1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
|
{-# LANGUAGE UnicodeSyntax, MultiParamTypeClasses, FlexibleInstances #-}
module T2902_A_PairingSum (Sum(..), PSum) where
import T2902_Sum
data PSum a b = Empty | Tree a b [(PSum a b)]
instance (Ord a, Num b) ⇒ Sum PSum a b where
insert = insertX
union = unionX
unions = unionsX
extractMin = extractMinX
fromList = fromListX
toList = toListX
insertX ∷ (Ord a, Num b) ⇒ a → b → PSum a b → PSum a b
insertX v r = unionX $ Tree v r []
unionX ∷ (Ord a, Num b) ⇒ PSum a b → PSum a b → PSum a b
unionX x Empty = x
unionX Empty x = x
unionX x@(Tree v r xs) y@(Tree w s ys) =
case compare v w of
LT → Tree v r (y:xs)
GT → Tree w s (x:ys)
EQ → case r + s of
0 → z
t → insertX v t z
where z = unionX (unionsX xs) (unionsX ys)
unionsX ∷ (Ord a, Num b) ⇒ [PSum a b] → PSum a b
unionsX [] = Empty
unionsX [x] = x
unionsX (x : y : zs) = unionX (unionX x y) (unionsX zs)
extractMinX ∷ (Ord a, Num b) ⇒ PSum a b → ((a,b), PSum a b)
extractMinX Empty = undefined
extractMinX (Tree v r xs) = ((v,r), unionsX xs)
fromListX ∷ (Ord a, Num b) ⇒ [(a,b)] → PSum a b
fromListX [] = Empty
fromListX ((v,r):xs) = insertX v r $ fromListX xs
toListX ∷ (Ord a, Num b) ⇒ PSum a b → [(a,b)]
toListX Empty = []
toListX x = let (y, z) = extractMinX x in y : toListX z
|
