Scala example source code file (FingerTree.scala)
The FingerTree.scala Scala example source code
package scalaz
import collection.Iterator
import syntax.Ops
import std.option._
/**View of the left end of a sequence.*/
sealed abstract class ViewL[S[_], A] {
def fold[B](b: => B, f: (=> A, => S[A]) => B): B
def headOption: Option[A] = fold(None, (a, sa) => Some(a))
def tailOption: Option[S[A]] = fold(None, (a, sa) => Some(sa))
def head: A = headOption.getOrElse(sys.error("Head on empty view"))
def tail: S[A] = tailOption.getOrElse(sys.error("Tail on empty view"))
}
/**View of the right end of a sequence.*/
sealed abstract class ViewR[S[_], A] {
def fold[B](b: => B, f: (=> S[A], => A) => B): B
def lastOption: Option[A] = fold(None, (sa, a) => Some(a))
def initOption: Option[S[A]] = fold(None, (sa, a) => Some(sa))
def last: A = lastOption.getOrElse(sys.error("Last on empty view"))
def init: S[A] = initOption.getOrElse(sys.error("Init on empty view"))
}
import FingerTree._
import std.option._
sealed abstract class Finger[V, A] {
def foldMap[B](f: A => B)(implicit m: Semigroup[B]): B
/**
* Append the given element to the right
*
* @throws if the finger is `Four`.
*/
def +:(a: A): Finger[V, A]
/**
* Prepends the given element to the left
*
* @throws if the finger is `Four`.
*/
def :+(a: A): Finger[V, A]
/** Replaces the first element of this finger with `a` */
def |-:(a: A): Finger[V, A]
/** Replaces the last element of this finger with `a` */
def :-|(a: A): Finger[V, A]
def lhead: A
def ltail: Finger[V, A]
def rhead: A
def rtail: Finger[V, A]
def toTree: FingerTree[V, A]
def map[B, V2](f: A => B)(implicit m: Reducer[B, V2]): Finger[V2, B]
/** Apply the given side effect to each element. */
def foreach(f: A => Unit): Unit
/** An iterator that visits each element. */
def iterator: Iterator[A]
/** An iterator that visits each element in reverse order. */
def reverseIterator: Iterator[A]
def measure: V
def toList: List[A] = map(x => x)(Reducer.ListReducer[A]).measure
private[scalaz] def split1(pred: V => Boolean, accV: V): (Option[Finger[V, A]], A, Option[Finger[V, A]])
}
case class One[V, A](v: V, a1: A)(implicit r: Reducer[A, V]) extends Finger[V, A] {
def foldMap[B](f: A => B)(implicit m: Semigroup[B]) = f(a1)
def +:(a: A) = Two(r.cons(a, v), a, a1)
def :+(a: A) = Two(r.snoc(v, a), a1, a)
def |-:(a: A) = one(a)
def :-|(a: A) = one(a)
def lhead = a1
def ltail = sys.error("Tail on the digit One")
def rhead = a1
def rtail = sys.error("Tail on the digit One")
def toTree = single(a1)
def map[B, V2](f: A => B)(implicit r: Reducer[B, V2]) = one(f(a1))
def foreach(f: A => Unit) {
f(a1)
}
def iterator = Iterator.single(a1)
def reverseIterator = Iterator.single(a1)
val measure = v
private[scalaz] def split1(pred: V => Boolean, accV: V) = (None, a1, None)
}
case class Two[V, A](v: V, a1: A, a2: A)(implicit r: Reducer[A, V]) extends Finger[V, A] {
def foldMap[B](f: A => B)(implicit m: Semigroup[B]) = m.append(f(a1), f(a2))
def +:(a: A) = Three(r.cons(a, v), a, a1, a2)
def :+(a: A) = Three(r.snoc(v, a), a1, a2, a)
def |-:(a: A) = two(a, a2)
def :-|(a: A) = two(a1, a)
def lhead = a1
def ltail = one(a2)
def rhead = a2
def rtail = one(a1)
def toTree = {
deep(v, one(a1), empty[V, Node[V, A]], one(a2))
}
def map[B, V2](f: A => B)(implicit r: Reducer[B, V2]) = two(f(a1), f(a2))
def foreach(f: A => Unit) {
f(a1)
f(a2)
}
def iterator = Iterator(a1, a2)
def reverseIterator = Iterator(a2, a1)
val measure = v
private implicit def sg: Semigroup[V] = r.monoid
private[scalaz] def split1(pred: V => Boolean, accV: V) = {
val va1 = r.unit(a1)
val accVa1 = sg.append(accV, va1)
if (pred(accVa1))
(None, a1, Some(one(a2)))
else
(Some(One(va1, a1)), a2, None)
}
}
case class Three[V, A](v: V, a1: A, a2: A, a3: A)(implicit r: Reducer[A, V]) extends Finger[V, A] {
