-
Notifications
You must be signed in to change notification settings - Fork 99
/
Dequeue.scala
348 lines (301 loc) · 11.9 KB
/
Dequeue.scala
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
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
/*
* Copyright (c) 2015 Typelevel
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
package cats.collections
import cats._
import cats.data.NonEmptyList
import scala.annotation.tailrec
import scala.collection.mutable.ListBuffer
import cats.collections.compat.Factory
/**
* Dequeue - A Double Ended Queue
*
* Front Back
*
* <- uncons --------- unsnoc -> cons -> --------- <- snoc
*
* Based on the Bankers Double Ended Queue as described by C. Okasaki in "Purely Functional Data Structures"
*
* A queue that allows items to be put onto either the front (cons) or the back (snoc) of the queue in constant time,
* and constant time access to the element at the very front or the very back of the queue. Dequeuing an element from
* either end is constant time when amortized over a number of dequeues.
*
* This queue maintains an invariant that whenever there are at least two elements in the queue, neither the front list
* nor back list are empty. In order to maintain this invariant, a dequeue from either side which would leave that side
* empty constructs the resulting queue by taking elements from the opposite side
*/
sealed abstract class Dequeue[+A] {
def isEmpty: Boolean
def frontOption: Option[A]
def backOption: Option[A]
/**
* destructure from the front of the queue
*/
def uncons: Option[(A, Dequeue[A])] = this match {
case SingletonDequeue(a) => Some((a, EmptyDequeue()))
case FullDequeue(NonEmptyList(f, Nil), 1, NonEmptyList(x, xx :: xs), bs) => {
val xsr = NonEmptyList(xx, xs).reverse
Some((f, FullDequeue(xsr, bs - 1, NonEmptyList(x, Nil), 1)))
}
case FullDequeue(NonEmptyList(f, Nil), 1, NonEmptyList(single, Nil), 1) => Some((f, SingletonDequeue(single)))
case FullDequeue(NonEmptyList(f, ff :: fs), s, back, bs) =>
Some((f, FullDequeue(NonEmptyList(ff, fs), s - 1, back, bs)))
case _ => None
}
/**
* destructure from the back of the queue
*/
def unsnoc: Option[(A, Dequeue[A])] = this match {
case SingletonDequeue(a) => Some((a, EmptyDequeue()))
case FullDequeue(NonEmptyList(x, xx :: xs), fs, NonEmptyList(b, Nil), 1) => {
val xsr = NonEmptyList(xx, xs).reverse
Some((b, FullDequeue(NonEmptyList(x, List.empty), 1, xsr, fs - 1)))
}
case FullDequeue(NonEmptyList(single, Nil), 1, NonEmptyList(b, Nil), 1) => Some((b, SingletonDequeue(single)))
case FullDequeue(front, fs, NonEmptyList(b, bb :: bs), s) =>
Some((b, FullDequeue(front, fs, NonEmptyList(bb, bs), s - 1)))
case _ => None
}
/**
* enqueue to the front of the queue
*/
def cons[AA >: A](a: AA): Dequeue[AA] = this match {
case SingletonDequeue(single) => FullDequeue(NonEmptyList(a, List.empty), 1, NonEmptyList(single, List.empty), 1)
case FullDequeue(front, fs, back, bs) => FullDequeue(NonEmptyList(a, front.toList), fs + 1, back, bs)
case _ => SingletonDequeue(a)
}
/**
* enqueue on to the back of the queue
*/
def snoc[AA >: A](a: AA): Dequeue[AA] = this match {
case SingletonDequeue(single) => FullDequeue(NonEmptyList(single, List.empty), 1, NonEmptyList(a, List.empty), 1)
