Data.BinaryTree

Several types of Binary trees.

Documentation

data BinLeafTree v a

Binary tree that stores its values (of type a) in the leaves. Internal nodes store something of type v.

Constructors

Leaf !a

Node (BinLeafTree v a) !v (BinLeafTree v a)

Instances

Bifunctor BinLeafTree

Defined in Data.BinaryTree

Methods

bimap :: (a -> b) -> (c -> d) -> BinLeafTree a c -> BinLeafTree b d

first :: (a -> b) -> BinLeafTree a c -> BinLeafTree b c

second :: (b -> c) -> BinLeafTree a b -> BinLeafTree a c

Measured v a => Measured v (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

measure :: BinLeafTree v a -> v

Functor (BinLeafTree v)

Defined in Data.BinaryTree

Methods

fmap :: (a -> b) -> BinLeafTree v a -> BinLeafTree v b

(<$) :: a -> BinLeafTree v b -> BinLeafTree v a

Foldable (BinLeafTree v)

Defined in Data.BinaryTree

Methods

fold :: Monoid m => BinLeafTree v m -> m

foldMap :: Monoid m => (a -> m) -> BinLeafTree v a -> m

foldMap' :: Monoid m => (a -> m) -> BinLeafTree v a -> m

foldr :: (a -> b -> b) -> b -> BinLeafTree v a -> b

foldr' :: (a -> b -> b) -> b -> BinLeafTree v a -> b

foldl :: (b -> a -> b) -> b -> BinLeafTree v a -> b

foldl' :: (b -> a -> b) -> b -> BinLeafTree v a -> b

foldr1 :: (a -> a -> a) -> BinLeafTree v a -> a

foldl1 :: (a -> a -> a) -> BinLeafTree v a -> a

toList :: BinLeafTree v a -> [a]

null :: BinLeafTree v a -> Bool

length :: BinLeafTree v a -> Int

elem :: Eq a => a -> BinLeafTree v a -> Bool

maximum :: Ord a => BinLeafTree v a -> a

minimum :: Ord a => BinLeafTree v a -> a

sum :: Num a => BinLeafTree v a -> a

product :: Num a => BinLeafTree v a -> a

Traversable (BinLeafTree v)

Defined in Data.BinaryTree

Methods

traverse :: Applicative f => (a -> f b) -> BinLeafTree v a -> f (BinLeafTree v b)

sequenceA :: Applicative f => BinLeafTree v (f a) -> f (BinLeafTree v a)

mapM :: Monad m => (a -> m b) -> BinLeafTree v a -> m (BinLeafTree v b)

sequence :: Monad m => BinLeafTree v (m a) -> m (BinLeafTree v a)

Foldable1 (BinLeafTree v)

Defined in Data.BinaryTree

Methods

fold1 :: Semigroup m => BinLeafTree v m -> m

foldMap1 :: Semigroup m => (a -> m) -> BinLeafTree v a -> m

toNonEmpty :: BinLeafTree v a -> NonEmpty a

(Eq a, Eq v) => Eq (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

(==) :: BinLeafTree v a -> BinLeafTree v a -> Bool

(/=) :: BinLeafTree v a -> BinLeafTree v a -> Bool

(Ord a, Ord v) => Ord (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

compare :: BinLeafTree v a -> BinLeafTree v a -> Ordering

(<) :: BinLeafTree v a -> BinLeafTree v a -> Bool

(<=) :: BinLeafTree v a -> BinLeafTree v a -> Bool

(>) :: BinLeafTree v a -> BinLeafTree v a -> Bool

(>=) :: BinLeafTree v a -> BinLeafTree v a -> Bool

max :: BinLeafTree v a -> BinLeafTree v a -> BinLeafTree v a

min :: BinLeafTree v a -> BinLeafTree v a -> BinLeafTree v a

(Read a, Read v) => Read (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

readsPrec :: Int -> ReadS (BinLeafTree v a)

readList :: ReadS [BinLeafTree v a]

readPrec :: ReadPrec (BinLeafTree v a)

readListPrec :: ReadPrec [BinLeafTree v a]

