Safe Haskell	None
Language	GHC2021

AtCoder.Extra.Monoid.V2

Contents

V2
Constructors

Description

A monoid acted on by Mat2x2 or Affine1, an affine transformation target.

As an `Affine1` action target

Compared to Sum, V2 hold the length in the second value.

Since: 1.1.0.0

Synopsis

newtype V2 a = V2 (V2Repr a)
type V2Repr a = (a, a)
new :: Num a => a -> V2 a
unV2 :: V2 a -> a
zero :: Num a => V2 a
isZero :: (Num a, Eq a) => V2 a -> Bool

V2

newtype V2 a Source #

A monoid acted on by Mat2x2, an affine transformation target.

Example

Expand

>>> import AtCoder.Extra.Monoid.Mat2x2 (Mat2x2(..))
>>> import AtCoder.Extra.Monoid.Mat2x2 qualified as Mat2x2
>>> import AtCoder.Extra.Monoid.V2 (V2(..))
>>> import AtCoder.Extra.Monoid.V2 qualified as V2
>>> import AtCoder.LazySegTree qualified as LST
>>> import Data.Vector.Unboxed qualified as VU
>>> seg <- LST.build @_ @(Mat2x2 Int) @(V2 Int) . VU.map V2.new $ VU.fromList [1, 2, 3, 4]
>>> LST.applyIn seg 1 3 $ Mat2x2.new 2 1 -- [1, 5, 7, 4]
>>> V2.unV2 <$> LST.prod seg 1 3
12

Since: 1.1.0.0

Constructors

V2 (V2Repr a)

Instances

Instances details

Unbox a => Vector Vector (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods basicUnsafeFreeze :: Mutable Vector s (V2 a) -> ST s (Vector (V2 a)) basicUnsafeThaw :: Vector (V2 a) -> ST s (Mutable Vector s (V2 a)) basicLength :: Vector (V2 a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) basicUnsafeIndexM :: Vector (V2 a) -> Int -> Box (V2 a) basicUnsafeCopy :: Mutable Vector s (V2 a) -> Vector (V2 a) -> ST s () elemseq :: Vector (V2 a) -> V2 a -> b -> b
Unbox a => MVector MVector (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods basicLength :: MVector s (V2 a) -> Int basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool basicUnsafeNew :: Int -> ST s (MVector s (V2 a)) basicInitialize :: MVector s (V2 a) -> ST s () basicUnsafeReplicate :: Int -> V2 a -> ST s (MVector s (V2 a)) basicUnsafeRead :: MVector s (V2 a) -> Int -> ST s (V2 a) basicUnsafeWrite :: MVector s (V2 a) -> Int -> V2 a -> ST s () basicClear :: MVector s (V2 a) -> ST s () basicSet :: MVector s (V2 a) -> V2 a -> ST s () basicUnsafeCopy :: MVector s (V2 a) -> MVector s (V2 a) -> ST s () basicUnsafeMove :: MVector s (V2 a) -> MVector s (V2 a) -> ST s () basicUnsafeGrow :: MVector s (V2 a) -> Int -> ST s (MVector s (V2 a))
Num a => Monoid (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods mempty :: V2 a # mappend :: V2 a -> V2 a -> V2 a # mconcat :: [V2 a] -> V2 a #
Num a => Semigroup (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods (<>) :: V2 a -> V2 a -> V2 a # sconcat :: NonEmpty (V2 a) -> V2 a # stimes :: Integral b => b -> V2 a -> V2 a #
Show a => Show (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Eq a => Eq (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Ord a => Ord (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 Methods compare :: V2 a -> V2 a -> Ordering # (<) :: V2 a -> V2 a -> Bool # (<=) :: V2 a -> V2 a -> Bool # (>) :: V2 a -> V2 a -> Bool # (>=) :: V2 a -> V2 a -> Bool # max :: V2 a -> V2 a -> V2 a # min :: V2 a -> V2 a -> V2 a #
Unbox a => Unbox (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2
Num a => SegAct (Affine1 a) (V2 a) Source #	Since: 1.2.2.0
Instance details Defined in AtCoder.Extra.Monoid.Affine1 Methods segAct :: Affine1 a -> V2 a -> V2 a Source # segActWithLength :: Int -> Affine1 a -> V2 a -> V2 a Source #
Num a => SegAct (Mat2x2 a) (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.Mat2x2 Methods segAct :: Mat2x2 a -> V2 a -> V2 a Source # segActWithLength :: Int -> Mat2x2 a -> V2 a -> V2 a Source #
Num a => SegAct (Dual (Affine1 a)) (V2 a) Source #	Since: 1.2.2.0
Instance details Defined in AtCoder.Extra.Monoid.Affine1 Methods segAct :: Dual (Affine1 a) -> V2 a -> V2 a Source # segActWithLength :: Int -> Dual (Affine1 a) -> V2 a -> V2 a Source #
Num a => SegAct (Dual (Mat2x2 a)) (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.Mat2x2 Methods segAct :: Dual (Mat2x2 a) -> V2 a -> V2 a Source # segActWithLength :: Int -> Dual (Mat2x2 a) -> V2 a -> V2 a Source #
newtype MVector s (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 newtype MVector s (V2 a) = MV_V2 (MVector s (V2Repr a))
newtype Vector (V2 a) Source #	Since: 1.1.0.0
Instance details Defined in AtCoder.Extra.Monoid.V2 newtype Vector (V2 a) = V_V2 (Vector (V2Repr a))