def foldMap[B](f: A => B)(implicit m: Semigroup[B]) = m.append(m.append(f(a1), f(a2)), f(a3))
def +:(a: A) = Four(r.cons(a, v), a, a1, a2, a3)
def :+(a: A) = Four(r.snoc(v, a), a1, a2, a3, a)
def |-:(a: A) = three(a, a2, a3)
def :-|(a: A) = three(a1, a2, a)
def lhead = a1
def ltail = two(a2, a3)
def rhead = a3
def rtail = two(a1, a2)
def toTree = {
deep(v, two(a1, a2), empty[V, Node[V, A]], one(a3))
}
def map[B, V2](f: A => B)(implicit r: Reducer[B, V2]) = three(f(a1), f(a2), f(a3))
def foreach(f: A => Unit) {
f(a1)
f(a2)
f(a3)
}
def iterator = Iterator(a1, a2, a3)
def reverseIterator = Iterator(a3, a2, a1)
val measure = v
private implicit def sg: Semigroup[V] = r.monoid
private[scalaz] def split1(pred: V => Boolean, accV: V) = {
val va1 = r.unit(a1)
val accVa1 = sg.append(accV, va1)
if (pred(accVa1))
(None, a1, Some(two(a2, a3)))
else {
val accVa2 = r.snoc(accVa1, a2)
if (pred(accVa2))
(Some(One(va1, a1)), a2, Some(one(a3)))
else
(Some(two(a1, a2)), a3, None)
}
}
}
case class Four[V, A](v: V, a1: A, a2: A, a3: A, a4: A)(implicit r: Reducer[A, V]) extends Finger[V, A] {
def foldMap[B](f: A => B)(implicit m: Semigroup[B]) = m.append(m.append(f(a1), f(a2)), m.append(f(a3), f(a4)))
def +:(a: A) = sys.error("Digit overflow")
def :+(a: A) = sys.error("Digit overflow")
def |-:(a: A) = four(a, a2, a3, a4)
def :-|(a: A) = four(a1, a2, a3, a)
def lhead = a1
def ltail = three(a2, a3, a4)
def rhead = a4
def rtail = three(a1, a2, a3)
def toTree = {
deep(v, two(a1, a2), empty[V, Node[V, A]], two(a3, a4))
}
def map[B, V2](f: A => B)(implicit r: Reducer[B, V2]) = four(f(a1), f(a2), f(a3), f(a4))
def foreach(f: A => Unit) {
f(a1)
f(a2)
f(a3)
f(a4)
}
def iterator = Iterator(a1, a2, a3, a4)
def reverseIterator = Iterator(a4, a3, a2, a1)
val measure = v
private implicit def sg: Semigroup[V] = r.monoid
private[scalaz] def split1(pred: V => Boolean, accV: V) = {
val va1 = r.unit(a1)
val accVa1 = sg.append(accV, va1)
if (pred(accVa1))
(None, a1, Some(three(a2, a3, a4)))
else {
val accVa2 = r.snoc(accVa1, a2)
if (pred(accVa2))
(Some(One(va1, a1)), a2, Some(two(a3, a4)))
else {
val accVa3 = r.snoc(accVa2, a3)
if (pred(accVa3))
(Some(two(a1, a2)), a3, Some(one(a4)))
else
(Some(three(a1, a2, a3)), a4, None)
}
}
}
}
sealed abstract class Node[V, A](implicit r: Reducer[A, V]) {
def fold[B](two: (V, => A, => A) => B, three: (V, => A, => A, => A) => B): B
def foldMap[B](f: A => B)(implicit m: Semigroup[B]): B = fold(
(v, a1, a2) => m.append(f(a1), f(a2)),
(v, a1, a2, a3) => m.append(m.append(f(a1), f(a2)), f(a3)))
def toDigit = fold(
(v, a1, a2) => Two(v, a1, a2),
(v, a1, a2, a3) => Three(v, a1, a2, a3))
val measure: V
def map[B, V2](f: A => B)(implicit m: Reducer[B, V2]) = fold(
(v, a1, a2) => node2(f(a1), f(a2)),
(v, a1, a2, a3) => node3(f(a1), f(a2), f(a3)))
def foreach(f: A => Unit) {
fold(
(_, a1, a2) => { f(a1); f(a2) },
(_, a1, a2, a3) => { f(a1); f(a2); f(a3) }
)}
def iterator = fold(
(_, a1, a2) => Iterator(a1, a2),
(_, a1, a2, a3) => Iterator(a1, a2, a3))
def reverseIterator = fold(
(_, a1, a2) => Iterator(a2, a1),
(_, a1, a2, a3) => Iterator(a3, a2, a1))
private implicit def sg: Semigroup[V] = r.monoid
private[scalaz] def split1(pred: V => Boolean, accV: V): (Option[Finger[V, A]], A, Option[Finger[V, A]]) = fold(
(v, a1, a2) => {
val va1 = r.unit(a1)
val accVa1 = sg.append(accV, va1)
if (pred(accVa1))
(None, a1, Some(one(a2)))
else
(Some(One(va1, a1)), a2, None)
},
(v, a1, a2, a3) => {
val va1 = r.unit(a1)
val accVa1 = sg.append(accV, va1)
if (pred(accVa1))
(None, a1, Some(two(a2, a3)))
else {
val accVa2 = r.snoc(accVa1, a2)
if (pred(accVa2))
(Some(One(va1, a1)), a2, Some(one(a3)))
else
(Some(two(a1, a2)), a3, None)
}
})
}
/**
* Finger trees with leaves of type A and Nodes that are annotated with type V.