case FullDequeue(front, fs, back, bs) => FullDequeue(front, fs, NonEmptyList(a, back.toList), bs + 1)
case _ => SingletonDequeue(a)
}
/**
* alias for cons
*/
def +:[AA >: A](a: AA): Dequeue[AA] = cons(a)
/**
* alias for snoc
*/
def :+[AA >: A](a: AA): Dequeue[AA] = snoc(a)
def toIterator: Iterator[A] = new Iterator[A] {
private var pos: Dequeue[A] = Dequeue.this
override def hasNext: Boolean = !pos.isEmpty
override def next(): A = pos.uncons match {
case None => throw new NoSuchElementException()
case Some((a, rest)) =>
pos = rest
a
}
}
def to[Col[_], AA >: A](implicit cbf: Factory[AA, Col[AA]]): Col[AA] = {
val builder = cbf.newBuilder
@tailrec def go(cur: Dequeue[A]): Unit = cur.uncons match {
case Some((a, rest)) =>
builder += a
go(rest)
case _ =>
}
go(this)
builder.result()
}
def toList: List[A] = to[List, A]
/**
* Append another Dequeue to this dequeue
*/
def ++[AA >: A](other: Dequeue[AA]): Dequeue[AA] = this match {
case SingletonDequeue(a) => a +: other
case FullDequeue(f, fs, b, bs) =>
other match {
case SingletonDequeue(a) => this :+ a
case FullDequeue(of, ofs, ob, obs) =>
FullDequeue(NonEmptyList(f.head, f.tail ++ (b.reverse.toList) ++ of.toList), fs + bs + ofs, ob, obs)
case _ => this
}
case _ => other
}
def foldLeft[B](b: B)(f: (B, A) => B): B = this match {
case SingletonDequeue(a) => f(b, a)
case FullDequeue(front, _, back, _) => {
val frontb = front.tail.foldLeft(f(b, front.head))(f)
val backb = back.tail.foldRight(Eval.now(frontb))((a, b) => b.map(f(_, a))).value
f(backb, back.head)
}
case _ => b
}
def foldRight[B](b: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] = this match {
case SingletonDequeue(a) => f(a, b)
case FullDequeue(front, _, back, _) =>
front.foldRight(Eval.defer(back.reverse.foldRight(b)(f)))(f)
case _ => b
}
def map[B](f: A => B): Dequeue[B] = {
this match {
case SingletonDequeue(a) => SingletonDequeue(f(a))
case FullDequeue(front, fs, back, bs) => {
FullDequeue(front.map(f), fs, back.map(f), bs)
}
case _ => EmptyDequeue()
}
}
def flatMap[B](f: A => Dequeue[B]): Dequeue[B] = {
def go(n: NonEmptyList[A]): (ListBuffer[B], Int, Option[B]) = {
val lb = new ListBuffer[B]
var s = 0
var o: Option[B] = None
n.toList.foreach { a =>
f(a) match {
case SingletonDequeue(b) =>
s = s + 1
o.toList.foreach { x =>
val _ = lb += x
}
o = Some(b)
case FullDequeue(f, _, b, _) =>
f.toList.foreach { b =>
s = s + 1
o.toList.foreach { x =>
val _ = lb += x
}
o = Some(b)
}
b.reverse.toList.foreach { b =>
s = s + 1
o.toList.foreach { x =>
val _ = lb += x
}
o = Some(b)
}
case _ =>
}
}
(lb, s, o)
}
this match {
case SingletonDequeue(a) => f(a)
case FullDequeue(front, _, back, _) =>
val (fl, fs, fo) = go(front)
val (bl, bs, bo) = go(back.reverse)
(fo, bo) match {
case (None, None) => EmptyDequeue()
case (Some(a), None) =>
if (fs == 1)
SingletonDequeue(a)
else
FullDequeue(fl.toList.asInstanceOf[NonEmptyList[B]], fs - 1, NonEmptyList(a, List.empty), 1)
case (None, Some(a)) =>
if (bs == 1)
SingletonDequeue(a)
else
FullDequeue(NonEmptyList(a, List.empty), 1, bl.toList.asInstanceOf[NonEmptyList[B]], bs - 1)
case (Some(f), Some(b)) =>
fl += f
bl += b
FullDequeue(fl.toList.asInstanceOf[NonEmptyList[B]],
fs,
bl.toList.reverse.asInstanceOf[NonEmptyList[B]],
bs
)
}
case _ => EmptyDequeue()
}
}
def coflatMap[B](f: Dequeue[A] => B): Dequeue[B] = {
def loop(op: Option[(A, Dequeue[A])], last: Dequeue[A], acc: Dequeue[B]): Dequeue[B] =
op match {
case None => acc
case Some((_, rest)) => loop(rest.uncons, rest, acc :+ f(last))
}
loop(this.uncons, this, EmptyDequeue())
}
def size: Int = this match {
case SingletonDequeue(_) => 1
case FullDequeue(_, fs, _, bs) => fs + bs
case _ => 0
}
def reverse: Dequeue[A] = this match {
case FullDequeue(front, fs, back, bs) => FullDequeue(back, bs, front, fs)
case x => x
}
}
/**
* special case of the queue when it contains just a single element which can be accessed from either side of the queue
*/
final private[collections] case class SingletonDequeue[A](single: A) extends Dequeue[A] {
override def isEmpty: Boolean = false
override def frontOption: Option[A] = Some(single)
override def backOption: Option[A] = Some(single)
}
/**
* a queue which has at least two elements, it is guaranteed that the front list and back lists cannot be empty
*/
final private[collections] case class FullDequeue[A](front: NonEmptyList[A],
fsize: Int,
back: NonEmptyList[A],
backSize: Int
) extends Dequeue[A] {
override def isEmpty: Boolean = false
override def frontOption: Option[A] = Some(front.head)
override def backOption: Option[A] = Some(back.head)
}
/**
* a queue which has no elements
*/
private[collections] case object EmptyDequeue extends Dequeue[Nothing] { self =>
override val isEmpty: Boolean = true
override val frontOption: Option[Nothing] = None
override val backOption: Option[Nothing] = None
override def toString: String = "EmptyDequeue"
def apply[A](): Dequeue[A] = self
def unapply[A](q: Dequeue[A]): Boolean = q.isEmpty
}
object Dequeue extends DequeueInstances {
def apply[A](as: A*): Dequeue[A] = as.foldLeft[Dequeue[A]](empty)((q, a) => q :+ a)
def fromFoldable[F[_], A](fa: F[A])(implicit F: Foldable[F]): Dequeue[A] =
F.foldLeft[A, Dequeue[A]](fa, empty)((q, a) => q :+ a)
def empty[A]: Dequeue[A] = EmptyDequeue()
}
sealed trait DequeueInstances {
implicit def dequeueEqual[A](implicit eqA: Eq[A]): Eq[Dequeue[A]] = new Eq[Dequeue[A]] {
final override def eqv(a: Dequeue[A], b: Dequeue[A]): Boolean =
iteratorEq(a.toIterator, b.toIterator)
}
implicit def dequeueMonoid[A]: Monoid[Dequeue[A]] = new Monoid[Dequeue[A]] {
override val empty: Dequeue[A] = Dequeue.empty
override def combine(l: Dequeue[A], r: Dequeue[A]) = l ++ r
}
implicit val dequeueInstance: Traverse[Dequeue] with MonoidK[Dequeue] with CoflatMap[Dequeue] = new Traverse[Dequeue]
with MonoidK[Dequeue]
with CoflatMap[Dequeue] {
override def empty[A]: Dequeue[A] = Dequeue.empty
override def combineK[A](l: Dequeue[A], r: Dequeue[A]): Dequeue[A] = l ++ r
override def map[A, B](fa: Dequeue[A])(f: A => B) = fa.map(f)
override def coflatMap[A, B](fa: Dequeue[A])(f: Dequeue[A] => B): Dequeue[B] = fa.coflatMap(f)
override def foldLeft[A, B](fa: Dequeue[A], b: B)(f: (B, A) => B): B =
fa.foldLeft(b)(f)
override def foldRight[A, B](fa: Dequeue[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] = fa.foldRight(lb)(f)
override def traverse[G[_], A, B](fa: Dequeue[A])(f: A => G[B])(implicit G: Applicative[G]): G[Dequeue[B]] = {
val gba = G.pure(EmptyDequeue[B]())
fa.foldLeft(gba)((bs, a) => G.map2(bs, f(a))(_ :+ _))
}
}
}