{-# LANGUAGE DisambiguateRecordFields #-}
{-# LANGUAGE TypeFamilies #-}

-- | A dynamic, persistent segment tree that covers a half-open interval \([l_0, r_0)\). Nodes are
-- instantinated as needed, with the required capacity being /approximately/ \(4q \log_2 L\), where
-- \(q\) is the number of mutable operations and \(L\) is the length of the interval.
--
-- ==== __Example__
--
-- >>> import AtCoder.Extra.DynSegTree.Persistent qualified as Seg
-- >>> import Data.Semigroup (Sum (..))
-- >>> import Data.Vector.Unboxed qualified as VU
--
-- Create a `DynSegTree` over \([0, 4)\) with some initial capacity:
--
-- >>> let len = 4; q = 2
-- >>> seg <- Seg.new @_ @(Sum Int) (Seg.recommendedCapacity len q) 0 4
--
-- Different from the @SegTree@ module, it requires explicit root handle:
--
-- >>> -- [0, 0, 0, 0]
-- >>> root <- Seg.newRoot seg
-- >>> root1 <- Seg.write seg root 1 $ Sum 10
-- >>> root2 <- Seg.write seg root1 2 $ Sum 20
-- >>> -- [0, 10, 20, 0]
-- >>> Seg.prod seg root2 0 3
-- Sum {getSum = 30}
--
-- >>> Seg.maxRight seg root2 (< (Sum 30))
-- 2
--
-- @since 1.2.1.0
module AtCoder.Extra.DynSegTree.Persistent
  ( -- * Dynamic segment tree
    Raw.DynSegTree (..),

    -- * Re-exports
    P.Index (..),

    -- * Constructors
    new,
    buildWith,
    recommendedCapacity,
    newRoot,
    newSeq,

    -- * Accessing elements
    write,
    modify,
    modifyM,
    -- exchange,
    -- read,

    -- * Products
    prod,
    -- prodMaybe,
    allProd, -- FIXME: rename it to prodAll

    -- * Tree operations
    resetInterval,

    -- * Binary searches
    maxRight,
    maxRightM,
    -- -- * Conversions
    -- freeze,

    -- * Clear
    clear,
  )
where

import AtCoder.Extra.DynSegTree.Raw qualified as Raw
import AtCoder.Extra.Pool qualified as P
import Control.Monad.Primitive (PrimMonad, PrimState, stToPrim)
import Data.Vector.Unboxed qualified as VU
import GHC.Stack (HasCallStack)
import Prelude hiding (read)

-- | \(O(n)\) Creates a `DynSegTree` of capacity \(n\) for interval \([l_0, r_0)\) with `mempty` as
-- initial leaf values.
--
-- @since 1.2.1.0
{-# INLINE new #-}
new ::
  (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) =>
  -- | Capacity \(n\)
  Int ->
  -- | Left index boundary \(l_0\)
  Int ->
  -- | Right index boundary \(r_0\)
  Int ->
  -- | Dynamic, persistent segment tree
  m (Raw.DynSegTree (PrimState m) a)
new :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
Int -> Int -> Int -> m (DynSegTree (PrimState m) a)
new Int
nDst Int
l Int
r = ST (PrimState m) (DynSegTree (PrimState m) a)
-> m (DynSegTree (PrimState m) a)
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) (DynSegTree (PrimState m) a)
 -> m (DynSegTree (PrimState m) a))
-> ST (PrimState m) (DynSegTree (PrimState m) a)
-> m (DynSegTree (PrimState m) a)
forall a b. (a -> b) -> a -> b
$ Bool
-> Int
-> Int
-> Int
-> (Int -> Int -> a)
-> ST (PrimState m) (DynSegTree (PrimState m) a)
forall a s.
(HasCallStack, Unbox a) =>
Bool
-> Int -> Int -> Int -> (Int -> Int -> a) -> ST s (DynSegTree s a)
Raw.newST Bool
True Int
nDst Int
l Int
r (\Int
_ Int
_ -> a
forall a. Monoid a => a
mempty)

-- | \(O(n)\) Creates a `DynSegTree` of capacity \(n\) for interval \([l_0, r_0)\) with initial
-- value assignment \(g(l, r)\).
--
-- @since 1.2.1.0
{-# INLINE buildWith #-}
buildWith ::
  (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) =>
  -- | Capacity \(n\)
  Int ->
  -- | Left index boundary \(l_0)\)
  Int ->
  -- | Right index boundary \(r_0)\)
  Int ->
  -- | Initial monoid value assignment \(g: (l, r) \rightarrow a\)
  (Int -> Int -> a) ->
  -- | Dynamic, persistent segment tree
  m (Raw.DynSegTree (PrimState m) a)
buildWith :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
Int
-> Int
-> Int
-> (Int -> Int -> a)
-> m (DynSegTree (PrimState m) a)
buildWith Int
nDst Int
l Int
r Int -> Int -> a
g = ST (PrimState m) (DynSegTree (PrimState m) a)
-> m (DynSegTree (PrimState m) a)
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) (DynSegTree (PrimState m) a)
 -> m (DynSegTree (PrimState m) a))
-> ST (PrimState m) (DynSegTree (PrimState m) a)
-> m (DynSegTree (PrimState m) a)
forall a b. (a -> b) -> a -> b
$ Bool
-> Int
-> Int
-> Int
-> (Int -> Int -> a)
-> ST (PrimState m) (DynSegTree (PrimState m) a)
forall a s.
(HasCallStack, Unbox a) =>
Bool
-> Int -> Int -> Int -> (Int -> Int -> a) -> ST s (DynSegTree s a)
Raw.newST Bool
True Int
nDst Int
l Int
r Int -> Int -> a
g

-- | \(O(1)\) Returns recommended capacity for \(L\) and \(q\): \(2q \log_2 L\).
--
-- @since 1.2.1.0
{-# INLINE recommendedCapacity #-}
recommendedCapacity :: Int -> Int -> Int
recommendedCapacity :: Int -> Int -> Int
recommendedCapacity Int
n Int
q = Int
2 Int -> Int -> Int
forall a. Num a => a -> a -> a
* Int
q Int -> Int -> Int
forall a. Num a => a -> a -> a
* (Int
2 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Double -> Int
forall b. Integral b => Double -> b
forall a b. (RealFrac a, Integral b) => a -> b
ceiling (Double -> Double -> Double
forall a. Floating a => a -> a -> a
logBase Double
2 (Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) :: Double))

-- | \(O(1)\) Creates a new root in \([l_0, r_0)\).
--
-- @since 1.2.1.0
newRoot :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> m P.Index
newRoot :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> m Index
newRoot DynSegTree (PrimState m) a
dst = ST (PrimState m) Index -> m Index
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) Index -> m Index)
-> ST (PrimState m) Index -> m Index
forall a b. (a -> b) -> a -> b
$ DynSegTree (PrimState m) a -> ST (PrimState m) Index
forall a s.
(HasCallStack, Monoid a, Unbox a) =>
DynSegTree s a -> ST s Index
Raw.newRootST DynSegTree (PrimState m) a
dst

-- | \(O(L)\) Creates a new root node with contiguous leaf values. User would want to use a strict
-- segment tree instead.
--
-- ==== Constraints
-- - \([l_0, r_0) = [0, L)\): The index boundary of the segment tree must match the sequence.
--
-- @since 1.2.1.0
newSeq :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> VU.Vector a -> m P.Index
newSeq :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Vector a -> m Index
newSeq DynSegTree (PrimState m) a
dst Vector a
xs = ST (PrimState m) Index -> m Index
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) Index -> m Index)
-> ST (PrimState m) Index -> m Index
forall a b. (a -> b) -> a -> b
$ DynSegTree (PrimState m) a -> Vector a -> ST (PrimState m) Index
forall a s.
(HasCallStack, Monoid a, Unbox a) =>
DynSegTree s a -> Vector a -> ST s Index
Raw.newSeqST DynSegTree (PrimState m) a
dst Vector a
xs

-- | \(O(\log L)\) Writes to the monoid value of the node at \(i\).
--
-- ==== Constraints
-- - \(l_0 \le i \lt r_0\)
--
-- @since 1.2.1.0
{-# INLINE write #-}
write :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> Int -> a -> m P.Index
write :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> Int -> a -> m Index
write DynSegTree (PrimState m) a
dst Index
root Int
i a
x = ST (PrimState m) Index -> m Index
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) Index -> m Index)
-> ST (PrimState m) Index -> m Index
forall a b. (a -> b) -> a -> b
$ do
  DynSegTree (PrimState (ST (PrimState m))) a
-> Index
-> (a -> ST (PrimState m) a)
-> Int
-> ST (PrimState m) Index
forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m a) -> Int -> m Index
Raw.modifyMST DynSegTree (PrimState m) a
DynSegTree (PrimState (ST (PrimState m))) a
dst Index
root (a -> ST (PrimState m) a
forall a. a -> ST (PrimState m) a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> ST (PrimState m) a) -> (a -> a) -> a -> ST (PrimState m) a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a -> a
forall a b. a -> b -> a
const a
x) Int
i

-- | \(O(\log L)\) Modifies the monoid value of the node at \(i\).
--
-- ==== Constraints
-- - \(l_0 \le i \lt r_0\)
--
-- @since 1.2.1.0
{-# INLINE modify #-}
modify :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> (a -> a) -> Int -> m P.Index
modify :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> a) -> Int -> m Index
modify DynSegTree (PrimState m) a
dst Index
root a -> a
f Int
i = ST (PrimState m) Index -> m Index
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) Index -> m Index)
-> ST (PrimState m) Index -> m Index
forall a b. (a -> b) -> a -> b
$ do
  DynSegTree (PrimState (ST (PrimState m))) a
-> Index
-> (a -> ST (PrimState m) a)
-> Int
-> ST (PrimState m) Index
forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m a) -> Int -> m Index
Raw.modifyMST DynSegTree (PrimState m) a
DynSegTree (PrimState (ST (PrimState m))) a
dst Index
root (a -> ST (PrimState m) a
forall a. a -> ST (PrimState m) a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> ST (PrimState m) a) -> (a -> a) -> a -> ST (PrimState m) a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a
f) Int
i

-- | \(O(\log L)\) Modifies the monoid value of the node at \(i\).
--
-- ==== Constraints
-- - \(l_0 \le i \lt r_0\)
--
-- @since 1.2.1.0
{-# INLINE modifyM #-}
modifyM :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> (a -> m a) -> Int -> m P.Index
modifyM :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m a) -> Int -> m Index
modifyM DynSegTree (PrimState m) a
dst Index
root a -> m a
f Int
i = do
  DynSegTree (PrimState m) a -> Index -> (a -> m a) -> Int -> m Index
forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m a) -> Int -> m Index
Raw.modifyMST DynSegTree (PrimState m) a
dst Index
root a -> m a
f Int
i

-- | \(O(\log L)\) Returns the monoid product in \([l, r)\).
--
-- ==== Constraints
-- - \(l_0 \le l \le r \le r_0\)
--
-- @since 1.2.1.0
{-# INLINE prod #-}
prod :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> Int -> Int -> m a
prod :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> Int -> Int -> m a
prod DynSegTree (PrimState m) a
dst Index
root Int
l Int
r = ST (PrimState m) a -> m a
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) a -> m a) -> ST (PrimState m) a -> m a
forall a b. (a -> b) -> a -> b
$ do
  DynSegTree (PrimState m) a
-> Index -> Int -> Int -> ST (PrimState m) a
forall a s.
(HasCallStack, Monoid a, Unbox a) =>
DynSegTree s a -> Index -> Int -> Int -> ST s a
Raw.prodST DynSegTree (PrimState m) a
dst Index
root Int
l Int
r

-- | \(O(\log L)\) Returns the monoid product in \([l_0, r_0)\).
--
-- @since 1.2.1.0
{-# INLINE allProd #-}
allProd :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> m a
allProd :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> m a
allProd dst :: DynSegTree (PrimState m) a
dst@Raw.DynSegTree {Int
l0Dst :: Int
l0Dst :: forall s a. DynSegTree s a -> Int
l0Dst, Int
r0Dst :: Int
r0Dst :: forall s a. DynSegTree s a -> Int
r0Dst} Index
root = ST (PrimState m) a -> m a
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) a -> m a) -> ST (PrimState m) a -> m a
forall a b. (a -> b) -> a -> b
$ do
  DynSegTree (PrimState m) a
-> Index -> Int -> Int -> ST (PrimState m) a
forall a s.
(HasCallStack, Monoid a, Unbox a) =>
DynSegTree s a -> Index -> Int -> Int -> ST s a
Raw.prodST DynSegTree (PrimState m) a
dst Index
root Int
l0Dst Int
r0Dst

-- | \(O(\log L)\) Resets an interval \([l, r)\) to initial monoid values.
--
-- ==== Constraints
-- - \(l_0 \le l \le r \le r_0\)
--
-- @since 1.2.1.0
{-# INLINE resetInterval #-}
resetInterval :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> Int -> Int -> m P.Index
resetInterval :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> Int -> Int -> m Index
resetInterval DynSegTree (PrimState m) a
dst Index
root Int
l Int
r = ST (PrimState m) Index -> m Index
forall (m :: * -> *) a. PrimMonad m => ST (PrimState m) a -> m a
stToPrim (ST (PrimState m) Index -> m Index)
-> ST (PrimState m) Index -> m Index
forall a b. (a -> b) -> a -> b
$ do
  DynSegTree (PrimState m) a
-> Index -> Int -> Int -> ST (PrimState m) Index
forall a s.
(HasCallStack, Monoid a, Unbox a) =>
DynSegTree s a -> Index -> Int -> Int -> ST s Index
Raw.resetIntervalST DynSegTree (PrimState m) a
dst Index
root Int
l Int
r

-- | \(O(\log L)\) Returns the maximum \(r \in [l_0, r_0)\) where \(f(a_{l_0} a_{l_0 + 1} \dots a_{r - 1})\) holds.
--
-- @since 1.2.1.0
{-# INLINE maxRight #-}
maxRight :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> (a -> Bool) -> m Int
maxRight :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> Bool) -> m Int
maxRight DynSegTree (PrimState m) a
dst Index
root a -> Bool
f = do
  DynSegTree (PrimState m) a -> Index -> (a -> m Bool) -> m Int
forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m Bool) -> m Int
Raw.maxRightM DynSegTree (PrimState m) a
dst Index
root (Bool -> m Bool
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Bool -> m Bool) -> (a -> Bool) -> a -> m Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
f)

-- | \(O(\log L)\) Returns the maximum \(r \in [l_0, r_0)\) where \(f(a_{l_0} a_{l_0 + 1} \dots a_{r - 1})\) holds.
--
-- @since 1.2.1.0
{-# INLINE maxRightM #-}
maxRightM :: (HasCallStack, PrimMonad m, Monoid a, VU.Unbox a) => Raw.DynSegTree (PrimState m) a -> P.Index -> (a -> m Bool) -> m Int
maxRightM :: forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m Bool) -> m Int
maxRightM DynSegTree (PrimState m) a
dst Index
root a -> m Bool
f = do
  DynSegTree (PrimState m) a -> Index -> (a -> m Bool) -> m Int
forall (m :: * -> *) a.
(HasCallStack, PrimMonad m, Monoid a, Unbox a) =>
DynSegTree (PrimState m) a -> Index -> (a -> m Bool) -> m Int
Raw.maxRightM DynSegTree (PrimState m) a
dst Index
root a -> m Bool
f

-- | \(O(\log L)\) Claers all the nodes from the storage.
--
-- @since 1.2.2.0
{-# INLINE clear #-}
clear :: (PrimMonad m) => Raw.DynSegTree (PrimState m) a -> m ()
clear :: forall (m :: * -> *) a.
PrimMonad m =>
DynSegTree (PrimState m) a -> m ()
clear DynSegTree (PrimState m) a
dst = do
  Pool (PrimState m) () -> m ()
forall (m :: * -> *) a. PrimMonad m => Pool (PrimState m) a -> m ()
P.clear (DynSegTree (PrimState m) a -> Pool (PrimState m) ()
forall s a. DynSegTree s a -> Pool s ()
Raw.poolDst DynSegTree (PrimState m) a
dst)