*
* Finger Trees provide a base for implementations of various collection types,
* as described in "Finger trees: a simple general-purpose data structure", by
* Ralf Hinze and Ross Paterson.
* A gentle introduction is presented in the blog post "Monoids and Finger Trees" by Heinrich Apfelmus.
*
* This is done by choosing a a suitable type to annotate the nodes. For example,
* a binary tree can be implemented by annotating each node with the size of its subtree,
* while a priority queue can be implemented by labelling the nodes by the minimum priority of its children.
*
* The operations on FingerTree enforce the constraint measured (in the form of a Reducer instance).
*
* Finger Trees have excellent (amortized) asymptotic performance:
*
* - Access to the first and last elements is `O(1)`
* - Appending/prepending a single value is `O(1)`
* - Concatenating two trees is `(O lg min(l1, l2))` where `l1` and `l2` are their sizes
* - Random access to an element at `n` is `O(lg min(n, l - n))`, where `l` is the size of the tree.
* - Constructing a tree with n copies of a value is O(lg n).
*
* @tparam V The type of the annotations of the nodes (the '''measure''')
* @tparam A The type of the elements stored at the leaves
*
* @see [[http://www.soi.city.ac.uk/~ross/papers/FingerTree.pdf Finger trees: a simple general-purpose data structure]]
* @see [[http://apfelmus.nfshost.com/articles/monoid-fingertree.html]]
*/
sealed abstract class FingerTree[V, A](implicit measurer: Reducer[A, V]) {
def measure: V = fingerTreeMeasure[A, V].unit(this)
def foldMap[B](f: A => B)(implicit s: Monoid[B]): B =
fold(v => s.zero, (v, x) => f(x), (v, pr, m, sf) =>
s.append(s.append(pr.foldMap(f), m.foldMap(x => x.foldMap(f))), sf.foldMap(f)))
def foldRight[B](z: => B)(f: (A, => B) => B): B = {
foldMap((a: A) => (Endo.endo(f(a, _: B)))) apply z
}
def foldLeft[B](b: B)(f: (B, A) => B): B = {
fold(v => b,
(v, a) => f(b, a),
(v, pr, m, sf) =>
fingerFoldable[V].foldLeft(sf, m.foldLeft[B](fingerFoldable[V].foldLeft(pr, b)(f))((x, y) => nodeFoldable[V].foldLeft(y, x)(f)))(f))
}
/**
* Fold over the structure of the tree. The given functions correspond to the three possible variations of the finger tree.
*
* @param empty if the tree is empty, convert the measure to a `B`
* @param single if the tree contains a single element, convert the measure and this element to a `B`
* @param deep otherwise, convert the measure, the two fingers, and the sub tree to a `B`.
*/
def fold[B](empty: V => B, single: (V, A) => B, deep: (V, Finger[V, A], => FingerTree[V, Node[V, A]], Finger[V, A]) => B): B
/** Prepends an element to the left of the tree. O(1). */
def +:(a: => A): FingerTree[V, A] = {
implicit val nm = nodeMeasure[A, V]
val az = Need(a)
fold(
v => single(measurer.cons(az.value, v), az.value),
(v, b) => deep(measurer.cons(az.value, v), one(az.value), empty[V, Node[V, A]], one(b)),
(v, pr, m, sf) => {
val mz = m
pr match {
case Four(vf, b, c, d, e) => deep(measurer.cons(az.value, v), two(az.value, b), node3(c, d, e) +: mz, sf)
case _ => deep(measurer.cons(az.value, v), az.value +: pr, mz, sf)
}})
}
/** Appends an element to the right of the tree. O(1). */
def :+(a: => A): FingerTree[V, A] = {
implicit val nm = nodeMeasure[A, V]
val az = Need(a)
fold(
v => single(measurer.snoc(v, az.value), az.value),
(v, b) => deep(measurer.snoc(v, az.value), one(b), empty[V, Node[V, A]], one(az.value)),
(v, pr, m, sf) => {
val mz = m
sf match {
case Four(vf, b, c, d, e) => deep(measurer.snoc(v, az.value), pr, (mz :+ node3(b, c, d)), two(e, az.value))
case _ => deep(measurer.snoc(v, az.value), pr, mz, sf :+ az.value)
}})
}
/** Replace the first element of the tree with the given value. O(1) */
def |-:(a: => A): FingerTree[V, A] = {
val az = Need(a)
fold(
v => sys.error("Replacing first element of an empty FingerTree"),
(v, b) => single(az.value),
(v, pr, m, sf) => deep(az.value |-: pr, m, sf))
}
/** Replace the last element of the tree with the given value. O(1) */
