QuadTree (empty) → 0.10.0

raw patch · 4 files changed

+1215/−0 lines, 4 filesdep +basedep +compositiondep +lenssetup-changed

Dependencies added: base, composition, lens

Files

• Data/QuadTree.hs +479/−0
• LICENSE +675/−0
• QuadTree.cabal +59/−0
• Setup.hs +2/−0

@@ -0,0 +1,479 @@+{-# OPTIONS_HADDOCK show-extensions #-}++{-# LANGUAGE Safe #-}++{-# LANGUAGE Rank2Types #-}+{-# LANGUAGE ScopedTypeVariables #-}++{-|+Module      : QuadTree+Description : Region quadtrees with Lens support.+Copyright   : (c) Ashley Moni, 2014+License     : GPL-3+Maintainer  : Ashley Moni <y30099923@gmail.com>+Stability   : Experimental+Portability : Rank 2 Types, Scoped Type Variables++The purpose of this module is to provide discrete region quadtrees+that can be used as simple functional alternatives to 2D arrays,+with lens support.++@+test = set ('atLocation' (0,0)) \'d\' $+       set ('atLocation' (5,5)) \'c\' $+       set ('atLocation' (3,2)) \'b\' $+       set ('atLocation' (2,4)) \'a\' $+       'makeTree' (6,6) \'.\'+@++>>> printTree id test+d.....+......+...b..+......+..a...+.....c+-}++module Data.QuadTree (+  -- * Data Type & Constructor+  QuadTree, makeTree,+  -- * Index access+  -- $locations+  Location, getLocation, setLocation, atLocation,+  -- * Functor+  fuseTree, tmap,+  -- * Foldable+  -- $foldables+  filterTree, sortTreeBy,+  -- ** Tiles+  -- $tiles+  Region, Tile,+  -- ** Tile functions+  -- $tileuse+  tile, expand, foldTiles,+  filterTiles, sortTilesBy,+  -- * Printers+  showTree, printTree,+  -- * Miscellaneous helpers+  outOfBounds, treeDimensions, regionArea, inRegion ) where++import Control.Lens.Type (Lens')+import Control.Lens.Lens (lens)+-- import Control.Lens.Setter (set)++import Data.List (find, sortBy)+import Data.Maybe (fromJust)+import Data.Function (on)+import Data.Composition ((.:))++-- Foldable:+import Data.Foldable (Foldable, foldr)+import Prelude hiding (foldr)++---- Structures:++-- |Tuple corresponds to (X, Y) co-ordinates.++type Location = (Int, Int)++-- |The eponymous data type.+--+-- 'QuadTree' is itself a wrapper around an internal tree structure+-- along with spatial metadata about the boundaries and depth of the+-- 2D area it maps to.++data QuadTree a = Wrapper { wrappedTree :: Quadrant a+                          , treeLength :: Int+                          , treeWidth  :: Int+                          , treeDepth :: Int }+  deriving (Show, Read)++instance Functor QuadTree where+  fmap fn = onQuads $ fmap fn++instance Foldable QuadTree where+  foldr = foldTree++--++data Quadrant a = Leaf a+                | Node (Quadrant a)+                       (Quadrant a)+                       (Quadrant a)+                       (Quadrant a)+  deriving (Show, Read)++instance Functor Quadrant where+  fmap fn (Leaf x)       = Leaf (fn x)+  fmap fn (Node a b c d) = Node (fmap fn a)+                                (fmap fn b)+                                (fmap fn c)+                                (fmap fn d)++---- Index access:++-- $locations+-- This provides an array-style interface to the 'QuadTree', albeit+-- with an O(log n) lookup and insertion speed. This is both faster+-- and slower than an actual array (O(1) lookup and O(n) insertion+-- respectively).+--+-- The user can imagine a two dimensional grid that can be modified+-- or queried via co-ordinate pair indices.+++-- |Lens for accessing and manipulating data at a specific+-- location.+--+-- This is simply 'getLocation' and 'setLocation' wrapped into a lens.+atLocation :: Eq a => Location -> Lens' (QuadTree a) a+atLocation index = lens (getLocation index) (setLocation index)++-- |Getter for the value at a given location for a 'QuadTree'.+getLocation :: Location -> QuadTree a -> a+getLocation index tree+  | outOfBounds tree index =+      error "Location index out of QuadTree bounds."+  | otherwise =+      go (offsetIndex tree index) (treeDepth tree) (wrappedTree tree)+  where+    go :: Location -> Int -> Quadrant a -> a+    go _ _ (Leaf x) = x+    go _ 0 _        = error "Wrapped tree is deeper than tree depth."+    go (x,y) n (Node a b c d) =+      go (x `mod` mid, y `mod` mid) (n - 1) node+      where mid = 2 ^ (n - 1)+            node | y < mid   = if x < mid then a+                                          else b+                 | otherwise = if x < mid then c+                                          else d++-- |Setter for the value at a given location for a 'QuadTree'.+--+-- This automatically compresses the 'QuadTree' nodes if possible with+-- the new value.+setLocation :: forall a. Eq a => Location -> QuadTree a -> a -> QuadTree a+setLocation index tree new+  | outOfBounds tree index =+      error "Location index out of QuadTree bounds."+  | otherwise =+      onQuads (go (offsetIndex tree index) (treeDepth tree)) tree+  where+    go :: Eq a => Location -> Int -> Quadrant a -> Quadrant a+    go (x,y) n (Leaf old)+      | old == new  = Leaf old+      |   n == 0    = Leaf new+      | otherwise   = go (x,y) n (Node l l l l)+      where l = Leaf old+    go _     0 _    = error "Wrapped tree is deeper than tree depth."