diff --git a/Data/QuadTree.hs b/Data/QuadTree.hs --- a/Data/QuadTree.hs +++ b/Data/QuadTree.hs @@ -6,10 +6,10 @@ {-# LANGUAGE ScopedTypeVariables #-} {-| -Module : QuadTree +Module : Data.QuadTree Description : Region quadtrees with lens support. -Copyright : (c) Ashley Moni, 2014 -License : GPL-3 +Copyright : (c) Ashley Moni, 2015 +License : BSD3 Maintainer : Ashley Moni Stability : Stable @@ -39,7 +39,7 @@ QuadTree, makeTree, -- * Index access -- $locations - Location, getLocation, setLocation, atLocation, + Location, atLocation, getLocation, setLocation, mapLocation, -- * Functor fuseTree, tmap, -- * Foldable @@ -57,61 +57,9 @@ -- * Miscellaneous helpers outOfBounds, treeDimensions, regionArea, inRegion ) where -import Control.Lens.Type (Lens') -import Control.Lens.Lens (lens) --- import Control.Lens.Setter (set) +import Data.QuadTree.Internal -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 @@ -122,130 +70,6 @@ -- 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... @@ -255,7 +79,7 @@ -- import "Prelude" hiding (foldr, foldl, any, sum, find...) -- @ -- --- ... Then you can directly call then on 'QuadTree's without +-- ... Then you can directly call them 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. @@ -286,193 +110,3 @@ -- '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) '.' diff --git a/Data/QuadTree/Internal.hs b/Data/QuadTree/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/QuadTree/Internal.hs @@ -0,0 +1,409 @@ +{-# OPTIONS_HADDOCK show-extensions #-} + +{-# LANGUAGE Safe #-} + +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE ScopedTypeVariables #-} + +{-| +Module : Data.QuadTree.Internal +Description : Internals for the Data.QuadTree library. +Copyright : (c) Ashley Moni, 2015 +License : BSD3 +Maintainer : Ashley Moni +Stability : Stable + +The QuadTree.Internals library is a separately encapsulated subset of +the QuadTree library, strictly for the purpose of exposing inner +structure and functions to the testing suites. +|-} + +module Data.QuadTree.Internal where + +import Control.Lens.Type (Lens') +import Control.Lens.Setter (over, set) +import Control.Lens.Getter (view) + +import Data.List (find, sortBy) +import Data.Function (on) +import Data.Composition ((.:)) + +---- 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, Eq) + +-- |'QuadTree's are 'Functor's, and their elements can be fmapped over. +instance Functor QuadTree where + fmap fn = onQuads $ fmap fn + +-- |'QuadTree's are 'Foldable', though the traversal path is a complex +-- recursive enumeration of internal 'Quadrant's. Don't use folds that aren't +-- ordering agnostic. +instance Foldable QuadTree where + foldr = foldTree + +-- Quadrants: + +-- |The internal data structure of a 'QuadTree'. +-- +-- Each 'Quadrant' consists of either a terminating Leaf node, or +-- four further 'Quadrant's. + +data Quadrant a = Leaf a + | Node (Quadrant a) + (Quadrant a) + (Quadrant a) + (Quadrant a) + deriving (Show, Read, Eq) + +-- |'Quadrant's are 'Functor's. -- You can fmap all their recursive leaf node. +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) + +---- Quadrant lenses: + +-- |Lens for the top left 'Quadrant' of a node. +_a :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a) +_a f (Node a b c d) = fmap (\x -> fuse $ Node x b c d) (f a) +_a f leaf = fmap embed (f leaf) + where embed :: Quadrant a -> Quadrant a + embed x | x == leaf = leaf + | otherwise = Node x leaf leaf leaf + +-- |Lens for the top right 'Quadrant' of a node. +_b :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a) +_b f (Node a b c d) = fmap (\x -> fuse $ Node a x c d) (f b) +_b f leaf = fmap embed (f leaf) + where embed :: Quadrant a -> Quadrant a + embed x | x == leaf = leaf + | otherwise = Node leaf x leaf leaf + +-- |Lens for the bottom left 'Quadrant' of a node. +_c :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a) +_c f (Node a b c d) = fmap (\x -> fuse $ Node a b x d) (f c) +_c f leaf = fmap embed (f leaf) + where embed :: Quadrant a -> Quadrant a + embed x | x == leaf = leaf + | otherwise = Node leaf leaf x leaf + +-- |Lens for the bottom right 'Quadrant' of a node. +_d :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a) +_d f (Node a b c d) = fmap (fuse . Node a b c) (f d) +_d f leaf = fmap embed (f leaf) + where embed :: Quadrant a -> Quadrant a + embed x | x == leaf = leaf + | otherwise = Node leaf leaf leaf x + +-- |Lens for a terminate leaf value of a node. +_leaf :: Lens' (Quadrant a) a +_leaf f (Leaf leaf) = Leaf <$> f leaf +_leaf _ _ = error "Wrapped tree is deeper than cached tree depth." + +-- |Lens to zoom into the internal data structure of a 'QuadTree', +-- lensing past the metadata to reveal the 'Quadrant' inside. +_wrappedTree :: Lens' (QuadTree a) (Quadrant a) +_wrappedTree f qt = (\x -> qt {wrappedTree = x}) <$> f (wrappedTree qt) + +-- |Unsafe sanity test lens that makes sure a given location index exists +-- within the relevant 'QuadTree'. +verifyLocation :: Location -> Lens' (QuadTree a) (QuadTree a) +verifyLocation index f qt + | index `outOfBounds` qt = error "Location index out of QuadTree bounds." + | otherwise = f qt + +---- Index access: + +-- |Lens for accessing and manipulating data at a specific +-- location. +atLocation :: forall a. Eq a => Location -> Lens' (QuadTree a) a +atLocation index fn qt = (verifyLocation index . _wrappedTree . + go (offsetIndex qt index) (treeDepth qt)) fn qt + where + go :: Eq a => Location -> Int -> Lens' (Quadrant a) a + go _ 0 = _leaf + go (x,y) n | y < mid = if x < mid then _a . recurse + else _b . recurse + | otherwise = if x < mid then _c . recurse + else _d . recurse + where recurse = go (x `mod` mid, y `mod` mid) (n - 1) + mid = 2 ^ (n - 1) + +-- |Getter for the value at a given location for a 'QuadTree'. +getLocation :: Eq a => Location -> QuadTree a -> a +getLocation = view . atLocation + +-- |Setter for the value at a given location for a 'QuadTree'. +-- +-- This automatically compresses the 'QuadTree' nodes if possible with +-- the new value. +setLocation :: Eq a => Location -> a -> QuadTree a -> QuadTree a +setLocation = set . atLocation + +-- |Modifies value at a given location for a 'QuadTree'. +-- +-- This automatically compresses the 'QuadTree' nodes if possible with +-- the new value. +mapLocation :: Eq a => Location -> (a -> a) -> QuadTree a -> QuadTree a +mapLocation = over . atLocation + +---- Helpers: + +-- |Checks if a 'Location' is outside the boundaries of a 'QuadTree'. +outOfBounds :: Location -> QuadTree a -> Bool +outOfBounds (x,y) tree = 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) + +-- |Add offsets to a location index for the purpose of querying +-- the 'QuadTree' 's true reference frame. +offsetIndex :: QuadTree a -> Location -> Location +offsetIndex tree (x,y) = (x + xOffset, y + yOffset) + where (xOffset, yOffset) = offsets tree + +-- |Offsets added to a 'QuadTree' 's true reference frame +-- to reference elements in the centralized width and height. +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 + +-- |Merge 'Quadrant' into a leaf node if possible. +fuse :: Eq a => Quadrant a -> Quadrant a +fuse (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d)) + | allEqual [a,b,c,d] = Leaf a +fuse oldNode = oldNode + +-- |Test if all elements in a list are equal. +allEqual :: Eq a => [a] -> Bool +allEqual = and . (zipWith (==) <*> tail) + +---- Functor: + +-- |Apply a function to a 'QuadTree's internal 'Quadrant'. +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 + where 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: + +-- |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) + +-- |Foldr elements within a 'QuadTree', by first decomposing it into +-- 'Tile's and then decomposing those into lists of identical data values. + +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 + +-- |The region denoting an entire 'QuadTree'. +treeRegion :: QuadTree a -> Region +treeRegion tree = (0, 0, limit, limit) + where limit = (2 ^ treeDepth tree) - 1 + +-- |The boundary 'Region' of the internal 'QuadTree' 's true reference frame. +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) + +-- |'Region' that's an intersection between two othe 'Region's. +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 = smallestDepth (x,y) } + +-- |Find the smallest tree depth that would encompass a given width and height. +smallestDepth :: (Int, Int) -> Int +smallestDepth (x,y) = depth + where (depth, _) = smallestPower + Just smallestPower = find bigEnough powersZip + bigEnough (_, e) = e >= max x y + powersZip = 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 :: Eq a => (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 :: Eq a => (a -> Char) -- ^ Function to generate characters for each + -- 'QuadTree' element. + -> QuadTree a -> IO () +printTree = putStr .: showTree diff --git a/LICENSE b/LICENSE --- a/LICENSE +++ b/LICENSE @@ -1,675 +1,23 @@ - GNU 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. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. 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IN NO EVENT SHALL BE LIABLE FOR ANY +DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES +(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND +ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/QuadTree.cabal b/QuadTree.cabal --- a/QuadTree.cabal +++ b/QuadTree.cabal @@ -10,7 +10,7 @@ -- PVP summary: +-+------- breaking API changes -- | | +----- non-breaking API additions -- | | | +--- code changes with no API change -version: 0.10.1 +version: 0.11.0 -- A short (one-line) description of the package. synopsis: QuadTree library for Haskell, with lens support. @@ -20,7 +20,7 @@ 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 +license: BSD3 -- The file containing the license text. license-file: LICENSE @@ -48,15 +48,21 @@ exposed-modules: Data.QuadTree -- Modules included in this library but not exported. - -- other-modules: + other-modules: Data.QuadTree.Internal -- Other library packages from which modules are imported. - build-depends: base >= 4.6 && <= 4.8, - lens >= 4.1 && <= 4.5, + build-depends: base >= 4.6 && < 4.10, + lens >= 4.1 && < 4.13, composition ==1.0.* -- http://www.vex.net/~trebla/haskell/cabal-cabal.xhtml default-language: Haskell2010 + +Test-Suite quadtree-tests + type: exitcode-stdio-1.0 + main-is: Test/quadtree-tests.hs + build-depends: base, lens, composition, QuickCheck + default-language: Haskell2010 source-repository head type: git diff --git a/Test/quadtree-tests.hs b/Test/quadtree-tests.hs new file mode 100644 --- /dev/null +++ b/Test/quadtree-tests.hs @@ -0,0 +1,273 @@ +{-# LANGUAGE TemplateHaskell #-} + +{-# LANGUAGE ScopedTypeVariables #-} + +module Main where + +import Data.QuadTree.Internal + +import Test.QuickCheck.Arbitrary (Arbitrary, arbitrary) +import Test.QuickCheck.Modifiers (Positive(..), NonNegative(..)) +import Test.QuickCheck.Gen (Gen, choose, oneof, suchThat, + listOf, infiniteListOf) +import Test.QuickCheck.Property (Property, (==>)) +import Test.QuickCheck.All (quickCheckAll) + +import Text.Show.Functions () +import System.Exit (exitSuccess, exitFailure) + +import Control.Lens.Type (Lens') +import Control.Lens.Setter (set) +import Control.Lens.Getter (view) +import Control.Monad (replicateM) +import Data.Functor ((<$>)) +import Data.Composition ((.:)) + +{- Structure + +The QuadTree type has two structural invariants/constraints: + + 1. The internal raw tree must not be deeper than its + declared depth. + + 2. No branch node can have four leaves that are identical. + These need to be fused into a single leaf node by the algorithms. + +We will acknowledge and manage these invariants by constructing +two separate Arbitrary generators for QuadTrees: + + 1. The first generator will construct QuadTrees strictly using the + exposed API (makeTree and setLocation). We'll use this to test if + the invariant is consistently maintained across the subset of QuadTrees + that the user can construct. + + 2. The second generator will generate QuadTrees ex nihilo that obey + the invariants. We'll use this for our primary testing purposes, since + it can theoretically generate valid non-user-constructable trees and + because it can generate large complex trees far far more efficiently. + +-} + +---- The API-constructable QuadTree generator + +newtype APITree a = Constructed (QuadTree a) + +instance Show a => Show (APITree a) where + show (Constructed qt) = show qt + +instance (Eq a, Arbitrary a) => Arbitrary (APITree a) where + arbitrary = do + Positive len <- arbitrary + Positive wid <- arbitrary + baseValue <- arbitrary + let baseTree = makeTree (len, wid) baseValue + + indices <- listOf $ generateIndexOf baseTree + values <- infiniteListOf arbitrary + let setList = zip indices values + + return . Constructed $ foldr (uncurry setLocation) baseTree setList + +-- Generates a random valid location index for a quadtree +generateIndexOf :: QuadTree a -> Gen Location +generateIndexOf qt = do + x <- choose (0, treeLength qt - 1) + y <- choose (0, treeWidth qt - 1) + return (x,y) + + +---- Ex-nihilo QuadTree generator + +newtype GenTree a = Generated (QuadTree a) + +instance Show a => Show (GenTree a) where + show (Generated qt) = show qt + +instance (Eq a, Arbitrary a) => Arbitrary (GenTree a) where + arbitrary = do + Positive len <- arbitrary + Positive wid <- arbitrary + let depth = smallestDepth (len, wid) + tree <- generateQuadrant depth + + return . Generated $ Wrapper { treeLength = len, + treeWidth = wid, + treeDepth = depth, + wrappedTree = tree } + +generateQuadrant :: (Eq a, Arbitrary a) => Int -> Gen (Quadrant a) +generateQuadrant 0 = generateLeaf +generateQuadrant n = oneof [generateLeaf, generateNode (n - 1)] + +generateLeaf :: Arbitrary a => Gen (Quadrant a) +generateLeaf = Leaf <$> arbitrary + +generateNode :: (Eq a, Arbitrary a) => Int -> Gen (Quadrant a) +generateNode n = do + [a,b,c,d] <- replicateM 4 (generateQuadrant n) `suchThat` (not . equalLeaves) + return (Node a b c d) + where equalLeaves :: Eq a => [Quadrant a] -> Bool + equalLeaves [Leaf a, Leaf b, Leaf c, Leaf d] = allEqual [a,b,c,d] + equalLeaves _ = False + + +-- Ex-nihilo Quadrant generator + +instance (Eq a, Arbitrary a) => Arbitrary (Quadrant a) where + arbitrary = do + NonNegative depth <- arbitrary + generateQuadrant depth + +---- General index generator + +-- Ideally, we'd be able to generate random dimensionally valid lenses as +-- part of the arguments to property functions that take quadtrees. +-- But we'd need dependent types for that, so we're just going to generate +-- independent random lenses and only test the ones that would work with +-- the tree. + +newtype Index = MkIndex (Int, Int) + +instance Arbitrary Index where + arbitrary = do + NonNegative x <- arbitrary + NonNegative y <- arbitrary + return $ MkIndex (x,y) + +instance Show Index where + show (MkIndex index) = show index + + +---- APITree structural tests + +-- We use Bools here since they're the most trivial Eq type. +-- A QuadTree constructed with Bool insertions is the fastest way +-- to build/fuse up a complex set of nodes at various heights. + +-- Inner tree representation cannot be deeper than defined depth +prop_APITreeDepth :: APITree Bool -> Bool +prop_APITreeDepth (Constructed qt) = go (treeDepth qt) (wrappedTree qt) + where go :: Int -> Quadrant a -> Bool + go _ (Leaf _) = True + go 0 _ = False + go n (Node a b c d) = and $ fmap (go (n - 1)) [a,b,c,d] + +-- Inner tree representation cannot have branches holding four equal leaves +prop_APITreeInequality :: APITree Bool -> Bool +prop_APITreeInequality (Constructed qt) = go $ wrappedTree qt + where go :: Eq a => Quadrant a -> Bool + go (Leaf _) = True + go (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d)) + | allEqual [a,b,c,d] = False + go (Node a b c d) = and $ fmap go [a,b,c,d] + + +---- Ex Nihilo QuadTree tests + +-- For completeness, we'll test the structural requirements here as well. +-- The requirements are baked into the generator, but this lets us test +-- that generator. + +-- Inner tree representation cannot be deeper than defined depth +prop_treeDepth :: GenTree Bool -> Bool +prop_treeDepth (Generated qt) = go (treeDepth qt) (wrappedTree qt) + where go :: Int -> Quadrant a -> Bool + go _ (Leaf _) = True + go 0 _ = False + go n (Node a b c d) = and $ fmap (go (n - 1)) [a,b,c,d] + +-- Inner tree representation cannot have branches holding four equal leaves +prop_treeInequality :: GenTree Bool -> Bool +prop_treeInequality (Generated qt) = go $ wrappedTree qt + where go :: Eq a => Quadrant a -> Bool + go (Leaf _) = True + go (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d)) + | allEqual [a,b,c,d] = False + go (Node a b c d) = and $ fmap go [a,b,c,d] + +{- Functor laws + + fmap id = id + fmap (f . g) = fmap f . fmap g -} + +prop_functor1 :: Eq a => GenTree a -> Bool +prop_functor1 (Generated qt) = fmap id qt == qt + +prop_functor2 :: Eq c => GenTree a -> (b -> c) -> (a -> b) -> Bool +prop_functor2 (Generated qt) f g = fmap (f . g) qt == (fmap f . fmap g) qt + +{- Lens laws + + view l (set l b a) = b + set l (view l a) a = a + set l c (set l b a) = set l c a -} + +prop_lens1 :: Eq a => GenTree a -> a -> Index -> Property +prop_lens1 (Generated a) b (MkIndex location) = + location `validIndexOf` a ==> view l (set l b a) == b + where l :: Eq a => Lens' (QuadTree a) a + l = atLocation location + +prop_lens2 :: Eq a => GenTree a -> Index -> Property +prop_lens2 (Generated a) (MkIndex location) = + location `validIndexOf` a ==> set l (view l a) a == a + where l :: Eq a => Lens' (QuadTree a) a + l = atLocation location + +prop_lens3 :: Eq a => GenTree a -> a -> a -> Index -> Property +prop_lens3 (Generated a) b c (MkIndex location) = + location `validIndexOf` a ==> set l c (set l b a) == set l c a + where l :: Eq a => Lens' (QuadTree a) a + l = atLocation location + + +validIndexOf :: Location -> QuadTree a -> Bool +validIndexOf = not .: outOfBounds + + +---- Collate and run tests: + +return [] -- Template Haskell splice. See QuickCheck hackage docs. +runTests :: IO Bool +runTests = $quickCheckAll + +main :: IO () +main = do + allClear <- runTests + if allClear + then exitSuccess + else exitFailure + +--------- Manual repl test fragments: + +-- 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) '.'