def :-|(a: => A): FingerTree[V, A] = {
val az = Need(a)
fold(
v => sys.error("Replacing last element of an empty FingerTree"),
(v, b) => single(az.value),
(v, pr, m, sf) => deep(pr, m, sf :-| az.value))
}
/** Appends the given finger tree to the right of this tree. */
def <++>(right: => FingerTree[V, A]): FingerTree[V, A] = {
val rightz = Need(right)
fold(
v => rightz.value,
(v, x) => x +: rightz.value,
(v1, pr1, m1, sf1) =>
rightz.value.fold(
v => this,
(v, x) => this :+ x,
(v2, pr2, m2, sf2) => deep(measurer.append(v1, v2), pr1, addDigits0(m1, sf1, pr2, m2), sf2)
)
)
}
private type ATree = FingerTree[V, A]
private type AFinger = Finger[V, A]
private type NodeTree = FingerTree[V, Node[V, A]]
private implicit def sg: Monoid[V] = measurer.monoid
def add1(n: A, right: => ATree): ATree = {
val rightz = Need(right)
fold(
v => n +: rightz.value,
(v, x) => x +: n +: rightz.value,
(v1, pr1, m1, sf1) =>
rightz.value.fold(
v => this :+ n,
(v, x) => this :+ n :+ x,
(v2, pr2, m2, sf2) =>
deep(measurer.append((measurer.snoc(v1, n)), v2), pr1, addDigits1(m1, sf1, n, pr2, m2), sf2)
)
)
}
def add2(n1t: => A, n2t: => A, right: => ATree): ATree = {
val rightz = Need(right)
val n1 = Need(n1t)
val n2 = Need(n2t)
fold(
v => n1.value +: n2.value +: rightz.value,
(v, x) => x +: n1.value +: n2.value +: rightz.value,
(v1, pr1, m1, sf1) =>
rightz.value.fold(
v => this :+ n1.value :+ n2.value,
(v, x) => this :+ n1.value :+ n2.value :+ x,
(v2, pr2, m2, sf2) =>
deep(measurer.append(measurer.snoc(measurer.snoc(v1, n1.value), n2.value), v2),
pr1, addDigits2(m1, sf1, n1.value, n2.value, pr2, m2), sf2)
)
)
}
def add3(n1t: => A, n2t: => A, n3t: => A, right: => ATree): ATree = {
val rightz = Need(right)
val n1 = Need(n1t)
val n2 = Need(n2t)
val n3 = Need(n3t)
fold(
v => n1.value +: n2.value +: n3.value +: rightz.value,
(v, x) => x +: n1.value +: n2.value +: n3.value +: rightz.value,
(v1, pr1, m1, sf1) =>
rightz.value.fold(
v => this :+ n1.value :+ n2.value :+ n3.value,
(v, x) => this :+ n1.value :+ n2.value :+ n3.value :+ x,
(v2, pr2, m2, sf2) =>
deep(measurer.append(measurer.snoc(measurer.snoc(measurer.snoc(v1, n1.value), n2.value), n3.value), v2),
pr1, addDigits3(m1, sf1, n1.value, n2.value, n3.value, pr2, m2), sf2)
)
)
}
def add4(n1t: => A, n2t: => A, n3t: => A, n4t: => A, right: => ATree): ATree = {
val rightz = Need(right)
val n1 = Need(n1t)
val n2 = Need(n2t)
val n3 = Need(n3t)
val n4 = Need(n4t)
fold(
v => n1.value +: n2.value +: n3.value +: n4.value +: rightz.value,
(v, x) => x +: n1.value +: n2.value +: n3.value +: n4.value +: rightz.value,
(v1, pr1, m1, sf1) =>
rightz.value.fold(
v => this :+ n1.value :+ n2.value :+ n3.value :+ n4.value,
(v, x) => this :+ n1.value :+ n2.value :+ n3.value :+ n4.value :+ x,
(v2, pr2, m2, sf2) =>
deep(measurer.append(measurer.snoc(measurer.snoc(measurer.snoc(measurer.snoc(v1, n1.value), n2.value), n3.value), n4.value), v2),
pr1, addDigits4(m1, sf1, n1.value, n2.value, n3.value, n4.value, pr2, m2), sf2)
)
)
}
def addDigits0(m1: NodeTree, dig1: AFinger, dig2: AFinger, m2: => NodeTree): NodeTree = dig1 match {
case One(_, a) => dig2 match {
case One(_, b) => m1.add1(node2(a, b), m2)
case Two(_, b,c) => m1.add1(node3(a,b,c), m2)
case Three(_, b,c,d) => m1.add2(node2(a,b), node2(c,d),m2)
case Four(_, b,c,d,e) => m1.add2(node3(a,b,c), node2(d,e), m2)
}
case Two(_, a,b) => dig2 match {
case One(_, c) => m1.add1(node3(a,b,c), m2)
case Two(_, c,d) => m1.add2(node2(a,b), node2(c,d), m2)
case Three(_, c,d,e) => m1.add2(node3(a,b,c), node2(d,e), m2)
case Four(_, c,d,e,f) => m1.add2(node3(a,b,c), node3(d,e,f), m2)
}
case Three(_, a,b,c) => dig2 match {
case One(_, d) => m1.add2(node2(a,b), node2(c,d), m2)
case Two(_, d,e) => m1.add2(node3(a,b,c), node2(d,e), m2)
case Three(_, d,e,f) => m1.add2(node3(a,b,c), node3(d,e,f), m2)
case Four(_, d,e,f,g) => m1.add3(node3(a,b,c), node2(d,e), node2(f,g), m2)
}
case Four(_, a,b,c,d) => dig2 match {
case One(_, e) => m1.add2(node3(a,b,c), node2(d,e), m2)
case Two(_, e,f) => m1.add2(node3(a,b,c), node3(d,e,f), m2)
case Three(_, e,f,g) => m1.add3(node3(a,b,c), node2(d,e), node2(f,g), m2)
case Four(_, e,f,g,h) => m1.add3(node3(a,b,c), node3(d,e,f), node2(g,h), m2)
}
}
def addDigits1(m1: NodeTree, d1: AFinger, xt: => A, d2: AFinger, m2t: => NodeTree): NodeTree = {
val x = Need(xt)
val m2 = Need(m2t)
d1 match {
case One(_, a) => d2 match {
case One(_, b) => m1.add1(node3(a,x.value,b), m2.value)
case Two(_, b,c) => m1.add2(node2(a,x.value), node2(b,c), m2.value)
case Three(_, b,c,d) => m1.add2(node3(a,x.value,b), node2(c,d), m2.value)
case Four(_, b,c,d,e) => m1.add2(node3(a,x.value,b), node3(c,d,e), m2.value)
}
case Two(_, a,b) => d2 match {
case One(_, c) => m1.add2(node2(a,b), node2(x.value,c), m2.value)
case Two(_, c,d) => m1.add2(node3(a,b,x.value), node2(c,d), m2.value)
case Three(_, c,d,e) => m1.add2(node3(a,b,x.value), node3(c,d,e), m2.value)
case Four(_, c,d,e,f) => m1.add3(node3(a,b,x.value), node2(c,d), node2(e,f), m2.value)
}
case Three(_, a,b,c) => d2 match {
case One(_, d) => m1.add2(node3(a,b,c), node2(x.value,d), m2.value)
case Two(_, d,e) => m1.add2(node3(a,b,c), node3(x.value,d,e), m2.value)
case Three(_, d,e,f) => m1.add3(node3(a,b,c), node2(x.value,d), node2(e,f), m2.value)
case Four(_, d,e,f,g) => m1.add3(node3(a,b,c), node3(x.value,d,e), node2(f,g), m2.value)
}
case Four(_, a,b,c,d) => d2 match {
case One(_, e) => m1.add2(node3(a,b,c), node3(d,x.value,e), m2.value)
case Two(_, e,f) => m1.add3(node3(a,b,c), node2(d,x.value), node2(e,f), m2.value)
case Three(_, e,f,g) => m1.add3(node3(a,b,c), node3(d,x.value,e), node2(f,g), m2.value)
case Four(_, e,f,g,h) => m1.add3(node3(a,b,c), node3(d,x.value,e), node3(f,g,h), m2.value)
}
}
}
def addDigits2(m1: NodeTree, d1: AFinger, xt: => A, yt: => A, d2: AFinger, m2t: => NodeTree): NodeTree = {
val x = Need(xt)
val y = Need(yt)
val m2 = Need(m2t)
d1 match {
case One(_, a) => d2 match {
case One(_, b) => m1.add2(node2(a,x.value), node2(y.value,b), m2.value)
case Two(_, b,c) => m1.add2(node3(a,x.value,y.value), node2(b,c), m2.value)
case Three(_, b,c,d) => m1.add2(node3(a,x.value,y.value), node3(b,c,d), m2.value)
case Four(_, b,c,d,e) => m1.add3(node3(a,x.value,y.value), node2(b,c), node2(d,e), m2.value)
}
case Two(_, a,b) => d2 match {
case One(_, c) => m1.add2(node3(a,b,x.value), node2(y.value,c), m2.value)
case Two(_, c,d) => m1.add2(node3(a,b,x.value), node3(y.value,c,d), m2.value)
case Three(_, c,d,e) => m1.add3(node3(a,b,x.value), node2(y.value,c), node2(d,e), m2.value)
case Four(_, c,d,e,f) => m1.add3(node3(a,b,x.value), node3(y.value,c,d), node2(e,f), m2.value)
}
case Three(_, a,b,c) => d2 match {
case One(_, d) => m1.add2(node3(a,b,c), node3(x.value,y.value,d), m2.value)
case Two(_, d,e) => m1.add3(node3(a,b,c), node2(x.value,y.value), node2(d,e), m2.value)
case Three(_, d,e,f) => m1.add3(node3(a,b,c), node3(x.value,y.value,d), node2(e,f), m2.value)
case Four(_, d,e,f,g) => m1.add3(node3(a,b,c), node3(x.value,y.value,d), node3(e,f,g), m2.value)
}
case Four(_, a,b,c,d) => d2 match {
case One(_, e) => m1.add3(node3(a,b,c), node2(d,x.value), node2(y.value,e), m2.value)
case Two(_, e,f) => m1.add3(node3(a,b,c), node3(d,x.value,y.value), node2(e,f), m2.value)
case Three(_, e,f,g) => m1.add3(node3(a,b,c), node3(d,x.value,y.value), node3(e,f,g), m2.value)
case Four(_, e,f,g,h) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node2(e,f), node2(g,h), m2.value)
}
}
}
def addDigits3(m1: NodeTree, d1: AFinger, xt: => A, yt: => A, zt: => A, d2: AFinger, m2t: => NodeTree): NodeTree = {
val x = Need(xt)
val y = Need(yt)
val z = Need(zt)
val m2 = Need(m2t)
d1 match {
case One(_, a) => d2 match {
case One(_, b) => m1.add2(node3(a,x.value,y.value), node2(z.value,b), m2.value)
case Two(_, b,c) => m1.add2(node3(a,x.value,y.value), node3(z.value,b,c), m2.value)
case Three(_, b,c,d) => m1.add3(node3(a,x.value,y.value), node2(z.value,b), node2(c,d), m2.value)
case Four(_, b,c,d,e) => m1.add3(node3(a,x.value,y.value), node3(z.value,b,c), node2(d,e), m2.value)
}
case Two(_, a,b) => d2 match {
case One(_, c) => m1.add2(node3(a,b,x.value), node3(y.value,z.value,c), m2.value)
case Two(_, c,d) => m1.add3(node3(a,b,x.value), node2(y.value,z.value), node2(c,d), m2.value)
case Three(_, c,d,e) => m1.add3(node3(a,b,x.value), node3(y.value,z.value,c), node2(d,e), m2.value)
case Four(_, c,d,e,f) => m1.add3(node3(a,b,x.value), node3(y.value,z.value,c), node3(d,e,f),m2.value)
}
case Three(_, a,b,c) => d2 match {
case One(_, d) => m1.add3(node3(a,b,c), node2(x.value,y.value), node2(z.value,d), m2.value)
case Two(_, d,e) => m1.add3(node3(a,b,c), node3(x.value,y.value,z.value), node2(d,e), m2.value)
case Three(_, d,e,f) => m1.add3(node3(a,b,c), node3(x.value,y.value,z.value), node3(d,e,f), m2.value)
case Four(_, d,e,f,g) => m1.add4(node3(a,b,c), node3(x.value,y.value,z.value), node2(d,e), node2(f,g), m2.value)
}
case Four(_, a,b,c,d) => d2 match {
case One(_, e) => m1.add3(node3(a,b,c), node3(d,x.value,y.value), node2(z.value,e), m2.value)
case Two(_, e,f) => m1.add3(node3(a,b,c), node3(d,x.value,y.value), node3(z.value,e,f), m2.value)
case Three(_, e,f,g) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node2(z.value,e),node2(f,g), m2.value)
case Four(_, e,f,g,h) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node3(z.value,e,f), node2(g,h), m2.value)
}
}
}
def addDigits4(m1: NodeTree, d1: AFinger, xt: => A, yt: => A, zt: => A, wt: => A, d2: AFinger, m2t: => NodeTree): NodeTree = {
val x = Need(xt)
val y = Need(yt)
val z = Need(zt)
val w = Need(wt)
val m2 = Need(m2t)
d1 match {
case One(_, a) => d2 match {
case One(_, b) => m1.add2(node3(a,x.value,y.value), node3(z.value,w.value,b), m2.value)
case Two(_, b,c) => m1.add3(node3(a,x.value,y.value), node2(z.value,w.value), node2(b,c), m2.value)
case Three(_, b,c,d) => m1.add3(node3(a,x.value,y.value), node3(z.value,w.value,b), node2(c,d), m2.value)
case Four(_, b,c,d,e) => m1.add3(node3(a,x.value,y.value), node3(z.value,w.value,b), node3(c,d,e), m2.value)
}
case Two(_, a,b) => d2 match {
case One(_, c) => m1.add3(node3(a,b,x.value), node2(y.value,z.value), node2(w.value,c), m2.value)
case Two(_, c,d) => m1.add3(node3(a,b,x.value), node3(y.value,z.value,w.value), node2(c,d), m2.value)
case Three(_, c,d,e) => m1.add3(node3(a,b,x.value), node3(y.value,z.value,w.value), node3(c,d,e), m2.value)
case Four(_, c,d,e,f) => m1.add4(node3(a,b,x.value), node3(y.value,z.value,w.value), node2(c,d), node2(e,f),m2.value)
}
case Three(_, a,b,c) => d2 match {
case One(_, d) => m1.add3(node3(a,b,c), node3(x.value,y.value,z.value), node2(w.value,d), m2.value)
case Two(_, d,e) => m1.add3(node3(a,b,c), node3(x.value,y.value,z.value), node3(w.value,d,e), m2.value)
case Three(_, d,e,f) => m1.add4(node3(a,b,c), node3(x.value,y.value,z.value), node2(w.value,d),node2(e,f), m2.value)
case Four(_, d,e,f,g) => m1.add4(node3(a,b,c), node3(x.value,y.value,z.value), node3(w.value,d,e), node2(f,g), m2.value)
}
case Four(_, a,b,c,d) => d2 match {
case One(_, e) => m1.add3(node3(a,b,c), node3(d,x.value,y.value), node3(z.value,w.value,e), m2.value)
case Two(_, e,f) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node2(z.value,w.value), node2(e,f), m2.value)
case Three(_, e,f,g) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node3(z.value,w.value,e),node2(f,g), m2.value)
case Four(_, e,f,g,h) => m1.add4(node3(a,b,c), node3(d,x.value,y.value), node3(z.value,w.value,e), node3(f,g,h), m2.value)
}
}
}
/**
* Splits this tree into a pair of subtrees at the point where the given predicate, based on the measure,
* changes from `true` to `false`. O(log(min(i,n-i)))
*
* @return `(as, bs)` `as`: the subtree containing elements before the point where `pred` first holds
* `fs` the subtree containing element at and after the point where `pred` first holds. Empty if `pred` never holds.
