicial order, or regulation then You must: (a) comply with +the terms of this License to the maximum extent possible; and (b) +describe the limitations and the code they affect. Such description must +be placed in a text file included with all distributions of the Covered +Software under this License. Except to the extent prohibited by statute +or regulation, such description must be sufficiently detailed for a +recipient of ordinary skill to be able to understand it. + +5. Termination +-------------- + +5.1. The rights granted under this License will terminate automatically +if You fail to comply with any of its terms. However, if You become +compliant, then the rights granted under this License from a particular +Contributor are reinstated (a) provisionally, unless and until such +Contributor explicitly and finally terminates Your grants, and (b) on an +ongoing basis, if such Contributor fails to notify You of the +non-compliance by some reasonable means prior to 60 days after You have +come back into compliance. Moreover, Your grants from a particular +Contributor are reinstated on an ongoing basis if such Contributor +notifies You of the non-compliance by some reasonable means, this is the +first time You have received notice of non-compliance with this License +from such Contributor, and You become compliant prior to 30 days after +Your receipt of the notice. + +5.2. If You initiate litigation against any entity by asserting a patent +infringement claim (excluding declaratory judgment actions, +counter-claims, and cross-claims) alleging that a Contributor Version +directly or indirectly infringes any patent, then the rights granted to +You by any and all Contributors for the Covered Software under Section +2.1 of this License shall terminate. + +5.3. In the event of termination under Sections 5.1 or 5.2 above, all +end user license agreements (excluding distributors and resellers) which +have been validly granted by You or Your distributors under this License +prior to termination shall survive termination. + +************************************************************************ +* * +* 6. Disclaimer of Warranty * +* ------------------------- * +* * +* Covered Software is provided under this License on an "as is" * +* basis, without warranty of any kind, either expressed, implied, or * +* statutory, including, without limitation, warranties that the * +* Covered Software is free of defects, merchantable, fit for a * +* particular purpose or non-infringing. The entire risk as to the * +* quality and performance of the Covered Software is with You. * +* Should any Covered Software prove defective in any respect, You * +* (not any Contributor) assume the cost of any necessary servicing, * +* repair, or correction. This disclaimer of warranty constitutes an * +* essential part of this License. No use of any Covered Software is * +* authorized under this License except under this disclaimer. * +* * +************************************************************************ + +************************************************************************ +* * +* 7. Limitation of Liability * +* -------------------------- * +* * +* Under no circumstances and under no legal theory, whether tort * +* (including negligence), contract, or otherwise, shall any * +* Contributor, or anyone who distributes Covered Software as * +* permitted above, be liable to You for any direct, indirect, * +* special, incidental, or consequential damages of any character * +* including, without limitation, damages for lost profits, loss of * +* goodwill, work stoppage, computer failure or malfunction, or any * +* and all other commercial damages or losses, even if such party * +* shall have been informed of the possibility of such damages. This * +* limitation of liability shall not apply to liability for death or * +* personal injury resulting from such party's negligence to the * +* extent applicable law prohibits such limitation. Some * +* jurisdictions do not allow the exclusion or limitation of * +* incidental or consequential damages, so this exclusion and * +* limitation may not apply to You. * +* * +************************************************************************ + +8. Litigation +------------- + +Any litigation relating to this License may be brought only in the +courts of a jurisdiction where the defendant maintains its principal +place of business and such litigation shall be governed by laws of that +jurisdiction, without reference to its conflict-of-law provisions. +Nothing in this Section shall prevent a party's ability to bring +cross-claims or counter-claims. + +9. Miscellaneous +---------------- + +This License represents the complete agreement concerning the subject +matter hereof. If any provision of this License is held to be +unenforceable, such provision shall be reformed only to the extent +necessary to make it enforceable. Any law or regulation which provides +that the language of a contract shall be construed against the drafter +shall not be used to construe this License against a Contributor. + +10. Versions of the License +--------------------------- + +10.1. New Versions + +Mozilla Foundation is the license steward. Except as provided in Section +10.3, no one other than the license steward has the right to modify or +publish new versions of this License. Each version will be given a +distinguishing version number. + +10.2. Effect of New Versions + +You may distribute the Covered Software under the terms of the version +of the License under which You originally received the Covered Software, +or under the terms of any subsequent version published by the license +steward. + +10.3. Modified Versions + +If you create software not governed by this License, and you want to +create a new license for such software, you may create and use a +modified version of this License if you rename the license and remove +any references to the name of the license steward (except to note that +such modified license differs from this License). + +10.4. Distributing Source Code