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

------------------------------------------------------------------------------
--- A simple trie data structure.
--- 
--- This implementation assumes that the keys are small. It is not (yet)
--- optimized for arbitrary keys. 
--- That is, no optimizations are done in regards to memory usage
--- (or access speed) when using different keys with unique prefixes.
---
--- Consider a Trie containing the keys a,b,c,aa,ab,ac:
---          root 
---         / | \
---        /  |  \
---       a   b   c
---     / | \    
---    a  b  c
---
--- This is fine. Now consider a Trie containing the keys a,b,Helloworld
---          root
---         / | \
---        /  |  \
---       a   b   H  
---               |
---               e
---               |
---               l
---               |
---               ...
--- This is an issue because lots of nodes without associated values are created
--- (only the leaf nodes a,b,d have values). 
---
--- @author Lasse Züngel
--- @version July 2024
------------------------------------------------------------------------------

module RW.Trie
  (
  --- * Data types
    Trie(),

  --- * Basic functions 
    empty, null, singleton, size,

  --- * Traversing functions
    insert, lookup,

  --- * List conversion functions
    fromList, toList) where

import Data.List
import Data.Maybe

import qualified Data.Map

--- The size of a trie
type Size = Int

--- Trie data structure
data Trie a = Trie Size (Maybe a) [(Char, Trie a)]
  deriving (Show, Eq)

--- An empty trie.
empty :: Trie a
empty = Trie 0 Nothing []

--- Is the trie empty?
null :: Trie a -> Bool
null x = case x of
  Trie _ Nothing [] -> True
  _                 -> False

--- Returns the size of the trie.
size :: Trie a -> Int
size (Trie s _ _) = s

--- A singleton trie.
singleton :: Eq a => String -> a -> Trie a
singleton str v = insert str v empty

--- Inserts a value into the trie.
insert :: Prelude.Eq a => String -> a -> Trie a -> Trie a
insert []     v (Trie s _ ts) = Trie (s+1) (Just v) ts
insert (c:cs) v (Trie s v' ts) = case Prelude.lookup c ts of
  Nothing -> Trie (s+1) v' ((c, insert cs v empty) : ts)
  Just t  -> Trie (s+1) v' ((c, insert cs v t) : (filter (\(c', _) -> c' /= c) ts))

--- Looks up a value in the trie.
lookup :: String -> Trie a -> Maybe a
lookup []     (Trie _ v _)  = v
lookup (c:cs) (Trie _ _ ts) = case Prelude.lookup c ts of
  Nothing -> Nothing
  Just t  -> RW.Trie.lookup cs t

--- Converts a list of key-value pairs into a trie.
fromList :: Eq a =>  [(String, a)] -> Trie a
fromList = foldr (uncurry insert) empty

--- Converts a trie into a list of key-value pairs.
toList :: Trie a -> [(String, a)]
toList (Trie _ v ts) = case v of
  Nothing -> concatMap (\(c, t) -> map (\(s, w) -> (c:s, w)) (toList t)) ts
  Just z  -> ("", z) :
             concatMap (\(c, t) -> map (\(s, w) -> (c:s, w)) (toList t)) ts

-------- tests

alphabet :: [Char]
alphabet = ['a'..'z']

sizeAlphabet :: Int
sizeAlphabet = 26

toKey :: Int -> String
toKey n | n < 0            = error "toKey: negative number"
        | n < sizeAlphabet = [alphabet !! n]
        | otherwise        = toKey (n `div` sizeAlphabet) ++
                             toKey (n `mod` sizeAlphabet)

{-
-- Tests:
keys = map toKey [0..1000]

input = zip keys [0..]

myList = fromList input

myMap = Data.Map.fromList input

lT :: Trie Int -> String -> Int
lT list k = fromJust $ RW.Trie.lookup k list

lP :: [(String, Int)] -> String -> Int
lP list k = fromJust $ Prelude.lookup k list

lMap :: Data.Map.Map String Int -> String -> Int
lMap list k = fromJust $ Data.Map.lookup k list

-- 487ms
sumAllT :: Trie Int -> Int
sumAllT list = sum $ map (lT list) keys

-- 1700ms
sumAllP :: [(String, Int)] -> Int
sumAllP list = sum $ map (lP list) keys

-- 930ms
sumAllMap :: Data.Map.Map String Int -> Int
sumAllMap list = sum $ map (lMap list) keys

tt = sumAllT myList  --  150ms (kics2, n=10000) -  520ms (pakcs, n=1000)
tp = sumAllP input   -- 3150ms (kics2         ) - 1750ms (pakcs        )
tm = sumAllMap myMap --  280ms (kics2         ) -  930ms (pakcs        )
-}