+    go (x,y) n (Node a b c d) = fusedNode+      where fusedNode = fuse newNode+            newNode+              | y < mid   = if x < mid then Node (recurse a) b c d+                                       else Node a (recurse b) c d+              | otherwise = if x < mid then Node a b (recurse c) d+                                       else Node a b c (recurse d)+            recurse = go (x `mod` mid, y `mod` mid) (n - 1)+            mid = 2 ^ (n - 1)++---- Helpers:++-- |Checks if a 'Location' is outside the boundaries of a 'QuadTree'.++outOfBounds :: QuadTree a -> Location -> Bool+outOfBounds tree (x,y) = x < 0 || y < 0+                         || x >= treeLength tree+                         || y >= treeWidth  tree++-- |Dimensions of a 'QuadTree', as an Int pair.++treeDimensions :: QuadTree a+               -> (Int, Int) -- ^ (Length, Width)+treeDimensions tree = (treeLength tree, treeWidth tree)++offsetIndex :: QuadTree a -> Location -> Location+offsetIndex tree (x,y) = (x + xOffset, y + yOffset)+  where (xOffset, yOffset) = offsets tree++offsets :: QuadTree a -> (Int, Int)+offsets tree = (xOffset, yOffset)+  where xOffset = (dimension - treeLength tree) `div` 2+        yOffset = (dimension - treeWidth  tree) `div` 2+        dimension = 2 ^ treeDepth tree++fuse :: Eq a => Quadrant a -> Quadrant a+fuse (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d))+  | a == b && b == c && c == d = Leaf a+fuse oldNode                   = oldNode++---- Functor:++onQuads :: (Quadrant a -> Quadrant b) -> QuadTree a -> QuadTree b+onQuads fn tree = tree {wrappedTree = fn (wrappedTree tree)}++-- |Cleanup function for use after any 'Control.Monad.fmap'.+--+-- When elements of a 'QuadTree' are modified by 'setLocation' (or +-- the 'atLocation' lens), it automatically compresses identical+-- adjacent nodes into larger ones. This keeps the 'QuadTree' from+-- bloating over constant use.+--+-- 'Control.Monad.fmap' does not do this. If you wish to treat the+-- 'QuadTree' as a 'Control.Monad.Functor', you should compose this+-- function after to collapse it down to its minimum size.+--+-- Example:+-- @+-- 'fuseTree' $ 'Control.Monad.fmap' fn tree+-- @+-- This particular example is reified in the function below.++fuseTree :: Eq a => QuadTree a -> QuadTree a+fuseTree = onQuads fuseQuads++fuseQuads :: Eq a => Quadrant a -> Quadrant a+fuseQuads (Node a b c d) = fuse $ Node (fuseQuads a)+                                       (fuseQuads b)+                                       (fuseQuads c)+                                       (fuseQuads d)+fuseQuads leaf           = leaf++-- |tmap is simply 'Control.Monad.fmap' with 'fuseTree' applied after.+--+-- prop> tmap fn tree == fuseTree $ fmap fn tree+tmap :: Eq b => (a -> b) -> QuadTree a -> QuadTree b+tmap = fuseTree .: fmap++---- Foldable:++-- $foldables+-- 'QuadTree's can be folded just like lists. If you simply replace+-- the "Prelude" fold functions with "Data.Foldable" ones...+--+-- @+-- import "Data.Foldable"+-- import "Prelude" hiding (foldr, foldl, any, sum, find...)+-- @+--+-- ... Then you can directly call then on 'QuadTree's without+-- qualification. No list functionality will be lost since the+-- "Data.Foldable" functions also work exactly like the "Prelude"+-- folds for list processing.+--+-- In addition you also get some extras like 'Data.Foldable.toList'.+++-- $tiles+-- Directly folding a 'QuadTree' will expand it into a sequence of+-- elements that are then folded over. For some types of operations+-- this can be incredibly inefficient; it may be faster to simply+-- manipulate a sequence of leaves and then later decompose the+-- results into a list of elements.+--+-- For these operations, we can use 'Tile's. 'Tile's are simply+-- blocks of elements, represented by a tuple of the leaf data and+-- some information on the spatial location and dimensions of the+-- block.+++-- $tileuse+-- The bread and butter method of manipulating 'Tile's is to first+-- decompose a 'QuadTree' with 'tile', process the intermediate+-- representation, and then decompose it into a final list of elements+-- with 'expand'.+--+-- @+-- 'expand' . fn . 'tile' $ tree+-- @++-- |Rectangular area, represented by a tuple of four Ints.+--+-- They correspond to (X floor, Y floor, X ceiling, Y ceiling).+--+-- The co-ordinates are inclusive of all the rows and columns in all+-- four Ints.+--+-- prop> regionArea (x, y, x, y) == 1++type Region = (Int, Int, Int, Int)++-- |Each 'Tile' is a tuple of an element from a 'QuadTree' and the+-- 'Region' it subtends.++type Tile a = (a, Region)++foldTree :: (a -> b -> b) -> b -> QuadTree a -> b+foldTree fn z = foldr fn z . expand . tile++-- |Takes a list of 'Tile's and then decomposes them into a list of+-- all their elements, properly weighted by 'Tile' size.++expand :: [Tile a] -> [a]+expand = concatMap decompose+  where decompose :: Tile a -> [a]+        decompose (a, r) = replicate (regionArea r) a++-- |Returns a list of 'Tile's. The block equivalent of+-- 'Data.Foldable.toList'.++tile :: QuadTree a -> [Tile a]+tile = foldTiles (:) []++-- |Decomposes a 'QuadTree' into its constituent 'Tile's, before+-- folding a 'Tile' consuming function over all of them.