Form that is Incompatible With Secondary +Licenses + +If You choose to distribute Source Code Form that is Incompatible With +Secondary Licenses under the terms of this version of the License, the +notice described in Exhibit B of this License must be attached. + +Exhibit A - Source Code Form License Notice +------------------------------------------- + + This Source Code Form is subject to the terms of the Mozilla Public + License, v. 2.0. If a copy of the MPL was not distributed with this + file, You can obtain one at http://mozilla.org/MPL/2.0/. + +If it is not possible or desirable to put the notice in a particular +file, then You may include the notice in a location (such as a LICENSE +file in a relevant directory) where a recipient would be likely to look +for such a notice. + +You may add additional accurate notices of copyright ownership. + +Exhibit B - "Incompatible With Secondary Licenses" Notice +--------------------------------------------------------- + + This Source Code Form is "Incompatible With Secondary Licenses", as + defined by the Mozilla Public License, v. 2.0. diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,73 @@ +# treap + +![Treap: tree logo](https://user-images.githubusercontent.com/4276606/56883228-9f32f180-6a98-11e9-9554-13735ff1ed30.png) +[![Hackage](https://img.shields.io/hackage/v/treap.svg)](https://hackage.haskell.org/package/treap) +[![Build status](https://secure.travis-ci.org/chshersh/treap.svg)](https://travis-ci.org/chshersh/treap) +[![MPL-2.0 license](https://img.shields.io/badge/license-MPL--2.0-blue.svg)](LICENSE) + +Efficient implementation of the implicit treap data structure. + +## What does this package provide? + +This package implements a tree-like data structure called _implicit treap_. This +data structure implements interface similar to random-access arrays, but with +fast (logarithmic time complexity) +`insert`/`delete`/`split`/`merge`/`take`/`drop`/`rotate` operations. In addition, +_treap_ allows you to specify and measure values of any monoids on a segment, +like a sum of elements or minimal element on some contiguous part of the array. + +## When to use this package? + +Use this package when you want the following operations to be fast: + +1. Access elements by index. +2. Insert elements by index. +3. Delete elements by index. +4. Calculate monoidal operation (like sum, product, min, etc.) of all elements + between two indices. +5. Call slicing operations like `take` or `drop` or `split`. + +Below you can find the table of time complexity for all operations (where `n` is +the size of the treap): + +| Operation | Time complexity | Description | +|-----------|-----------------|--------------------------------------| +| `size` | `O(1)` | Get number of elements in the treap | +| `at` | `O(log n)` | Access by index | +| `insert` | `O(log n)` | Insert by index | +| `delete` | `O(log n)` | Delete by index | +| `query` | `O(log n)` | Measure monoid on the segment | +| `splitAt` | `O(log n)` | Split treap by index into two treaps | +| `merge` | `O(log n)` | Merge two treaps into a single one | +| `take` | `O(log n)` | Take first `i` elements of the treap | +| `drop` | `O(log n)` | Drop first `i` elements of the treap | +| `rotate` | `O(log n)` | Put first `i` elements to the end | + +The package also comes with nice pretty-printing! + +```haskell +ghci> t = fromList [1..5] :: RTreap (Sum Int) Int +ghci> prettyPrint t + 5,15:2 + ╱╲ + ╱ ╲ + ╱ ╲ + ╱ ╲ +1,1:1 3,12:4 + ╱╲ + ╱ ╲ + ╱ ╲ + 1,3:3 1,5:5 + +``` + +## Alternatives + +If you don't need to calculate monoidal operations, you may alternatively use +[`Seq`](https://hackage.haskell.org/package/containers-0.6.0.1/docs/Data-Sequence.html#t:Seq) +from the `containers` package as it provides more extended interface but doesn't +allow to measure monoidal values on segments. + +## Acknowledgement + +Icons made by [Freepik](http://www.freepik.com) from [www.flaticon.com](https://www.flaticon.com/) is licensed by [CC 3.0 BY](http://creativecommons.org/licenses/by/3.0/). diff --git a/src/Treap.hs b/src/Treap.hs new file mode 100644 --- /dev/null +++ b/src/Treap.hs @@ -0,0 +1,94 @@ +{- | + +== General description + +Package @treap@ implements a tree-like data structure called /implicit treap/. This +data structure implements interface similar to random-access arrays, but with +fast (logarithmic time complexity) +@'insert'@ \/ @'delete'@ \/ @'Treap.splitAt'@ \/ @'merge'@ \/ @'Treap.take'@ \/ @'Treap.drop'@ \/ @'rotate'@ operations. + +In addition, 'Treap.Pure.Treap' and 'RTreap' allow you to specify and measure +values of any monoids on a segment, like a sum of elements or minimal element on +some contiguous part of the array. + +== Package structure + +This package contains the following modules: + +* __"Treap.Measured":__ typeclass 'Measured' that allows telling how to measure + tree values as monoids. +* __"Treap.Pure":__ the 'Treap.Pure.Treap' data type and functions – pure + implementation of the implicit treap data structure. +* __"Treap.Rand":__ the 'RTreap' data type and functions – pure implementation + of the implicit treap which uses a pure random generator to generate + priorities automatically. +* __"Treap.Pretty":__ pretty-printer for the treap. + +Module __"Treap"__ reexports only __"Treap.Measured"__ and __"Treap.Rand"__ modules. + +== Usage example + +Consider the following example of creating 'RTreap' from list @[1..5]@ where +each element stores the sum of elements in its subtree: + +>>> import Data.Monoid (Sum (..)) +>>> import GHC.Exts (IsList (..)) +>>> t = fromList [1..5] :: RTreap (Sum Int) Int +>>> prettyPrint t + 5,15:2 + ╱╲ + ╱ ╲ + ╱ ╲ + ╱ ╲ +1,1:1 3,12:4 + ╱╲ + ╱ ╲ + ╱ ╲ + 1,3:3 1,5:5 + +Each node shows: + +1. The overall size of the tree +2. The total monoidal measure of the tree +3. The element itself after @:@ + +You can try to play with this tree now! + +>>> at 0 t +Just 1 +>>> at 10 t +Nothing +>>> query 1 4 t +Sum {getSum = 9} + +>>> prettyPrint $ Treap.take 2 t + 2,3:2 + ╱ +1,1:1 + +>>> prettyPrint $ Treap.drop 2 t + 3,12:4 + ╱╲ + ╱ ╲ + ╱ ╲ +1,3:3 1,5:5 + +>>> prettyPrint $ rotate 2 t + 5,15:2 + ╱ + 4,13:4 + ╱╲ + ╱ ╲ + ╱ ╲ +1,3:3 2,6:5 + ╲ + 1,1:1 + +-} + +module Treap + ( module Treap + ) where + +import Treap.Measured as Treap +import Treap.Rand as Treap diff --git a/src/Treap/Measured.hs b/src/Treap/Measured.hs new file mode 100644 --- /dev/null +++ b/src/Treap/Measured.hs @@ -0,0 +1,73 @@ +{-# LANGUAGE FlexibleInstances #-} + +{- | Typeclass that tells how to measure different values as 'Monoid'. +-} + +module Treap.Measured + ( Measured (..) + ) where + +import Data.Functor.Identity (Identity (..)) +import Data.Monoid (All (..), Any (..), Dual (..), Endo (..), First (..), Last (..), Product (..), + Sum (..)) +import Data.Semigroup (Max (..), Min (..)) + + +{- | This typeclass allows to specify how to convert value of type @a@ into +monoidal value of type @m@. +-} +class Monoid m => Measured m a where + measure :: a -> m + +-- | Measure every 'Monoid' as itself. +instance Monoid a => Measured (Identity a) a where + measure = Identity + {-# INLINE measure #-} + +-- | Measure every 'Monoid' as its dual. +instance Monoid a => Measured (Dual a) a where + measure = Dual + {-# INLINE measure #-} + +-- | Measure every endomorphic function with compostion. +instance Measured (Endo a) (a -> a) where + measure = Endo + {-# INLINE measure #-} + +-- | Measure every numeric value with addition. +instance Num a => Measured (Sum a) a where + measure = Sum + {-# INLINE measure #-} + +-- | Measure every numeric value with multiplication. +instance Num a => Measured (Product a) a where + measure = Product + {-# INLINE measure #-} + +-- | Measure every comparable value with minimum. +instance (Ord a, Bounded a) => Measured (Min a) a where + measure = Min + {-# INLINE measure #-} + +-- | Measure every comparable value with maximum. +instance (Ord a, Bounded a) => Measured (Max a) a where + measure = Max + {-# INLINE measure #-} + +-- | Measure every value as the 'First' monoid. +instance Measured (First a) a where + measure = First . Just + {-# INLINE measure #-} + +-- | Measure every value as the 'Last' monoid. +instance Measured (Last a) a where + measure = Last . Just + {-# INLINE measure #-} + +-- | Measure boolean value with '&&'. +instance Measured All Bool where + measure = All + +-- | Measure boolean value with '||'. +instance Measured Any Bool where + measure = Any diff --git a/src/Treap/Pretty.hs b/src/Treap/Pretty.hs new file mode 100644 --- /dev/null +++ b/src/Treap/Pretty.hs @@ -0,0 +1,182 @@ +-- | Very nice 'Treap' visualisation. + +module Treap.Pretty + ( pretty + , prettyPrint + , prettyWith + , compactShowNode + + -- * Internal implementation details + , BinTree (..) + , showTree + , middleLabelPos + , branchLines + ) where + +import Data.Char (isSpace) +import Data.Coerce (Coercible, coerce) +import Data.List (dropWhileEnd, intercalate) + +import Treap.Pure (Priority (..), Size (..), Treap (..)) + + +{- | Show 'Treap' in a pretty way using 'compactShowNode' function. +-} +pretty :: forall m a . (Coercible m a, Show a) => Treap m a -> String +pretty = prettyWith compactShowNode + +-- | Call 'pretty' function and output the result directly to @stdout@. +prettyPrint :: forall m a . (Coercible m a, Show a) => Treap m a -> IO () +prettyPrint = putStrLn . pretty + +{- | Show 'Treap' node in a format: + +@ +\,\:a +@ +-} +compactShowNode + :: forall m a . (Coercible m a, Show a) + => Size + -> Priority + -> m + -> a + -> String +compactShowNode (Size sz) _ m a = + show sz ++ "," ++ show (coerce @m @a m) ++ ":" ++ show a + +-- | Show 'Treap' in a nice way using given function to display node. +prettyWith + :: forall m a . + (Size -> Priority -> m -> a -> String) + -> Treap m a + -> String +prettyWith display = showTree . toBinTree + where + toBinTree :: Treap m a -> BinTree + toBinTree Empty = Leaf + toBinTree (Node sz p m a left right) = Branch (display sz p m a) (toBinTree left) (toBinTree right) + +-- | Intermidiate structure to help string conversion. +data BinTree + = Leaf + | Branch String BinTree BinTree + +-- | Hardcore function responsible for pretty showing of the 'BinTree' data type. +showTree :: BinTree -> String +showTree Leaf = "" +showTree (Branch label left right) = case (left, right) of + (Leaf, Leaf) -> label + + (_, Leaf) -> toLines $ + [ spaces rootShiftOnlyLeft ++ label + , spaces branchShiftOnlyLeft ++ "╱" + ] ++ map (spaces leftShiftOnlyLeft ++) leftLines + + (Leaf, _) -> toLines $ + [ spaces rootShiftOnlyRight ++ label + , spaces branchShiftOnlyRight ++ "╲" + ] ++ map (spaces rightShiftOnlyRight ++) rightLines + + (_, _) -> toLines $ + [ spaces rootOffset ++ label + ] + ++ map (spaces rootOffset ++ ) (branchLines branchHeight) + ++ map (spaces childrenOffset ++) (zipChildren leftLines rightLines) + where + leftStr, rightStr :: String + leftStr = showTree left + rightStr = showTree right + + leftLines :: [String] + leftLines = lines leftStr + rightLines = lines rightStr + + rootLabelMiddle, leftLabelMiddle, rightLabelMiddle :: Int + rootLabelMiddle = middleLabelPos label + leftLabelMiddle = middleLabelPos $ head leftLines + rightLabelMiddle = middleLabelPos $ head rightLines + + -- Case 1: all offsets when node has only left branch + rootShiftOnlyLeft, leftShiftOnlyLeft, branchShiftOnlyLeft :: Int + (rootShiftOnlyLeft, leftShiftOnlyLeft) = case compare rootLabelMiddle leftLabelMiddle of + EQ -> (1, 0) + GT -> (0, rootLabelMiddle - leftLabelMiddle - 1) + LT -> (leftLabelMiddle - rootLabelMiddle + 1, 0) + branchShiftOnlyLeft = rootLabelMiddle + rootShiftOnlyLeft - 1 + + -- Case 2: all offsets when node has only right branch + rootShiftOnlyRight, rightShiftOnlyRight, branchShiftOnlyRight :: Int + (rootShiftOnlyRight, rightShiftOnlyRight) = case compare rootLabelMiddle rightLabelMiddle of + EQ -> (0, 1) + GT -> (0, rootLabelMiddle - rightLabelMiddle + 1) + LT -> (rightLabelMiddle - rootLabelMiddle - 1, 0) + branchShiftOnlyRight = rootLabelMiddle + rootShiftOnlyRight + 1 + + -- Case 3: both + leftWidth, rightOffMiddle, childDistance, branchHeight, rootMustMiddle :: Int + leftWidth = 1 + maximum (map length leftLines) + rightOffMiddle = leftWidth + rightLabelMiddle + childDistance = rightOffMiddle - leftLabelMiddle + branchHeight = childDistance `div` 2 + rootMustMiddle = (leftLabelMiddle + rightOffMiddle) `div` 2 + + rootOffset, childrenOffset :: Int + (rootOffset, childrenOffset) = case compare rootLabelMiddle rootMustMiddle of + EQ -> (0, 0) + LT -> (rootMustMiddle - rootLabelMiddle, 0) + GT -> (0, rootLabelMiddle - rootMustMiddle) + + zipChildren :: [String] -> [String] -> [String] + zipChildren l [] = l + zipChildren [] r = map (spaces leftWidth ++ ) r + zipChildren (x:xs) (y:ys) = + let xLen = length x + newX = x ++ spaces (leftWidth - xLen) + in (newX ++ y) : zipChildren xs ys + +-- | Generates strings containing of @n@ spaces. +spaces :: Int -> String +spaces n = replicate n ' ' + +{- | Calculates position of middle of non-space part of the string. + +>>> s = " abc " +>>> length s +7 +>>> middleLabelPos s +4 +-} +middleLabelPos :: String -> Int +middleLabelPos s = + let (spacePrefix, rest) = span isSpace s + in length spacePrefix + (length (dropWhileEnd isSpace rest) `div` 2) + +-- | Like 'unlines' but doesn't add "\n" to the end. +toLines :: [String] -> String +toLines = intercalate "\n" + +{- | Draws branches of the given height. + +>>> putStrLn $ toLines $ branchLines 1 +╱╲ + +>>> putStrLn $ toLines $ branchLines 2 + ╱╲ +╱ ╲ + +>>> putStrLn $ toLines $ branchLines 3 + ╱╲ + ╱ ╲ +╱ ╲ +-} +branchLines :: Int -> [String] +branchLines n = go 0 + where + go :: Int -> [String] + go i + | i == n = [] + | otherwise = line : go (i + 1) + where + line :: String + line = spaces (n - i - 1) ++ "╱" ++ spaces (2 * i) ++ "╲" diff --git a/src/Treap/Pure.hs b/src/Treap/Pure.hs new file mode 100644 --- /dev/null +++ b/src/Treap/Pure.hs @@ -0,0 +1,368 @@ +{- | Pure efficient implementation of the implicit treap data structure with the +segment tree interface. + +__NOTE:__ Letter \( d \) in the documentation below means depth of the tree. Real +depth depends on the strategy for creating 'Priority'. If the strategy is poor, +the depth can be linear. However, if priorities are generated randomly, expected +depth is \( O(\log \ n) \). +-} + +{-# LANGUAGE DeriveAnyClass #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE TypeFamilies #-} + +module Treap.Pure + ( -- * Data structure + Size (..) + , Priority (..) + , Treap (..) + + -- * Smart constructors + , empty + , one + + -- * Query functions + , size + , sizeInt + , monoid + , at + , query + + -- * Cuts and joins + , splitAt + , merge + , take + , drop + , rotate + + -- * Modification functions + , insert + , delete + + -- * Core internal functions + , recalculate + ) where + +import Prelude hiding (drop, lookup, splitAt, take) + +import Control.DeepSeq (NFData) +import Data.Foldable (foldl') +import Data.Word (Word64) +import GHC.Exts (IsList (..)) +import GHC.Generics (Generic) + +import Treap.Measured (Measured (..)) + +-- $setup +-- >>> import Data.Monoid +-- >>> import Treap.Pretty + +---------------------------------------------------------------------------- +-- Data structure and instances +---------------------------------------------------------------------------- + +{- | Size of the 'Treap' data structure. Guaranteed to be always non-negative. +-} +newtype Size = Size + { unSize :: Int + } deriving stock (Show, Read, Generic) + deriving newtype (Eq, Ord, Num, NFData) + +{- | Priority in the 'Treap' data structure. +-} +newtype Priority = Priority + { unPriority :: Word64 + } deriving stock (Show, Read, Generic) + deriving newtype (Eq, Ord, NFData) + +-- | 'Treap' data structure. +data Treap m a + = Node !Size !Priority !m a !(Treap m a) !(Treap m a) + | Empty + deriving stock (Show, Read, Eq, Generic, Foldable) + deriving anyclass (NFData) + +-- | \( O(1) \). Takes cached value from the root. +instance Monoid m => Measured m (Treap m a) where + measure = monoid + {-# INLINE measure #-} + +-- #if __GLASGOW_HASKELL__ >= 806 +-- -- | Safe 'Functor' instance that performs recalculation of monoidal accumulator. +-- instance (forall b . Measured m b) => Functor (Treap m) where +-- fmap :: forall a b . (a -> b) -> Treap m a -> Treap m b +-- fmap f = go +-- where +-- go :: Treap m a -> Treap m b +-- go Empty = Empty +-- go (Node _ p _ a l r) = recalculate $ new p (f a) (go l) (go r) +-- #endif + +{- | This instance allows to create 'Treap' from the list of triples. If all +priorities are random then the expected performance of the @fromList@ function +is \( O(n\ \log \ n)\). + +__TODO:__ It's possible to implement \( O(n) \) algorithm however. +See issue #15: +-} +instance Measured m a => IsList (Treap m a) where + type Item (Treap m a) = (Priority, a) + + -- TODO: implement O(n) algorithm + fromList :: [(Priority, a)] -> Treap m a + fromList = + foldl' (\t (i, p, a) -> insert i p a t) Empty + . zipWith (\i (p, a) -> (i, p, a)) [0..] + {-# INLINE fromList #-} + + -- TODO: make more efficient + toList :: Treap m a -> [(Priority, a)] + toList Empty = [] + toList (Node _ p _ a l r) = toList l ++ (p, a) : toList r + +---------------------------------------------------------------------------- +-- Smart constructors +---------------------------------------------------------------------------- + +-- | \( O(1) \). Creates empty 'Treap'. +empty :: Treap m a +empty = Empty +{-# INLINE empty #-} + +-- | \( O(1) \). Creates singleton 'Treap'. +one :: Measured m a => Priority -> a -> Treap m a +one p a = Node (Size 1) p (measure a) a Empty Empty +{-# INLINE one #-} + +---------------------------------------------------------------------------- +-- Query functions +---------------------------------------------------------------------------- + +{- | \( O(1) \). Returns the number of the elements in the 'Treap'. Always +non-negative. + +__Properties:__ + +* \( \forall (t\ ::\ \mathrm{Treap}\ m\ a)\ .