(Show a, Show v) => Show (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

showsPrec :: Int -> BinLeafTree v a -> ShowS

show :: BinLeafTree v a -> String

showList :: [BinLeafTree v a] -> ShowS

Generic (BinLeafTree v a)

Defined in Data.BinaryTree

Associated Types

type Rep (BinLeafTree v a) :: Type -> Type

Methods

from :: BinLeafTree v a -> Rep (BinLeafTree v a) x

to :: Rep (BinLeafTree v a) x -> BinLeafTree v a

Measured v a => Semigroup (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

(<>) :: BinLeafTree v a -> BinLeafTree v a -> BinLeafTree v a

sconcat :: NonEmpty (BinLeafTree v a) -> BinLeafTree v a

stimes :: Integral b => b -> BinLeafTree v a -> BinLeafTree v a

(Arbitrary a, Arbitrary v) => Arbitrary (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

arbitrary :: Gen (BinLeafTree v a)

shrink :: BinLeafTree v a -> [BinLeafTree v a]

(NFData v, NFData a) => NFData (BinLeafTree v a)

Defined in Data.BinaryTree

Methods

rnf :: BinLeafTree v a -> ()

type Rep (BinLeafTree v a)

Defined in Data.BinaryTree

type Rep (BinLeafTree v a) = D1 ('MetaData "BinLeafTree" "Data.BinaryTree" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "Leaf" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :+: C1 ('MetaCons "Node" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BinLeafTree v a)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 v) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BinLeafTree v a)))))

node :: Measured v a => BinLeafTree v a -> BinLeafTree v a -> BinLeafTree v a

smart constructor

asBalancedBinLeafTree :: NonEmpty a -> BinLeafTree Size (Elem a)

Create a balanced tree, i.e. a tree of height \(O(\log n)\) with the elements in the leaves.

\(O(n)\) time.

foldUp :: (b -> v -> b -> b) -> (a -> b) -> BinLeafTree v a -> b

Given a function to combine internal nodes into b's and leafs into b's, traverse the tree bottom up, and combine everything into one b.

foldUpData :: (w -> v -> w -> w) -> (a -> w) -> BinLeafTree v a -> BinLeafTree w a

Traverses the tree bottom up, recomputing the assocated values.

zipExactWith :: (u -> v -> w) -> (a -> b -> c) -> BinLeafTree u a -> BinLeafTree v b -> BinLeafTree w c

Takes two trees, that have the same structure, and uses the provided functions to "zip" them together

Converting into a Data.Tree

toRoseTree :: BinLeafTree v a -> Tree (TreeNode v a)

\( O(n) \) Convert binary tree to a rose tree, aka Tree.

drawTree :: (Show v, Show a) => BinLeafTree v a -> String

2-dimensional ASCII drawing of a tree.

Internal Node Tree

data BinaryTree a

Binary tree in which we store the values of type a in internal nodes.

Constructors

Nil

Internal (BinaryTree a) !a (BinaryTree a)

Instances

Functor BinaryTree

Defined in Data.BinaryTree

Methods

fmap :: (a -> b) -> BinaryTree a -> BinaryTree b

(<$) :: a -> BinaryTree b -> BinaryTree a

Foldable BinaryTree

Defined in Data.BinaryTree

Methods

fold :: Monoid m => BinaryTree m -> m

foldMap :: Monoid m => (a -> m) -> BinaryTree a -> m

foldMap' :: Monoid m => (a -> m) -> BinaryTree a -> m

foldr :: (a -> b -> b) -> b -> BinaryTree a -> b

foldr' :: (a -> b -> b) -> b -> BinaryTree a -> b

foldl :: (b -> a -> b) -> b -> BinaryTree a -> b

foldl' :: (b -> a -> b) -> b -> BinaryTree a -> b

foldr1 :: (a -> a -> a) -> BinaryTree a -> a

foldl1 :: (a -> a -> a) -> BinaryTree a -> a

toList :: BinaryTree a -> [a]

null :: BinaryTree a -> Bool

length :: BinaryTree a -> Int

elem :: Eq a => a -> BinaryTree a -> Bool

maximum :: Ord a => BinaryTree a -> a

minimum :: Ord a => BinaryTree a -> a

sum :: Num a => BinaryTree a -> a

product :: Num a => BinaryTree a -> a

Traversable BinaryTree

Defined in Data.BinaryTree

Methods

traverse :: Applicative f => (a -> f b) -> BinaryTree a -> f (BinaryTree b)

sequenceA :: Applicative f => BinaryTree (f a) -> f (BinaryTree a)

mapM :: Monad m => (a -> m b) -> BinaryTree a -> m (BinaryTree b)

sequence :: Monad m => BinaryTree (m a) -> m (BinaryTree a)

Eq a => Eq (BinaryTree a)

Defined in Data.BinaryTree

Methods

(==) :: BinaryTree a -> BinaryTree a -> Bool

(/=) :: BinaryTree a -> BinaryTree a -> Bool

Ord a => Ord (BinaryTree a)

Defined in Data.BinaryTree

Methods

compare :: BinaryTree a -> BinaryTree a -> Ordering

(<) :: BinaryTree a -> BinaryTree a -> Bool

(<=) :: BinaryTree a -> BinaryTree a -> Bool

(>) :: BinaryTree a -> BinaryTree a -> Bool

(>=) :: BinaryTree a -> BinaryTree a -> Bool

max :: BinaryTree a -> BinaryTree a -> BinaryTree a

min :: BinaryTree a -> BinaryTree a -> BinaryTree a

Read a => Read (BinaryTree a)

Defined in Data.BinaryTree

Methods

readsPrec :: Int -> ReadS (BinaryTree a)

readList :: ReadS [BinaryTree a]

readPrec :: ReadPrec (BinaryTree a)

readListPrec :: ReadPrec [BinaryTree a]

Show a => Show (BinaryTree a)

Defined in Data.BinaryTree

Methods

showsPrec :: Int -> BinaryTree a -> ShowS

show :: BinaryTree a -> String

showList :: [BinaryTree a] -> ShowS

Generic (BinaryTree a)

Defined in Data.BinaryTree

Associated Types

type Rep (BinaryTree a) :: Type -> Type

Methods

from :: BinaryTree a -> Rep (BinaryTree a) x

to :: Rep (BinaryTree a) x -> BinaryTree a

Arbitrary a => Arbitrary (BinaryTree a)

Defined in Data.BinaryTree

Methods

arbitrary :: Gen (BinaryTree a)

shrink :: BinaryTree a -> [BinaryTree a]

NFData a => NFData (BinaryTree a)

Defined in Data.BinaryTree

Methods

rnf :: BinaryTree a -> ()

type Rep (BinaryTree a)

Defined in Data.BinaryTree

type Rep (BinaryTree a) = D1 ('MetaData "BinaryTree" "Data.BinaryTree" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "Nil" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Internal" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BinaryTree a)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BinaryTree a)))))

access :: BinaryTree a -> Maybe a

Get the element stored at the root, if it exists

asBalancedBinTree :: [a] -> BinaryTree a

Create a balanced binary tree.

running time: \(O(n)\)

foldBinaryUp :: b -> (a -> b -> b -> b) -> BinaryTree a -> BinaryTree (a, b)

Fold function for folding over a binary tree.

toRoseTree' :: BinaryTree a -> Maybe (Tree a)

Convert a BinaryTree into a RoseTree

drawTree' :: Show a => BinaryTree a -> String

Draw a binary tree.