++foldTiles :: forall a b. (Tile a -> b -> b) -> b -> QuadTree a -> b+foldTiles fn z tree = go (treeRegion tree) (wrappedTree tree) z+  where go :: Region -> Quadrant a -> b -> b+        go r (Leaf a) = fn (a, normalizedIntersection)+          where normalizedIntersection =+                  (interXl - xOffset, interYt - yOffset,+                   interXr - xOffset, interYb - yOffset)+                (interXl, interYt, interXr, interYb) = +                  treeIntersection r+        go (xl, yt, xr, yb) (Node a b c d) =+          go (xl,       yt,       midx, midy) a .+          go (midx + 1, yt,       xr,   midy) b .+          go (xl,       midy + 1, midx, yb)   c .+          go (midx + 1, midy + 1, xr,   yb)   d+          where midx = (xr + xl) `div` 2+                midy = (yt + yb) `div` 2++        (xOffset, yOffset) = offsets tree+        treeIntersection   = regionIntersection $ boundaries tree++treeRegion :: QuadTree a -> Region+treeRegion tree = (0, 0, limit, limit)+  where limit = (2 ^ treeDepth tree) - 1++boundaries :: QuadTree a -> Region+boundaries tree = (left, top, right, bottom)+  where (left,  top)    = offsetIndex tree (0,0)+        (right, bottom) = offsetIndex tree (treeLength tree - 1,+                                            treeWidth  tree - 1)++regionIntersection :: Region -> Region -> Region+regionIntersection (xl , yt , xr , yb )+                   (xl', yt', xr', yb') =+  (max xl xl', max yt yt',+   min xr xr', min yb yb')++-- |Simple helper function that lets you calculate the area of a+-- 'Region', usually for 'Data.List.replicate' purposes.++regionArea :: Region -> Int+regionArea (xl,yt,xr,yb) = (xr + 1 - xl) * (yb + 1 - yt)++-- |Does the region contain this location?++inRegion :: Location -> Region -> Bool+inRegion (x,y) (xl,yt,xr,yb) = xl <= x && x <= xr &&+                               yt <= y && y <= yb++---- Foldable extras:++-- |'Data.List.filter's a list of the 'QuadTree' 's elements.++filterTree :: (a -> Bool) -> QuadTree a -> [a]+filterTree fn = expand . filterTiles fn . tile++-- |'Data.List.sortBy's a list of the 'QuadTree' 's elements.++sortTreeBy :: (a -> a -> Ordering) -> QuadTree a -> [a]+sortTreeBy fn = expand . sortTilesBy fn . tile++-- |'Data.List.filter's a list of the 'Tile's of a 'QuadTree'.++filterTiles :: (a -> Bool) -> [Tile a] -> [Tile a]+filterTiles _  [] = []+filterTiles fn ((a,r) : rs)+  | fn a      = (a,r) : filterTiles fn rs+  | otherwise =         filterTiles fn rs++-- |'Data.List.sortBy's a list of the 'Tile's of a 'QuadTree'.++sortTilesBy :: (a -> a -> Ordering) -> [Tile a] -> [Tile a]+sortTilesBy fn = sortBy (fn `on` fst)++---- Constructor:++-- |Constructor that generates a 'QuadTree' of the given dimensions,+-- with all cells filled with a default value.++makeTree :: (Int, Int) -- ^ (Length, Width)+                  -> a -- ^ Initial element to fill+                  -> QuadTree a+makeTree (x,y) a+  | x <= 0 || y <= 0 = error "Invalid dimensions for tree."+  | otherwise = Wrapper { wrappedTree = Leaf a+                        , treeLength = x+                        , treeWidth  = y+                        , treeDepth = fst . fromJust $+                            find ((>= max x y) . snd) $+                              zip [0..] (iterate (*2) 1) }+++---- Sample Printers:++-- |Generates a newline delimited string representing a 'QuadTree' as+-- a 2D block of characters.+--+-- Note that despite the word 'show' in the function name, this does+-- not 'Text.show' the 'QuadTree'. It pretty prints it. The name+-- is simply a mnemonic for its @'QuadTree' -> String@ behaviour.++showTree :: (a -> Char) -- ^ Function to generate characters for each+                        -- 'QuadTree' element.+         -> QuadTree a -> String+showTree printer tree = breakString (treeLength tree) string+  where string   = map printer grid+        grid = [getLocation (x,y) tree |+                y <- [0 .. treeWidth  tree - 1],+                x <- [0 .. treeLength tree - 1]]+        breakString :: Int -> String -> String+        breakString _ [] = []+        breakString n xs = a ++ "\n" ++ breakString n b+          where (a,b) = splitAt n xs++-- |As 'showTree' above, but also prints it.++printTree :: (a -> Char) -- ^ Function to generate characters for each+                         -- 'QuadTree' element.+          -> QuadTree a -> IO ()+printTree = putStr .: showTree+++--------- Test:++-- x' :: QuadTree Int+-- x' = Wrapper { treeLength = 6+--             , treeWidth = 5+--             , treeDepth = 3+--             , wrappedTree = y' }++-- y' :: Quadrant Int+-- y' = Node (Leaf 0)+--           (Node (Leaf 2)+--                 (Leaf 3)+--                 (Leaf 4)+--                 (Leaf 5))+--           (Leaf 1)+--           (Leaf 9)++-- basic :: QuadTree Int+-- basic = Wrapper {treeLength = 4, treeWidth = 5, treeDepth = 3,+--                  wrappedTree = Node (Leaf 0)+--                                     (Leaf 1)+--                                     (Leaf 2)+--                                     (Leaf 3)}++-- x5 = set (atLocation (2,3)) 1 (makeTree (5,7) 0)+-- x6 = set (atLocation (2,3)) 1 (makeTree (6,7) 0)+-- p n = printTree (head . show) n++-- test = set (atLocation (0,0)) 'd' $+--        set (atLocation (5,5)) 'c' $+--        set (atLocation (3,2)) 'b' $+--        set (atLocation (2,4)) 'a' $+--        makeTree (6,6) '.'