\ \mathrm{size}\ t \geqslant 0 \) +-} +size :: Treap m a -> Size +size = \case + Empty -> Size 0 + Node s _ _ _ _ _ -> s +{-# INLINE size #-} + +-- | Take size of the 'Treap' as 'Int'. +sizeInt :: Treap m a -> Int +sizeInt = unSize . size +{-# INLINE sizeInt #-} + +-- | \( O(1) \). Returns accumulated value in the root of the tree. +monoid :: Monoid m => Treap m a -> m +monoid = \case + Empty -> mempty + Node _ _ m _ _ _ -> m +{-# INLINE monoid #-} + +-- | \( O(d) \). Lookup a value inside 'Treap' by a given index. +at :: forall m a . Int -> Treap m a -> Maybe a +at i t + | i < 0 = Nothing + | i >= sizeInt t = Nothing + | otherwise = go i t + where + go :: Int -> Treap m a -> Maybe a + go _ Empty = Nothing + go k (Node _ _ _ a l r) = + let lSize = sizeInt l + in case compare k lSize of + EQ -> Just a + LT -> go k l + GT -> go (k - lSize - 1) r + +-- | \( O(d) \). Return value of monoidal accumulator on a segment @[l, r)@. +query :: forall m a . Measured m a => Int -> Int -> Treap m a -> m +query from to t + | to <= from = mempty + | otherwise = + let (l, _) = splitAt to t + (_, m) = splitAt from l + in monoid m + +---------------------------------------------------------------------------- +-- Cuts and joins +---------------------------------------------------------------------------- + +-- | Create new 'Node' and recalculate its values. +new :: Measured m a => Priority -> a -> Treap m a -> Treap m a -> Treap m a +new p a l r = recalculate $ Node 0 p mempty a l r +{-# INLINE new #-} + +{- | \( O(d) \). @splitAt i t@ splits 'Treap' by the given index into two treaps +@(t1, t2)@ such that the following properties hold: + +1. \( \mathrm{size}\ t_1 = i \) +2. \( \mathrm{size}\ t_2 = n - i \) +3. \( \mathrm{merge}\ t_1\ t_2 \equiv t \) + +__Special cases:__ + +1. If \( i \leqslant 0 \) then the result is @('empty', t)@. +2. If \( i \geqslant n \) then the result is @(t, 'empty')@. +-} +splitAt :: forall m a . Measured m a => Int -> Treap m a -> (Treap m a, Treap m a) +splitAt i t + | i <= 0 = (empty, t) + | i >= sizeInt t = (t, empty) + | otherwise = go i t + where + go :: Int -> Treap m a -> (Treap m a, Treap m a) + go k = \case + Empty -> (Empty, Empty) + Node _ p _ a left right -> + let lSize = sizeInt left + in case compare k lSize of + EQ -> (left, new p a Empty right) + LT -> + let (!t1, !newLeft) = go k left + in (t1, new p a newLeft right) + GT -> + let (!newRight, !t2) = go (k - lSize - 1) right + in (new p a left newRight, t2) + +{- | \( O(\max\ d_1\ d_2) \). Merge two 'Treap's into single one. + +>>> pone p a = one (Priority p) a :: Treap (Sum Int) Int +>>> prettyPrint $ merge (merge (pone 1 3) (pone 4 5)) (merge (pone 3 0) (pone 5 9)) + 4,17:9 + ╱ + 3,8:5 + ╱╲ + ╱ ╲ + ╱ ╲ +1,3:3 1,0:0 +-} +merge :: Measured m a => Treap m a -> Treap m a -> Treap m a +merge Empty r = r +merge l Empty = l +merge l@(Node _ p1 _ a1 l1 r1) r@(Node _ p2 _ a2 l2 r2) + | p1 > p2 = recalculate $ new p1 a1 l1 (merge r1 r) + | otherwise = recalculate $ new p2 a2 (merge l l2) r2 + +{- | \( O(d) \). @'take' n t@ returns 'Treap' that contains first @n@ elements of the given +'Treap' @t@. + +__Special cases:__ + +1. If \( i \leqslant 0 \) then the result is 'empty'. +2. If \( i \geqslant n \) then the result is @t@. +-} +take :: forall m a . Measured m a => Int -> Treap m a -> Treap m a +take n t + | n <= 0 = Empty + | n >= sizeInt t = t + | otherwise = go n t + where + go :: Int -> Treap m a -> Treap m a + go _ Empty = Empty + go 0 _ = Empty + go i (Node _ p _ a l r) = + let lSize = sizeInt l + in case compare i lSize of + LT -> go i l + EQ -> l + GT -> new p a l $ go (i - lSize - 1) r + +{- | \( O(d) \). @'drop' n t@ returns 'Treap' without first @n@ elements of the given +'Treap' @t@. + +__Special cases:__ + +1. If \( i \leqslant 0 \) then the result is @t@. +2. If \( i \geqslant n \) then the result is 'empty'. +-} +drop :: forall m a . Measured m a => Int -> Treap m a -> Treap m a +drop n t + | n <= 0 = t + | n >= sizeInt t = Empty + | otherwise = go n t + where + go :: Int -> Treap m a -> Treap m a + go _ Empty = Empty + go 0 tree = tree + go i (Node _ p _ a l r) = + let lSize = sizeInt l + in case compare i lSize of + LT -> new p a (go i l) r + EQ -> new p a Empty r + GT -> go (i - lSize - 1) r + +{- | \( O(d) \). Rotate a 'Treap' to the right by a given number of elements +modulo treap size. In simple words, @'rotate' n t@ takes first @n@ elements of +@t@ and puts them at the end of @t@ in the same order. If the given index is +negative, then this function rotates left. +-} +rotate :: forall m a . Measured m a => Int -> Treap m a -> Treap m a +rotate n t = case t of + Empty -> Empty + _ | n == 0 -> t + | otherwise -> let (left, right) = splitAt shift t in merge right left + where + shift :: Int + shift = n `mod` sizeInt t + +---------------------------------------------------------------------------- +-- Modification functions +---------------------------------------------------------------------------- + +{- | \( O(d) \). Insert a value into 'Treap' with given key and priority. +Updates monoidal accumulator accordingly. +-} +insert :: forall m a . Measured m a => Int -> Priority -> a -> Treap m a -> Treap m a +insert i p a t + | i < 0 = go 0 t + | i >= sizeInt t = go (sizeInt t) t + | otherwise = go i t + where + go :: Int -> Treap m a -> Treap m a + go _ Empty = one p a + go k node@(Node _ tp _ ta l r) + | p <= tp = + let lSize = sizeInt l + in if k <= lSize + then recalculate $ new tp ta (go k l) r + else recalculate $ new tp ta l (go (k - lSize - 1) r) + | otherwise = + let (!newL, !newR) = splitAt k node + in recalculate $ new p a newL newR + +{- | \( O(d) \). Delete element from 'Treap' by the given index. If index is out +of bounds, 'Treap' remains unchanged. +-} +delete :: forall m a . Measured m a => Int -> Treap m a -> Treap m a +delete i t + | i < 0 = t + | i >= sizeInt t = t + | otherwise = go i t + where + go :: Int -> Treap m a -> Treap m a + go _ Empty = Empty + go k (Node _ p _ a l r) = + let lSize = sizeInt l + in case compare k lSize of + EQ -> merge l r + LT -> recalculate $ new p a (go k l) r + GT -> recalculate $ new p a l (go (k - lSize - 1) r) + +---------------------------------------------------------------------------- +-- Core internal functions +---------------------------------------------------------------------------- + +{- | \( O(1) \). Calculate size and the value of the monoidal accumulator +in the given root node. This function doesn't perform any recursive calls and it +assumes that the values in the children are already correct. So use this +function only in bottom-up manner. +-} +recalculate :: Measured m a => Treap m a -> Treap m a +recalculate Empty = Empty +recalculate (Node _ p _ a l r) = + Node (1 + size l + size r) p (measure l <> measure a <> measure r) a l r diff --git a/src/Treap/Rand.hs b/src/Treap/Rand.hs new file mode 100644 --- /dev/null +++ b/src/Treap/Rand.hs @@ -0,0 +1,236 @@ +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE TypeFamilies #-} + +{- | Fair implementation of the 'Treap' data structure that uses random +generator for priorities. +-} + +module Treap.Rand + ( -- * Data structure + RTreap (..) + + -- * Smart constructors + , emptyWithGen + , oneWithGen + , empty + , one + + -- * Query functions + , size + , at + , query + + -- * Cuts and joins + , splitAt + , merge + , take + , drop + , rotate + + -- * Modification functions + , insert + , delete + + -- * General purpose functions + , withTreap + , overTreap + + -- * Pretty printing functions + , prettyPrint + ) where + +import Prelude hiding (drop, lookup, splitAt, take) + +import Control.DeepSeq (NFData (..)) +import Data.Coerce (Coercible) +import Data.Foldable (foldl') +import GHC.Exts (IsList (..)) +import GHC.Generics (Generic) + +import Treap.Measured (Measured (..)) +import Treap.Pure (Priority (..), Size (..), Treap) + +import qualified System.Random.Mersenne.Pure64 as Random +import qualified Treap.Pretty as Treap +import qualified Treap.Pure as Treap + +-- $setup +-- >>> import Data.Monoid + +---------------------------------------------------------------------------- +-- Data structure and instances +---------------------------------------------------------------------------- + +{- | Specialized version of 'Treap' where priority is +generated by the stored random generator. +-} +data RTreap m a = RTreap + { rTreapGen :: !Random.PureMT + , rTreapTree :: !(Treap m a) + } deriving (Show, Generic, Foldable) + +-- | \( O(n) \). This instance doesn't compare random generators inside trees. +instance (Eq m, Eq a) => Eq (RTreap m a) where + (==) :: RTreap m a -> RTreap m a -> Bool + RTreap _ t1 == RTreap _ t2 = t1 == t2 + +-- | \( O(1) \). Takes cached value from the root. +instance Monoid m => Measured m (RTreap m a) where + measure :: RTreap m a -> m + measure = withTreap measure + {-# INLINE measure #-} + +{- | Pure implementation of 'RTreap' construction functions. Uses +@'empty' :: RTreap k a@ as a starting point. Functions have the following +time complexity: + +1. 'fromList': \( O(n\ \log \ n) \) +2. 'toList': \( O(n) \) + +>>> prettyPrint $ fromList @(RTreap (Sum Int) Int) [1..5] + 5,15:2 + ╱╲ + ╱ ╲ + ╱ ╲ + ╱ ╲ +1,1:1 3,12:4 + ╱╲ + ╱ ╲ + ╱ ╲ + 1,3:3 1,5:5 +-} +instance Measured m a => IsList (RTreap m a) where + type Item (RTreap m a) = a + + fromList :: [a] -> RTreap m a + fromList = foldl' (\t (i, a) -> insert i a t) empty . zip [0..] + {-# INLINE fromList #-} + + toList :: RTreap m a -> [a] + toList = map snd . toList . rTreapTree + {-# INLINE toList #-} + +instance (NFData m, NFData a) => NFData (RTreap m a) where + rnf RTreap{..} = rnf rTreapTree `seq` () + +---------------------------------------------------------------------------- +-- Smart constructors +---------------------------------------------------------------------------- + +defaultRandomGenerator :: Random.PureMT +defaultRandomGenerator = Random.pureMT 0 + +-- | \( O(1) \). Create empty 'RTreap' with given random generator. +emptyWithGen :: Random.PureMT -> RTreap m a +emptyWithGen gen = RTreap gen Treap.Empty +{-# INLINE emptyWithGen #-} + +-- | \( O(1) \). Create empty 'RTreap' using random generator with seed @0@. +empty :: RTreap m a +empty = emptyWithGen defaultRandomGenerator +{-# INLINE empty #-} + +-- | \( O(1) \). Create singleton 'RTreap' with given random generator. +oneWithGen :: Measured m a => Random.PureMT -> a -> RTreap m a +oneWithGen gen a = + let (priority, newGen) = Random.randomWord64 gen + in RTreap newGen $ Treap.one (Priority priority) a +{-# INLINE oneWithGen #-} + +-- | \( O(1) \). Create singleton 'RTreap' using random generator with seed @0@. +one :: Measured m a => a -> RTreap m a +one = oneWithGen defaultRandomGenerator +{-# INLINE one #-} + +---------------------------------------------------------------------------- +-- Query functions +---------------------------------------------------------------------------- + +{- | \( O(1) \). Returns the size of the 'RTreap'. + +__Properties:__ + +* \( \forall (t\ ::\ \mathrm{Treap}\ m\ a)\ .\ \mathrm{size}\ t \geqslant 0 \) +-} +size :: RTreap m a -> Int +size = unSize . withTreap Treap.size +{-# INLINE size #-} + +-- | \( O(\log \ n) \). Lookup a value by a given key inside 'RTreap'. +at :: Int -> RTreap m a -> Maybe a +at i = withTreap $ Treap.at i +{-# INLINE at #-} + +-- | \( O(\log \ n) \). Return value of monoidal accumulator on a segment @[l, r)@. +query :: forall m a . Measured m a => Int -> Int -> RTreap m a -> m +query l r = withTreap (Treap.query l r) +{-# INLINE query #-} + +---------------------------------------------------------------------------- +-- Cuts and joins +---------------------------------------------------------------------------- + +-- | \( O(\log \ n) \). Lifted to 'RTreap' version of 'Treap.splitAt'. +splitAt :: forall m a . Measured m a => Int -> RTreap m a -> (RTreap m a, RTreap m a) +splitAt i (RTreap gen t) = let (l, r) = Treap.splitAt i t in (RTreap gen l, RTreap gen r) +{-# INLINE splitAt #-} + +-- | \( O(\log \ n) \). Lifted to 'RTreap' version of 'Treap.merge'. +merge :: Measured m a => RTreap m a -> RTreap m a -> RTreap m a +merge (RTreap gen t1) (RTreap _ t2) = RTreap gen (Treap.merge t1 t2) +{-# INLINE merge #-} + +-- | \( O(\log \ n) \). Lifted to 'RTreap' version of 'Treap.take'. +take :: forall m a . Measured m a => Int -> RTreap m a -> RTreap m a +take n = overTreap (Treap.take n) +{-# INLINE take #-} + +-- | \( O(\log \ n) \). Lifted to 'RTreap' version of 'Treap.drop'. +drop :: forall m a . Measured m a => Int -> RTreap m a -> RTreap m a +drop n = overTreap (Treap.drop n) +{-# INLINE drop #-} + +-- | \( O(\log \ n) \). Lifted to 'RTreap' version of 'Treap.rotate'. +rotate :: forall m a . Measured m a => Int -> RTreap m a -> RTreap m a +rotate n = overTreap (Treap.rotate n) +{-# INLINE rotate #-} + +---------------------------------------------------------------------------- +-- Modification functions +---------------------------------------------------------------------------- + +-- | \( O(\log \ n) \). Insert a value into 'RTreap' by given key. +insert :: forall m a . Measured m a => Int -> a -> RTreap m a -> RTreap m a +insert i a (RTreap gen t) = + let (priority, newGen) = Random.randomWord64 gen + in RTreap newGen $ Treap.insert i (Priority priority) a t +{-# INLINE insert #-} + +{- | \( O(\log \ n) \). Delete 'RTreap' node that contains given key. If there is no +such key, 'RTreap' remains unchanged. +-} +delete :: forall m a . Measured m a => Int -> RTreap m a -> RTreap m a +delete i (RTreap gen t) = RTreap gen $ Treap.delete i t +{-# INLINE delete #-} + +---------------------------------------------------------------------------- +-- Generic functions +---------------------------------------------------------------------------- + +-- | Lift a function that works with 'Treap' to 'RTreap'. +withTreap :: (Treap m a -> r) -> (RTreap m a -> r) +withTreap f = f . rTreapTree +{-# INLINE withTreap #-} + +-- | Lift a function that works with 'Treap' to 'RTreap'. +overTreap :: (Treap m a -> Treap m a) -> (RTreap m a -> RTreap m a) +overTreap set t = t { rTreapTree = set $ rTreapTree t } +{-# INLINE overTreap #-} + +---------------------------------------------------------------------------- +-- Pretty printing functions +---------------------------------------------------------------------------- + +-- | Pretty prints 'RTreap' without printing random generator. +prettyPrint :: forall m a . (Coercible m a, Show a) => RTreap m a -> IO () +prettyPrint = withTreap Treap.prettyPrint diff --git a/test/Doctest.hs b/test/Doctest.hs new file mode 100644 --- /dev/null +++ b/test/Doctest.hs @@ -0,0 +1,23 @@ +module Main (main) where + +import System.FilePath.Glob (glob) +import Test.DocTest (doctest) + + +main :: IO () +main = do + sourceFiles <- glob "src/**/*.hs" + doctest + $ "-XInstanceSigs" + : "-XScopedTypeVariables" + : "-XRecordWildCards" + : "-XMultiParamTypeClasses" + : "-XLambdaCase" + : "-XBangPatterns" + : "-XGeneralizedNewtypeDeriving" + : "-XDerivingStrategies" + : "-XDeriveAnyClass" + : "-XDeriveGeneric" + : "-XDeriveFoldable" + : "-XTypeApplications" + : sourceFiles diff --git a/test/Spec.hs b/test/Spec.hs new file mode 100644 --- /dev/null +++ b/test/Spec.hs @@ -0,0 +1,17 @@ +module Main (main) where + +import System.IO (hSetEncoding, stderr, stdout, utf8) +import Test.Hspec (Spec, hspec) + +import Test.Rand (randSpec) + + +allUnitTests :: Spec +allUnitTests = randSpec + +main :: IO () +main = do + hSetEncoding stdout utf8 + hSetEncoding stderr utf8 + + hspec allUnitTests diff --git a/test/Test/Common.hs b/test/Test/Common.hs new file mode 100644 --- /dev/null +++ b/test/Test/Common.hs @@ -0,0 +1,21 @@ +module Test.Common + ( TestTreap + , smallTreap + , extractSum + ) where + +import Data.Monoid (Sum (..)) +import GHC.Exts (IsList (..)) + +import Treap (RTreap, measure) + + +-- | Specialized version of 'RTreap' for testing. +type TestTreap = RTreap (Sum Int) Int + +-- | Small treap of total size 5. +smallTreap :: TestTreap +smallTreap = fromList [1..5] + +extractSum :: TestTreap -> Int +extractSum = getSum . measure diff --git a/test/Test/Rand.hs b/test/Test/Rand.hs new file mode 100644 --- /dev/null +++ b/test/Test/Rand.hs @@ -0,0 +1,16 @@ +module Test.Rand + ( randSpec + ) where + +import Test.Hspec (Spec, describe) + +import Test.Rand.Cuts (cutsSpec) +import Test.Rand.Query (querySpec) +import Test.Rand.Update (updateSpec) + + +randSpec :: Spec +randSpec = describe "RTreap" $ do + querySpec + cutsSpec + updateSpec diff --git a/test/Test/Rand/Cuts.hs b/test/Test/Rand/Cuts.hs new file mode 100644 --- /dev/null +++ b/test/Test/Rand/Cuts.hs @@ -0,0 +1,70 @@ +module Test.Rand.Cuts + ( cutsSpec + ) where + +import Data.Bifunctor (bimap) +import GHC.Exts (IsList (..)) +import Test.Hspec (Spec, describe, it, shouldBe) + +import Test.Common (TestTreap, smallTreap) + +import qualified Treap + + +cutsSpec :: Spec +cutsSpec = describe "Cuts and joins tests" $ do + splitAtSpec + mergeSpec + takeSpec + dropSpec + rotateSpec + +splitAtSpec :: Spec +splitAtSpec = describe "splitAt" $ do + it "splitAt negative returns treap itself" $ + snd (Treap.splitAt (-1) smallTreap) `shouldBe` smallTreap + it "splitAt 0 returns treap itself" $ + snd (Treap.splitAt 0 smallTreap) `shouldBe` smallTreap + it "splitAt n returns treap itself" $ + fst (Treap.splitAt 5 smallTreap) `shouldBe` smallTreap + it "splitAt 2 returns two treaps" $ + bimap toList toList (Treap.splitAt 2 smallTreap) `shouldBe` ([1..2], [3..5]) + +mergeSpec :: Spec +mergeSpec = describe "merge" $ do + it "merge with empty should be treap itself" $ do + Treap.merge Treap.empty smallTreap `shouldBe` smallTreap + Treap.merge smallTreap Treap.empty `shouldBe` smallTreap + it "merge two treaps works" $ + toList (Treap.merge (fromList [1..2]) (fromList [3..5]) :: TestTreap) `shouldBe` [1..5] + +takeSpec :: Spec +takeSpec = describe "take" $ do + it "take negative returns empty treap" $ + Treap.take (-1) smallTreap `shouldBe` Treap.empty + it "take 0 returns empty treap" $ + Treap.take 0 smallTreap `shouldBe` Treap.empty + it "take size returns treap itself" $ + Treap.take 5 smallTreap `shouldBe` smallTreap + it "take 2 returns first two elements" $ + Treap.take 2 smallTreap `shouldBe` fromList [1..2] + +dropSpec :: Spec +dropSpec = describe "drop" $ do + it "drop negative returns treap itself" $ + Treap.drop (-1) smallTreap `shouldBe` smallTreap + it "drop 0 returns treap itself" $ + Treap.drop 0 smallTreap `shouldBe` smallTreap + it "drop size returns empty treap" $ + Treap.drop 5 smallTreap `shouldBe` Treap.empty + it "drop 2 returns first two elements" $ + toList (Treap.drop 2 smallTreap) `shouldBe` [3..5] + +rotateSpec :: Spec +rotateSpec = describe "rotate" $ do + it "rotate 0 does nothing" $ + Treap.rotate 0 smallTreap `shouldBe` smallTreap + it "rotate 1 moves first element to the end" $ + toList (Treap.rotate 1 smallTreap) `shouldBe` [2, 3, 4, 5, 1] + it "rotate -1 moves last element to the beginning" $ + toList (Treap.rotate (-1) smallTreap) `shouldBe` [5, 1, 2, 3, 4] diff --git a/test/Test/Rand/Query.hs b/test/Test/Rand/Query.hs new file mode 100644 --- /dev/null +++ b/test/Test/Rand/Query.hs @@ -0,0 +1,51 @@ +module Test.Rand.Query + ( querySpec + ) where + +import Data.Monoid (Sum (..)) +import GHC.Exts (IsList (..)) +import Test.Hspec (Spec, describe, it, shouldBe) + +import Test.Common (TestTreap, extractSum, smallTreap) + +import qualified Treap + + +querySpec :: Spec +querySpec = describe "Query tests" $ do + basicSpec + advancedSpec + +basicSpec :: Spec +basicSpec = describe "Sanity checks" $ do + it "size of empty treap is 0" $ + Treap.size Treap.empty `shouldBe` 0 + it "size of singletone treap is 1" $ + Treap.size (Treap.one 1 :: TestTreap) `shouldBe` 1 + it "size of smallTreap is 5" $ + Treap.size smallTreap `shouldBe` 5 + it "measure of empty treap is mempty" $ + extractSum Treap.empty `shouldBe` 0 + it "measure of singleton treap is mempty" $ + extractSum (Treap.one 42) `shouldBe` 42 + it "toList smallTreap is [1..5]" $ + toList smallTreap `shouldBe` [1..5] + it "total sum of smallTreap is [1..5]" $ + extractSum smallTreap `shouldBe` sum [1..5] + +advancedSpec :: Spec +advancedSpec = describe "Different checks on query functions" $ do + it "elements by indices are correct" $ + map (`Treap.at` smallTreap) [-1..5] `shouldBe` + [Nothing, Just 1, Just 2, Just 3, Just 4, Just 5, Nothing] + it "query on empty segment returns 'mempty'" $ + Treap.query 0 (-1) smallTreap `shouldBe` mempty + it "query on the non-intersected segment returns 'mempty'" $ do + Treap.query (-2) (-1) smallTreap `shouldBe` mempty + Treap.query 5 6 smallTreap `shouldBe` mempty + it "query on subsegments works" $ do + Treap.query 0 0 smallTreap `shouldBe` 0 + Treap.query 0 1 smallTreap `shouldBe` 1 + Treap.query 0 2 smallTreap `shouldBe` 3 + Treap.query 1 3 smallTreap `shouldBe` 5 + Treap.query (-1) 10 smallTreap `shouldBe` Sum (sum [1..5]) diff --git a/test/Test/Rand/Update.hs b/test/Test/Rand/Update.hs new file mode 100644 --- /dev/null +++ b/test/Test/Rand/Update.hs @@ -0,0 +1,38 @@ +module Test.Rand.Update + ( updateSpec + ) where + +import GHC.Exts (IsList (..)) +import Test.Hspec (Spec, describe, it, shouldBe) + +import Test.Common (smallTreap) + +import qualified Treap + + +updateSpec :: Spec +updateSpec = describe "Modification operations tests" $ do + insertSpec + deleteSpec + +insertSpec :: Spec +insertSpec = describe "insert" $ do + it "insert negative inserts at the beginning" $ + toList (Treap.insert (-1) 42 smallTreap) `shouldBe` 42 : [1..5] + it "insert 0 inserts at the beginning" $ + toList (Treap.insert 0 42 smallTreap) `shouldBe` 42 : [1..5] + it "insert size inserts at the end" $ + toList (Treap.insert 5 42 smallTreap) `shouldBe` [1, 2, 3, 4, 5, 42] + it "insert in the middle works" $ + toList (Treap.insert 2 42 smallTreap) `shouldBe` [1, 2, 42, 3, 4, 5] + +deleteSpec :: Spec +deleteSpec = describe "delete" $ do + it "delete negative does nothing" $ + Treap.delete (-1) smallTreap `shouldBe` smallTreap + it "delete size does nothing" $ + Treap.delete 5 smallTreap `shouldBe` smallTreap + it "delete 0 removes first element" $ + toList (Treap.delete 0 smallTreap) `shouldBe` [2..5] + it "deletes from the middle works" $ + toList (Treap.delete 2 smallTreap) `shouldBe` [1, 2, 4, 5] diff --git a/treap.cabal b/treap.cabal new file mode 100644 --- /dev/null +++ b/treap.cabal @@ -0,0 +1,98 @@ +cabal-version: 2.4 +name: treap +version: 0.0.0.0 +synopsis: Efficient implementation of the implicit treap data structure +description: + Efficient implementation of the implicit treap data structure. + Use this data structure if you want dynamic arrays with fast operations on segments. +homepage: https://github.com/chshersh/treap +bug-reports: https://github.com/chshersh/treap/issues +license: MPL-2.0 +license-file: LICENSE +author: Dmitrii Kovanikov +maintainer: kovanikov@gmail.com +copyright: 2019 Dmitrii Kovanikov +category: Data Structure, Tree +build-type: Simple +extra-doc-files: README.md + , CHANGELOG.md +tested-with: GHC == 8.4.4 + , GHC == 8.6.4 + +source-repository head + type: git + location: https://github.com/chshersh/treap.git + +common common-options + build-depends: base >= 4.11 && < 4.13 + + ghc-options: -Wall + -Wincomplete-uni-patterns + -Wincomplete-record-updates + -Wcompat + -Widentities + -Wredundant-constraints + -Wpartial-fields + -fhide-source-paths + -freverse-errors + + default-language: Haskell2010 + default-extensions: BangPatterns + ConstraintKinds + DataKinds + DeriveFunctor + DeriveFoldable + DeriveTraversable + DeriveGeneric + DerivingStrategies + GeneralizedNewtypeDeriving + InstanceSigs + KindSignatures + LambdaCase + MultiParamTypeClasses + OverloadedStrings + RecordWildCards + ScopedTypeVariables + TypeApplications + + +library + import: common-options + build-depends: deepseq ^>= 1.4 + , mersenne-random-pure64 ^>= 0.2.2 + + hs-source-dirs: src + exposed-modules: Treap + Treap.Measured + Treap.Pretty + Treap.Pure + Treap.Rand + + +test-suite treap-test + import: common-options + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Spec.hs + other-modules: Test.Common + Test.Rand + Test.Rand.Cuts + Test.Rand.Query + Test.Rand.Update + + build-depends: treap + , hspec + , hspec-core + + +test-suite treap-doctest + import: common-options + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Doctest.hs + + build-depends: doctest + , Glob + + ghc-options: -threaded + default-language: Haskell2010