diff --git a/Data/SegmentTree.hs b/Data/SegmentTree.hs new file mode 100644 --- /dev/null +++ b/Data/SegmentTree.hs @@ -0,0 +1,75 @@ +-- | This module contains the 'SegmentTree' data structure, its +-- constructor and the query function. +-- +-- Example Usage: +-- +-- @ +-- import Data.Monoid +-- import Data.SegmentTree +-- ... +-- st = mkTree $ map Sum [0..10] +-- ... +-- queryTree st (0, 10) == Sum 55 +-- queryTree st (5, 10) == Sum 45 +-- queryTree st (0, 4) == Sum 10 +-- @ + +module Data.SegmentTree ( SegmentTree(..), mkTree, queryTree ) where + +import Data.Monoid +import Text.Printf + +data (Monoid a) => Tree a = Branch a (Tree a) (Tree a) | Leaf a + +getCargo (Branch x _ _) = x +getCargo (Leaf x) = x + +-- | A 'SegmentTree' is a binary tree and the bounds of its +-- corresponding interval. +data (Monoid a) => SegmentTree a = SegmentTree (Tree a) (Int, Int) + +instance (Monoid a) => Show (SegmentTree a) where + show (SegmentTree t (l, u)) = unlines $ go t (l, u) + where + go (Branch _ lc rc) (l, u) = + let m = (u-l) `div` 2 + (ls, rs) = (go lc (l, l+m), go rc (l+m+1, u)) + (ls', rs') = (indentTree True ls, indentTree False rs) + ts = printf "[%d..%d]" l u + in concat [[ts], ls', rs'] + go (Leaf _) (l, u) = [printf "[%d]" l] + indentTree _ [] = [] + indentTree True [x] = [printf "|-- %s" x] + indentTree False [x] = [printf "`-- %s" x] + indentTree True (x:xs) = indentTree True [x] ++ map ("| "++) xs + indentTree False (x:xs) = indentTree False [x] ++ map (" "++) xs + +-- | Build the 'SegmentTree' for the given list. Time: O(n*log n) +mkTree :: (Monoid a) => [a] -> SegmentTree a +mkTree xs = SegmentTree (go xs listBounds) listBounds + where + listBounds = (0, length xs - 1) + go ys (l, u) + -- invariant: head ys == xs !! l + | l == u = Leaf (head ys) + | otherwise = + let m = (u-l) `div` 2 + leftc = go ys (l, l+m) + rightc = go (drop (m+1) ys) (l+m+1, u) + in Branch (getCargo leftc `mappend` getCargo rightc) + leftc rightc + +-- | Query the 'SegmentTree' for the specified closed interval. Time: +-- O(log n) +queryTree :: (Monoid a) => SegmentTree a -> (Int, Int) -> a +queryTree (SegmentTree t (s, e)) (l, u) = go t (s, e) + where + -- we're querying for (l, u) + go t (s, e) + | (l > e) || (u < s) = mempty + | (l <= s) && (u >= e) = getCargo t + | otherwise = let (Branch _ leftc rightc) = t + m = (e-s) `div` 2 + lv = go leftc (s, s+m) + rv = go rightc (s+m+1, e) + in lv `mappend` rv diff --git a/Data/SegmentTree/Examples.hs b/Data/SegmentTree/Examples.hs new file mode 100644 --- /dev/null +++ b/Data/SegmentTree/Examples.hs @@ -0,0 +1,73 @@ +-- | Example uses of 'SegmentTree's. + +module Data.SegmentTree.Examples + ( -- * Sum Monoid + intervalSum + -- * Any Monoid + , intervalAny + -- * GCD Monoid + , GCD(..), intervalGCD + -- * String Monoid + , intervalConcat + -- * Unwords Monoid + , Unwords(..), intervalUnwords + ) where + +import Data.SegmentTree + +import Data.Monoid + +------------- +-- Sum monoid +------------- + +-- | Find the sum of the elements in the interval [l, u]. +intervalSum :: SegmentTree (Sum Int) -> (Int, Int) -> Int +intervalSum t bds@(l, u) = getSum $ queryTree t bds + +------------- +-- Any monoid +------------- + +-- | Find out if any of the elements are True in the interval [l, u]. +intervalAny :: SegmentTree Any -> (Int, Int) -> Bool +intervalAny t bds@(l, u) = getAny $ queryTree t bds + +------------- +-- GCD monoid +------------- + +newtype (Integral a) => GCD a = GCD { getGCD :: a } + +instance (Integral a) => Monoid (GCD a) where + mempty = GCD $ fromIntegral 1 + (GCD x) `mappend` (GCD y) = GCD $ gcd x y + +-- | Find the greatest common divisor of the elements in the interval +-- [l, u]. +intervalGCD :: SegmentTree (GCD Int) -> (Int, Int) -> Int +intervalGCD t bds@(l, u) = getGCD $ queryTree t bds + +---------------- +-- String monoid +---------------- + +-- | Concatenate the strings in the interval [l, u]. +intervalConcat :: SegmentTree String -> (Int, Int) -> String +intervalConcat t bds@(l, u) = queryTree t bds + +--------------- +-- Unwords monoid +--------------- + +newtype Unwords = Unwords { getUnwords :: String } + +instance Monoid Unwords where + mempty = Unwords "" + (Unwords "") `mappend` y = y + x `mappend` (Unwords "") = x + (Unwords x) `mappend` (Unwords y) = Unwords (x ++ " " ++ y) + +-- | Unwords the words in the interval [l, u]. +intervalUnwords :: SegmentTree Unwords -> (Int, Int) -> String +intervalUnwords t bds@(l, u) = getUnwords $ queryTree t bds diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. Additional Definitions. + + As used herein, "this License" refers to version 3 of the GNU Lesser +General Public License, and the "GNU GPL" refers to version 3 of the GNU +General Public License. + + "The Library" refers to a covered work governed by this License, +other than an Application or a Combined Work as defined below. + + An "Application" is any work that makes use of an interface provided +by the Library, but which is not otherwise based on the Library. +Defining a subclass of a class defined by the Library is deemed a mode +of using an interface provided by the Library. + + A "Combined Work" is a work produced by combining or linking an +Application with the Library. The particular version of the Library +with which the Combined Work was made is also called the "Linked +Version". + + The "Minimal Corresponding Source" for a Combined Work means the +Corresponding Source for the Combined Work, excluding any source code +for portions of the Combined Work that, considered in isolation, are +based on the Application, and not on the Linked Version. + + The "Corresponding Application Code" for a Combined Work means the +object code and/or source code for the Application, including any data +and utility programs needed for reproducing the Combined Work from the +Application, but excluding the System Libraries of the Combined Work. + + 1. Exception to