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@@ -0,0 +1,59 @@+-- Initial QuadTree.cabal generated by cabal init.  For further+-- documentation, see http://haskell.org/cabal/users-guide/++-- The name of the package.+name:                QuadTree++-- The package version.  See the Haskell package versioning policy (PVP)+-- for standards guiding when and how versions should be incremented.+-- http://www.haskell.org/haskellwiki/Package_versioning_policy+-- PVP summary:      +-+------- breaking API changes+--                   | | +----- non-breaking API additions+--                   | | | +--- code changes with no API change+version:             0.10.0++-- A short (one-line) description of the package.+synopsis:            QuadTree library for Haskell, with lens support.++-- A longer description of the package.+-- description:+description:         The purpose of this package is to provide discrete region quadtrees that can be used as effective functional alternatives to 2D arrays, with lens support.++-- The license under which the package is released.+license:             GPL-3++-- The file containing the license text.+license-file:        LICENSE++-- The package author(s).+author:              Ashley Moni++-- An email address to which users can send suggestions, bug reports, and+-- patches.+maintainer:          y30099923@gmail.com++-- A copyright notice.+-- copyright:++category:            Data++build-type:          Simple++-- Constraint on the version of Cabal needed to build this package.+cabal-version:       >=1.8+++library+  -- Modules exported by the library.+  exposed-modules:     Data.QuadTree++  -- Modules included in this library but not exported.+  -- other-modules:++  -- Other library packages from which modules are imported.+  build-depends:       base ==4.6.*, lens ==4.0.*, composition ==1.0.*+++source-repository head+  type: git+  location: git@github.com:AshleyMoni/QuadTree.git

@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain