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
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
{-# LANGUAGE BangPatterns, ScopedTypeVariables #-}
-- |An efficient implementation of 'Data.Graph.Inductive.Graph.Graph'
-- using big-endian patricia tree (i.e. "Data.IntMap").
--
-- This module provides the following specialised functions to gain
-- more performance, using GHC's RULES pragma:
--
-- * 'Data.Graph.Inductive.Graph.insNode'
--
-- * 'Data.Graph.Inductive.Graph.insEdge'
--
-- * 'Data.Graph.Inductive.Graph.gmap'
--
-- * 'Data.Graph.Inductive.Graph.nmap'
--
-- * 'Data.Graph.Inductive.Graph.emap'
module Data.Graph.Inductive.PatriciaTree
( Gr
, UGr
)
where
import Data.Graph.Inductive.Graph
import Data.IntMap (IntMap)
import qualified Data.IntMap as IM
import Data.List
import Data.Maybe
import Control.Arrow(second)
newtype Gr a b = Gr (GraphRep a b)
type GraphRep a b = IntMap (Context' a b)
type Context' a b = (IntMap [b], a, IntMap [b])
type UGr = Gr () ()
instance Graph Gr where
-- required members
empty = Gr IM.empty
isEmpty (Gr g) = IM.null g
match = matchGr
mkGraph vs es = (insEdges' . insNodes vs) empty
where
insEdges' g = foldl' (flip insEdge) g es
labNodes (Gr g) = [ (node, label)
| (node, (_, label, _)) <- IM.toList g ]
-- overriding members for efficiency
noNodes (Gr g) = IM.size g
nodeRange (Gr g)
| IM.null g = (0, 0)
| otherwise = (ix (IM.minViewWithKey g), ix (IM.maxViewWithKey g))
where
ix = fst . fst . fromJust
labEdges (Gr g) = do (node, (_, _, s)) <- IM.toList g
(next, labels) <- IM.toList s
label <- labels
return (node, next, label)
instance DynGraph Gr where
(p, v, l, s) & (Gr g)
= let !g1 = IM.insert v (fromAdj p, l, fromAdj s) g
!g2 = addSucc g1 v p
!g3 = addPred g2 v s
in
Gr g3
matchGr :: Node -> Gr a b -> Decomp Gr a b
matchGr node (Gr g)
= case IM.lookup node g of
Nothing
-> (Nothing, Gr g)
Just (p, label, s)
-> let !g1 = IM.delete node g
!p' = IM.delete node p
!s' = IM.delete node s
!g2 = clearPred g1 node (IM.keys s')
!g3 = clearSucc g2 node (IM.keys p')
in
(Just (toAdj p', node, label, toAdj s), Gr g3)
{-# RULES
"insNode/Data.Graph.Inductive.PatriciaTree" insNode = fastInsNode
#-}
fastInsNode :: LNode a -> Gr a b -> Gr a b
fastInsNode (v, l) (Gr g) = g' `seq` Gr g'
where
g' = IM.insert v (IM.empty, l, IM.empty) g
{-# RULES
"insEdge/Data.Graph.Inductive.PatriciaTree" insEdge = fastInsEdge
#-}
fastInsEdge :: LEdge b -> Gr a b -> Gr a b
fastInsEdge (v, w, l) (Gr g) = g2 `seq` Gr g2
where
g1 = IM.adjust addSucc' v g
g2 = IM.adjust addPred' w g1
addSucc' (ps, l', ss) = (ps, l', IM.insertWith addLists w [l] ss)
addPred' (ps, l', ss) = (IM.insertWith addLists v [l] ps, l', ss)
{-# RULES
"gmap/Data.Graph.Inductive.PatriciaTree" gmap = fastGMap
#-}
fastGMap :: forall a b c d. (Context a b -> Context c d) -> Gr a b -> Gr c d
fastGMap f (Gr g) = Gr (IM.mapWithKey f' g)
where
f' :: Node -> Context' a b -> Context' c d
f' = ((fromContext . f) .) . toContext
{-# RULES
"nmap/Data.Graph.Inductive.PatriciaTree" nmap = fastNMap
#-}
fastNMap :: forall a b c. (a -> c) -> Gr a b -> Gr c b
fastNMap f (Gr g) = Gr (IM.map f' g)
where
f' :: Context' a b -> Context' c b
f' (ps, a, ss) = (ps, f a, ss)
{-# RULES
"emap/Data.Graph.Inductive.PatriciaTree" emap = fastEMap
#-}
fastEMap :: forall a b c. (b -> c) -> Gr a b -> Gr a c
fastEMap f (Gr g) = Gr (IM.map f' g)
where
f' :: Context' a b -> Context' a c
f' (ps, a, ss) = (IM.map (map f) ps, a, IM.map (map f) ss)
toAdj :: IntMap [b] -> Adj b
toAdj = concatMap expand . IM.toList
where
expand (n,ls) = map (flip (,) n) ls
fromAdj :: Adj b -> IntMap [b]
fromAdj = IM.fromListWith addLists . map (second return . swap)
toContext :: Node -> Context' a b -> Context a b
toContext v (ps, a, ss)
= (toAdj ps, v, a, toAdj ss)
fromContext :: Context a b -> Context' a b
fromContext (ps, _, a, ss)
= (fromAdj ps, a, fromAdj ss)
swap :: (a, b) -> (b, a)
swap (a, b) = (b, a)
-- A version of @++@ where order isn't important, so @xs ++ [x]@
-- becomes @x:xs@. Used when we have to have a function of type @[a]
-- -> [a] -> [a]@ but one of the lists is just going to be a single
-- element (and it isn't possible to tell which).
addLists :: [a] -> [a] -> [a]
addLists [a] as = a : as
addLists as [a] = a : as
addLists xs ys = xs ++ ys
addSucc :: GraphRep a b -> Node -> [(b, Node)] -> GraphRep a b
addSucc g _ [] = g
addSucc g v ((l, p) : rest) = addSucc g' v rest
where
g' = IM.adjust f p g
f (ps, l', ss) = (ps, l', IM.insertWith addLists v [l] ss)
addPred :: GraphRep a b -> Node -> [(b, Node)] -> GraphRep a b
addPred g _ [] = g
addPred g v ((l, s) : rest) = addPred g' v rest
where
g' = IM.adjust f s g
f (ps, l', ss) = (IM.insertWith addLists v [l] ps, l', ss)
clearSucc :: GraphRep a b -> Node -> [Node] -> GraphRep a b
clearSucc g _ [] = g
clearSucc g v (p:rest) = clearSucc g' v rest
where
g' = IM.adjust f p g
f (ps, l, ss) = (ps, l, IM.delete v ss)
clearPred :: GraphRep a b -> Node -> [Node] -> GraphRep a b
clearPred g _ [] = g
clearPred g v (s:rest) = clearPred g' v rest
where
g' = IM.adjust f s g
f (ps, l, ss) = (IM.delete v ps, l, ss)
|