Section 3 of the GNU GPL. + + You may convey a covered work under sections 3 and 4 of this License +without being bound by section 3 of the GNU GPL. + + 2. Conveying Modified Versions. + + If you modify a copy of the Library, and, in your modifications, a +facility refers to a function or data to be supplied by an Application +that uses the facility (other than as an argument passed when the +facility is invoked), then you may convey a copy of the modified +version: + + a) under this License, provided that you make a good faith effort to + ensure that, in the event an Application does not supply the + function or data, the facility still operates, and performs + whatever part of its purpose remains meaningful, or + + b) under the GNU GPL, with none of the additional permissions of + this License applicable to that copy. + + 3. Object Code Incorporating Material from Library Header Files. + + The object code form of an Application may incorporate material from +a header file that is part of the Library. You may convey such object +code under terms of your choice, provided that, if the incorporated +material is not limited to numerical parameters, data structure +layouts and accessors, or small macros, inline functions and templates +(ten or fewer lines in length), you do both of the following: + + a) Give prominent notice with each copy of the object code that the + Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the object code with a copy of the GNU GPL and this license + document. + + 4. Combined Works. + + You may convey a Combined Work under terms of your choice that, +taken together, effectively do not restrict modification of the +portions of the Library contained in the Combined Work and reverse +engineering for debugging such modifications, if you also do each of +the following: + + a) Give prominent notice with each copy of the Combined Work that + the Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the Combined Work with a copy of the GNU GPL and this license + document. + + c) For a Combined Work that displays copyright notices during + execution, include the copyright notice for the Library among + these notices, as well as a reference directing the user to the + copies of the GNU GPL and this license document. + + d) Do one of the following: + + 0) Convey the Minimal Corresponding Source under the terms of this + License, and the Corresponding Application Code in a form + suitable for, and under terms that permit, the user to + recombine or relink the Application with a modified version of + the Linked Version to produce a modified Combined Work, in the + manner specified by section 6 of the GNU GPL for conveying + Corresponding Source. + + 1) Use a suitable shared library mechanism for linking with the + Library. A suitable mechanism is one that (a) uses at run time + a copy of the Library already present on the user's computer + system, and (b) will operate properly with a modified version + of the Library that is interface-compatible with the Linked + Version. + + e) Provide Installation Information, but only if you would otherwise + be required to provide such information under section 6 of the + GNU GPL, and only to the extent that such information is + necessary to install and execute a modified version of the + Combined Work produced by recombining or relinking the + Application with a modified version of the Linked Version. (If + you use option 4d0, the Installation Information must accompany + the Minimal Corresponding Source and Corresponding Application + Code. If you use option 4d1, you must provide the Installation + Information in the manner specified by section 6 of the GNU GPL + for conveying Corresponding Source.) + + 5. Combined Libraries. + + You may place library facilities that are a work based on the +Library side by side in a single library together with other library +facilities that are not Applications and are not covered by this +License, and convey such a combined library under terms of your +choice, if you do both of the following: + + a) Accompany the combined library with a copy of the same work based + on the Library, uncombined with any other library facilities, + conveyed under the terms of this License. + + b) Give prominent notice with the combined library that part of it + is a work based on the Library, and explaining where to find the + accompanying uncombined form of the same work. + + 6. Revised Versions of the GNU Lesser General Public License. + + The Free Software Foundation may publish revised and/or new versions +of the GNU Lesser General Public License from time to time. Such new +versions will be similar in spirit to the present version, but may +differ in detail to address new problems or concerns. + + Each version is given a distinguishing version number. If the +Library as you received it specifies that a certain numbered version +of the GNU Lesser General Public License "or any later version" +applies to it, you have the option of following the terms and +conditions either of that published version or of any later version +published by the Free Software Foundation. If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. diff --git a/SegmentTree.cabal b/SegmentTree.cabal new file mode 100644 --- /dev/null +++ b/SegmentTree.cabal @@ -0,0 +1,17 @@ +Name: SegmentTree +Version: 0.1 +Cabal-Version: >= 1.2 +Build-type: Simple +License: LGPL +License-File: LICENSE +Author: Alexandru Scvortov +Maintainer: scvalex@gmail.com +Homepage: http://scvalex.github.com/articles/SegmentTree.html +Category: Data +Synopsis: Data structure for O(log n) mconcats on list intervals +Description: The 'SegmentTree' data structure allows for logarithmic + time accumulations on preprocessed lists of 'Monoid's. + +Library + Build-Depends: base + Exposed-modules: Data.SegmentTree, Data.SegmentTree.Examples diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain