-- |
-- Module     : Simulation.Aivika.PriorityQueue.EventQueue.Pure
-- Copyright  : Copyright (c) 2023, David Sorokin <davsor@mail.ru>
-- License    : BSD3
-- Maintainer : David Sorokin <david.sorokin@gmail.com>
-- Stability  : experimental
-- Tested with: GHC 9.2.8
--
-- An immutable heap-based priority queue based on book
-- Algorithms: A Functional Programming Approach by
-- Fethi Rabhi and Guy Lapalme.
--
-- The queue allows specifying priorities along with keys.
--
module Simulation.Aivika.PriorityQueue.EventQueue.Pure 
       (PriorityQueue, 
        Priority,
        queueNull, 
        queueCount,
        emptyQueue, 
        enqueue, 
        dequeue, 
        queueFront) where 

import Control.Monad

-- | The priority value (greater is higher).
type Priority = Int

-- | The 'PriorityQueue' type represents an immutable heap-based priority queue.
data PriorityQueue a = EmptyQueue
                     | Queue !Int !Double !Priority a !Int (PriorityQueue a) (PriorityQueue a)
                       deriving Priority -> PriorityQueue a -> ShowS
forall a. Show a => Priority -> PriorityQueue a -> ShowS
forall a. Show a => [PriorityQueue a] -> ShowS
forall a. Show a => PriorityQueue a -> String
forall a.
(Priority -> a -> ShowS)
-> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [PriorityQueue a] -> ShowS
$cshowList :: forall a. Show a => [PriorityQueue a] -> ShowS
show :: PriorityQueue a -> String
$cshow :: forall a. Show a => PriorityQueue a -> String
showsPrec :: Priority -> PriorityQueue a -> ShowS
$cshowsPrec :: forall a. Show a => Priority -> PriorityQueue a -> ShowS
Show

-- | Test whether the priority queue is empty.
queueNull :: PriorityQueue a -> Bool
queueNull :: forall a. PriorityQueue a -> Bool
queueNull PriorityQueue a
EmptyQueue = Bool
True
queueNull PriorityQueue a
_          = Bool
False

-- | Return the number of elements in the priority queue.
queueCount :: PriorityQueue a -> Int
queueCount :: forall a. PriorityQueue a -> Priority
queueCount PriorityQueue a
EmptyQueue = Priority
0
queueCount (Queue Priority
n Double
k Priority
p a
v Priority
r PriorityQueue a
a PriorityQueue a
b) = Priority
n

-- | An empty priority queue.
emptyQueue :: PriorityQueue a
emptyQueue :: forall a. PriorityQueue a
emptyQueue = forall a. PriorityQueue a
EmptyQueue

-- | Enqueue a new element with the specified priority.
enqueue :: PriorityQueue a -> Double -> Priority -> a -> PriorityQueue a
enqueue :: forall a.
PriorityQueue a -> Double -> Priority -> a -> PriorityQueue a
enqueue PriorityQueue a
pq Double
k Priority
p a
v = forall a. PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues PriorityQueue a
pq (forall a.
Priority
-> Double
-> Priority
-> a
-> Priority
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
Queue Priority
1 Double
k Priority
p a
v Priority
1 forall a. PriorityQueue a
EmptyQueue forall a. PriorityQueue a
EmptyQueue)

-- | Dequeue the element with the minimal priority.
dequeue :: PriorityQueue a -> PriorityQueue a
dequeue :: forall a. PriorityQueue a -> PriorityQueue a
dequeue PriorityQueue a
EmptyQueue = forall a. HasCallStack => String -> a
error String
"The queue is empty: dequeue"
dequeue (Queue Priority
n Double
k Priority
p a
v Priority
r PriorityQueue a
a PriorityQueue a
b) = forall a. PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues PriorityQueue a
a PriorityQueue a
b

-- | Return the element with the minimal priority.
queueFront :: PriorityQueue a -> (Double, Priority, a)
queueFront :: forall a. PriorityQueue a -> (Double, Priority, a)
queueFront PriorityQueue a
EmptyQueue = forall a. HasCallStack => String -> a
error String
"The queue is empty: queueFront"
queueFront (Queue Priority
n Double
k Priority
p a
v Priority
r PriorityQueue a
a PriorityQueue a
b) = (Double
k, Priority
p, a
v)

-- | Return the rank of the priority queue.
queueRank :: PriorityQueue a -> Int
queueRank :: forall a. PriorityQueue a -> Priority
queueRank PriorityQueue a
EmptyQueue = Priority
0
queueRank (Queue Priority
n Double
k Priority
p a
v Priority
r PriorityQueue a
a PriorityQueue a
b) = Priority
r

-- | Construct a new priority queue.
makeQueue :: Double -> Priority -> a -> PriorityQueue a -> PriorityQueue a -> PriorityQueue a
makeQueue :: forall a.
Double
-> Priority
-> a
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
makeQueue Double
k Priority
p a
v PriorityQueue a
a PriorityQueue a
b
  | forall a. PriorityQueue a -> Priority
queueRank PriorityQueue a
a forall a. Ord a => a -> a -> Bool
>= forall a. PriorityQueue a -> Priority
queueRank PriorityQueue a
b = Priority
n seq :: forall a b. a -> b -> b
`seq` forall a.
Priority
-> Double
-> Priority
-> a
-> Priority
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
Queue Priority
n Double
k Priority
p a
v (forall a. PriorityQueue a -> Priority
queueRank PriorityQueue a
b forall a. Num a => a -> a -> a
+ Priority
1) PriorityQueue a
a PriorityQueue a
b
  | Bool
otherwise                  = Priority
n seq :: forall a b. a -> b -> b
`seq` forall a.
Priority
-> Double
-> Priority
-> a
-> Priority
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
Queue Priority
n Double
k Priority
p a
v (forall a. PriorityQueue a -> Priority
queueRank PriorityQueue a
a forall a. Num a => a -> a -> a
+ Priority
1) PriorityQueue a
b PriorityQueue a
a
  where n :: Priority
n = forall a. PriorityQueue a -> Priority
queueCount PriorityQueue a
a forall a. Num a => a -> a -> a
+ forall a. PriorityQueue a -> Priority
queueCount PriorityQueue a
b forall a. Num a => a -> a -> a
+ Priority
1

-- | Merge two priority queues.
mergeQueues :: PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues :: forall a. PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues PriorityQueue a
h PriorityQueue a
EmptyQueue = PriorityQueue a
h
mergeQueues PriorityQueue a
EmptyQueue PriorityQueue a
h = PriorityQueue a
h
mergeQueues h1 :: PriorityQueue a
h1@(Queue Priority
_ Double
k1 Priority
p1 a
v1 Priority
_ PriorityQueue a
a1 PriorityQueue a
b1) h2 :: PriorityQueue a
h2@(Queue Priority
_ Double
k2 Priority
p2 a
v2 Priority
_ PriorityQueue a
a2 PriorityQueue a
b2)
  | Double -> Priority -> Double -> Priority -> Bool
lte Double
k1 Priority
p1 Double
k2 Priority
p2 = forall a.
Double
-> Priority
-> a
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
makeQueue Double
k1 Priority
p1 a
v1 PriorityQueue a
a1 (forall a. PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues PriorityQueue a
b1 PriorityQueue a
h2)
  | Bool
otherwise       = forall a.
Double
-> Priority
-> a
-> PriorityQueue a
-> PriorityQueue a
-> PriorityQueue a
makeQueue Double
k2 Priority
p2 a
v2 PriorityQueue a
a2 (forall a. PriorityQueue a -> PriorityQueue a -> PriorityQueue a
mergeQueues PriorityQueue a
h1 PriorityQueue a
b2)

-- | Whether the first pair is greater than the second one.
gt :: Double -> Priority -> Double -> Priority -> Bool
{-# INLINE gt #-}
gt :: Double -> Priority -> Double -> Priority -> Bool
gt Double
k1 Priority
p1 Double
k2 Priority
p2 = (Double
k1 forall a. Ord a => a -> a -> Bool
> Double
k2) Bool -> Bool -> Bool
|| (Double
k1 forall a. Eq a => a -> a -> Bool
== Double
k2 Bool -> Bool -> Bool
&& Priority
p1 forall a. Ord a => a -> a -> Bool
< Priority
p2)

-- | Whether the first pair is greater than or equal to the second one.
gte :: Double -> Priority -> Double -> Priority -> Bool
{-# INLINE gte #-}
gte :: Double -> Priority -> Double -> Priority -> Bool
gte Double
k1 Priority
p1 Double
k2 Priority
p2 = (Double
k1 forall a. Ord a => a -> a -> Bool
> Double
k2) Bool -> Bool -> Bool
|| (Double
k1 forall a. Eq a => a -> a -> Bool
== Double
k2 Bool -> Bool -> Bool
&& Priority
p1 forall a. Ord a => a -> a -> Bool
<= Priority
p2)

-- | Whether the first pair is less than the second one.
lt :: Double -> Priority -> Double -> Priority -> Bool
{-# INLINE lt #-}
lt :: Double -> Priority -> Double -> Priority -> Bool
lt Double
k1 Priority
p1 Double
k2 Priority
p2 = Double -> Priority -> Double -> Priority -> Bool
gt Double
k2 Priority
p2 Double
k1 Priority
p1

-- | Whether the first pair is less than or equal to the second one.
lte :: Double -> Priority -> Double -> Priority -> Bool
{-# INLINE lte #-}
lte :: Double -> Priority -> Double -> Priority -> Bool
lte Double
k1 Priority
p1 Double
k2 Priority
p2 = Double -> Priority -> Double -> Priority -> Bool
gte Double
k2 Priority
p2 Double
k1 Priority
p1