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event world with efficient common postfix
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Robbert van Dalen
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Mar 9, 2021
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| package data | ||
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| /** | ||
| * Purely functional Random Access (RA) List. | ||
| * | ||
| * An RAList is very easy to implement and understand. | ||
| * | ||
| * Another very nice (and underrated!) property is their canonical/unique representation. | ||
| * We leverage that property to calculate the common postfix between two RALists in O(log(n)). | ||
| * | ||
| * See https://dl.acm.org/doi/abs/10.1145/224164.224187. | ||
| */ | ||
| object RAList { | ||
| import scala.util.hashing.MurmurHash3._ | ||
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| trait RATree[A] { | ||
| def hash: Int | ||
| def first: A | ||
| def second: RATree[A] | ||
| def third: RATree[A] | ||
| def toList: List[A] | ||
| override def hashCode = hash | ||
| } | ||
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| case class RAEmptyTree[A]() extends RATree[A] { | ||
| def hash = 0 | ||
| def first = err | ||
| def second = err | ||
| def third = err | ||
| def toList = List() | ||
| def err = sys.error("EMPTY TREE") | ||
| } | ||
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| case class RALeafTree[A](first: A) extends RATree[A] { | ||
| def hash = mix(first.hashCode, -first.hashCode) | ||
| def second = RAEmptyTree() | ||
| def third = RAEmptyTree() | ||
| def toList = List(first) | ||
| } | ||
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| case class RABinTree[A](first: A, second: RATree[A], third: RATree[A]) extends RATree[A] { | ||
| val hash = mix(third.hash, mix(second.hash, first.hashCode())) | ||
| def toList = first +: (second.toList ++ third.toList) | ||
| } | ||
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| case class RANode[A](size: Long, tree: RATree[A]) | ||
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| object RAList { | ||
| def apply[A](): RAList[A] = RAEmpty() | ||
| } | ||
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| sealed trait RAList[A] { | ||
| def head: RANode[A] | ||
| def tail: RAList[A] | ||
| def depth: Int | ||
| def size: Long | ||
| def isEmpty: Boolean | ||
| def toList: List[A] = reverse(this).reverse.map(_.tree.toList).fold(List[A]())(_ ++ _) | ||
| def +:(a: A): RAList[A] = { | ||
| if(isEmpty || tail.isEmpty) RACons(RANode(1, RALeafTree(a)), this) | ||
| else { | ||
| val n1 = head | ||
| val n2 = tail.head | ||
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| if (n1.size != n2.size) RACons(RANode(1, RALeafTree[A](a)), this) | ||
| else RACons(RANode(1 + n1.size + n2.size, RABinTree(a, n1.tree, n2.tree)), tail.tail) | ||
| } | ||
| } | ||
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| private def reverse(l: RAList[A]): List[RANode[A]] = { | ||
| var result = List[RANode[A]]() | ||
| var self = l | ||
| while (!self.isEmpty) { result = self.head +: result ; self = self.tail } | ||
| result | ||
| } | ||
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| private def reverse(l: List[RANode[A]]): RAList[A] = { | ||
| var result = RAList[A]() | ||
| var self = l | ||
| while (self.nonEmpty) { result = RACons(self.head, result) ; self = self.tail } | ||
| result | ||
| } | ||
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| def postfix(p: Long): RAList[A] = { | ||
| if (isEmpty || p >= size) this | ||
| else { | ||
| var pst = List[RANode[A]]() | ||
| var rvs = reverse(this) | ||
| var pp = p | ||
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| while (pp >= rvs.head.size) { pst = rvs.head +: pst ; pp = pp - rvs.head.size ; rvs = rvs.tail } | ||
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| reverse(pst.reverse ++ postfix(pp, rvs.head)) | ||
| } | ||
| } | ||
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| private def postfix(p: Long, node: RANode[A]): List[RANode[A]] = postfix(p, node.size, node.tree) | ||
| private def postfix(p: Long, size: Long, tree: RATree[A]): List[RANode[A]] = { | ||
| if (p == 0) List() | ||
| else if (p >= size) List(RANode(size, tree)) | ||
| else { | ||
| val half = size / 2 | ||
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| if (p == (size - 1)) List(RANode(half, tree.third), RANode(half, tree.second)) | ||
| else { | ||
| if (p <= half) postfix(p, half, tree.third) | ||
| else RANode(half, tree.third) +: postfix(p - half, half, tree.second) | ||
| } | ||
| } | ||
| } | ||
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| def commonPostfix(other: RAList[A]): Long = { | ||
| if (other.size > size) other.commonPostfix(this) | ||
| else { | ||
| val self = postfix(other.size) | ||
| assert(self.size == other.size) | ||
| commonPostfix(self, other) | ||
| } | ||
| } | ||
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| private def commonPostfix(l1: RAList[A], l2: RAList[A]): Long = { | ||
| var r1 = reverse(l1) | ||
| var r2 = reverse(l2) | ||
| var s = 0L | ||
| while (r1.nonEmpty && r2.nonEmpty && r1.head.tree == r2.head.tree) { | ||
| assert(r1.head.size == r2.head.size) | ||
| s = s + r1.head.size | ||
| r1 = r1.tail | ||
| r2 = r2.tail | ||
| } | ||
| if (r1.isEmpty) s | ||
| else { | ||
| assert(r1.head.size == r2.head.size) | ||
| commonPostfix(r1.head.tree, r2.head.tree, r1.head.size) + s | ||
| } | ||
| } | ||
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| private def commonPostfix(l1: RATree[A], l2: RATree[A], size: Long): Long = { | ||
| if (size == 0) 0 | ||
| else if (size == 1) { | ||
| if (l1.first == l2.first) 1 | ||
| else 0 | ||
| } | ||
| else { | ||
| val halve = size / 2 | ||
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| if (l1.third != l2.third) commonPostfix(l1.third, l2.third, halve) | ||
| else if (l1.second != l2.second) halve + commonPostfix(l1.second, l2.second, halve) | ||
| else if (l1.first != l2.first) size - 1 | ||
| else size | ||
| } | ||
| } | ||
| } | ||
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| case class RAEmpty[A]() extends RAList[A] { | ||
| def head = err | ||
| def tail = err | ||
| def depth = 0 | ||
| def size = 0 | ||
| def isEmpty = true | ||
| def err = sys.error("Empty RAList") | ||
| } | ||
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| case class RACons[A](head: RANode[A], tail: RAList[A]) extends RAList[A] { | ||
| def depth = 1 + tail.depth | ||
| def size = head.size + tail.size | ||
| def isEmpty = false | ||
| } | ||
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| def main(arg: Array[String]): Unit = { | ||
| val x = 40 | ||
| var l = RAList[Int]() | ||
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| for (i <- 0 until x) l = i +: l | ||
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| var r = l | ||
| while (!r.isEmpty) { | ||
| println(r.head.size) | ||
| r = r.tail | ||
| } | ||
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| val r1 = 999 +: 1000 +: 1001 +: 2 +: 1 +: 0 +: RAEmpty[Int]() | ||
| val r2 = 1000 +: 1001 +: l | ||
| val pst = r1.commonPostfix(r2) | ||
| println("pst: " + l.toList) | ||
| } | ||
| } |
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