*/
def split(pred: V => Boolean): (FingerTree[V, A], FingerTree[V, A]) =
if (!isEmpty && pred(measure)) {
val (l, x, r) = split1(pred)
(l, x +: r)
}
else
(this, empty)
/**
* Like `split`, but returns the element where `pred` first holds separately
*
* @throws if the tree is empty.
*/
def split1(pred: V => Boolean): (FingerTree[V, A], A, FingerTree[V, A]) = split1(pred, measurer.monoid.zero)
private def split1(pred: V => Boolean, accV: V): (FingerTree[V, A], A, FingerTree[V, A]) = fold(
v => sys.error("Splitting an empty FingerTree"), // we can never get here
(v, x) => (empty, x, empty),
(v, pr, m, sf) => {
val accVpr = fingerMeasure[A, V].snoc(accV, pr)
if (pred(accVpr)) {
val (l, x, r) = pr.split1(pred, accV)
(cata(l)(_.toTree, empty), x, deepL(r, m, sf))
} else {
val accVm = mappendVal(accVpr, m)
if (pred(accVm)) {
val (ml, xs, mr) = m.split1(pred, accVpr)
val (l, x, r) = xs.split1(pred, mappendVal(accVpr, ml))
(deepR(pr, ml, l), x, deepL(r, mr, sf))
} else {
val (l, x, r) = sf.split1(pred, accVm)
(deepR(pr, m, l), x, cata(r)(_.toTree, empty))
}
}
}
)
def isEmpty: Boolean = fold(v => true, (v, x) => false, (v, pr, m, sf) => false)
def viewl: ViewL[FingerTree[V, ?], A] =
fold(
v => EmptyL[FingerTree[V, ?], A],
(v, x) => OnL[FingerTree[V, ?], A](x, empty[V, A]),
(v, pr, m, sf) =>
pr match {
case One(v, x) => OnL[FingerTree[V, ?], A](x, rotL(m, sf))
case _ => OnL[FingerTree[V, ?], A](pr.lhead, deep(pr.ltail, m, sf))
})
def viewr: ViewR[FingerTree[V, ?], A] =
fold(
v => EmptyR[FingerTree[V, ?], A],
(v, x) => OnR[FingerTree[V, ?], A](empty[V, A], x),
(v, pr, m, sf) =>
sf match {
case One(v, x) => OnR[FingerTree[V, ?], A](rotR(pr, m), x)
case _ => OnR[FingerTree[V, ?], A](deep(pr, m, sf.rtail), sf.rhead)
})
/**
* Selects the first element in the tree.
*
* @throws if the tree is empty
*/
def head: A = viewl.head
/**
* Selects the last element in the tree.
*
* @throws if the tree is empty
*/
def last: A = viewr.last
/**
* Selects a subtree containing all elements except the first
*
* @throws if the tree is empty
*/
def tail: FingerTree[V, A] = viewl.tail
/**
* Selects a subtree containing all elements except the last
*
* @throws if the tree is empty
*/
def init: FingerTree[V, A] = viewr.init
/** Maps the given function across the tree, annotating nodes in the resulting tree according to the provided `Reducer`. */
def map[B, V2](f: A => B)(implicit m: Reducer[B, V2]): FingerTree[V2, B] = {
implicit val nm = nodeMeasure[B, V2]
fold(
v => empty,
(v, x) => single(f(x)),
(v, pr, mt, sf) => deep(pr map f, mt.map(x => x.map(f)), sf map f))
}
/**
* Like traverse, but with a more constraint type: we need the additional measure to construct the new tree.
*/
def traverseTree[F[_], V2, B](f: A => F[B])(implicit ms: Reducer[B, V2], F: Applicative[F]): F[FingerTree[V2, B]] = {
def mkDeep(pr: Finger[V2, B])(m: FingerTree[V2, Node[V2, B]])(sf: Finger[V2, B]): FingerTree[V2, B] = deep(pr, m, sf)
fold(_ => F.pure(FingerTree.empty[V2, B]),
(v, a) => F.map(f(a))(a => single(ms.unit(a), a)),
(v, pr, m, sf) => {
//F.ap(traverseFinger(sf)(f))(F.ap(m.traverseTree(n => traverseNode(n)(f)))(F.map(traverseFinger(pr)(f))(pr => mkDeep(pr)_)))
//the implementation below seems most efficient. The straightforward implementation using F.map3 leads to an explosion of traverseTree calls
val fmap2 = F.apply2(traverseFinger(pr)(f), m.traverseTree(n => traverseNode(n)(f)))((a,b) => mkDeep(a)(b)_)
F.ap(traverseFinger(sf)(f))(fmap2)
})
}
private def traverseNode[F[_], V2, B](node: Node[V, A])(f: A => F[B])(implicit ms: Reducer[B, V2], F: Applicative[F]): F[Node[V2, B]] = {
def mkNode(x: B)(y: B)(z: B): Node[V2, B] = node3(x, y, z)
node.fold((v, a, b) => F.apply2(f(a), f(b))((x, y) => node2(x, y)),
(v, a, b, c) => {
F.ap(f(c))(F.ap(f(b))(F.map(f(a))(x => mkNode(x)_)))
}
)
}
private def traverseFinger[F[_], A, B, V2](digit: Finger[V, A])(f: A => F[B])(implicit ms: Reducer[B, V2], F: Applicative[F]): F[Finger[V2, B]] = {
def mkTwo(x: B)(y: B): Finger[V2, B] = two(x, y)
def mkThree(x: B)(y: B)(z: B): Finger[V2, B] = three(x, y, z)
def mkFour(w: B)(x: B)(y: B)(z: B): Finger[V2, B] = four(w, x, y, z)
digit match {
case One(v, a) => F.map(f(a))(x => one(x))
case Two(v, a, b) => F.ap(f(b))(F.map(f(a))(x => mkTwo(x)_))
case Three(v, a, b, c) => F.ap(f(c))(F.ap(f(b))(F.map(f(a))(x => mkThree(x)_)))
case Four(v, a, b, c, d) => F.ap(f(d))(F.ap(f(c))(F.ap(f(b))(F.map(f(a))(x => mkFour(x)_))))
}
}
/** Execute the provided side effect for each element in the tree. */
def foreach(f: A => Unit) {
fold(
_ => {},
(_, x) => { f(x) },
(_, pr, m, sf) => { pr.foreach(f); m.foreach(_.foreach(f)); sf.foreach(f) }
)}
/** An iterator that visits each element in the tree. */
def iterator: Iterator[A] = fold(
_ => Iterator.empty,
(_, x) => Iterator.single(x),
(_, pr, m, sf) => pr.iterator ++ m.iterator.flatMap(_.iterator) ++ sf.iterator)
/** An iterator that visits each element in the tree in reverse order. */
def reverseIterator: Iterator[A] = fold(
_ => Iterator.empty,
(_, x) => Iterator.single(x),
(_, pr, m, sf) => sf.reverseIterator ++ m.reverseIterator.flatMap(_.reverseIterator) ++ pr.reverseIterator)
/** Convert the leaves of the tree to a `scala.Stream` */
def toStream: Stream[A] = map(x => x)(Reducer.StreamReducer[A]).measure
/** Convert the leaves of the tree to a `scala.List` */
def toList: List[A] = toStream.toList
/** Convert the tree to a `String`. Unsafe: this uses `Any#toString` for types `V` and `A` */
override def toString = {
val showV = Show.showFromToString[V]
val showA = Show.showFromToString[A]
fingerTreeShow(showV, showA).shows(this)
}
}
sealed abstract class FingerTreeInstances {
import FingerTree._
implicit def viewLFunctor[S[_]](implicit s: Functor[S]): Functor[ViewL[S, ?]] =
new Functor[ViewL[S, ?]] {
def map[A, B](t: ViewL[S, A])(f: A => B): ViewL[S, B] =
t.fold(EmptyL[S, B], (x, xs) => OnL(f(x), s.map(xs)(f))) //TODO define syntax for &: and :&
}
implicit def viewRFunctor[S[_]](implicit s: Functor[S]): Functor[ViewR[S, ?]] =
new Functor[ViewR[S, ?]] {
def map[A, B](t: ViewR[S, A])(f: A => B): ViewR[S, B] =
t.fold(EmptyR[S, B], (xs, x) => OnR(s.map(xs)(f), f(x)))
}
implicit def fingerFoldable[V] =
new Foldable[Finger[V, ?]] with Foldable.FromFoldMap[Finger[V, ?]] {
override def foldMap[A, M: Monoid](v: Finger[V, A])(f: A => M) = v.foldMap(f)
}
implicit def fingerMeasure[A, V](implicit m: Reducer[A, V]): Reducer[Finger[V, A], V] = {
implicit val vm = m.monoid
UnitReducer((a: Finger[V, A]) => a.measure)
}
implicit def nodeMeasure[A, V](implicit m: Reducer[A, V]): Reducer[Node[V, A], V] = {
implicit val vm = m.monoid
UnitReducer((a: Node[V, A]) => a fold (
(v, _, _) => v,
(v, _, _, _) => v))
}
implicit def fingerTreeMeasure[A, V](implicit m: Reducer[A, V]): Reducer[FingerTree[V, A], V] = {
implicit val vm = m.monoid
UnitReducer((a: FingerTree[V, A]) => a.fold(v => v, (v, x) => v, (v, x, y, z) => v))
}
implicit def nodeFoldable[V] =
new Foldable[Node[V, ?]] {
def foldMap[A, M: Monoid](t: Node[V, A])(f: A => M): M = t foldMap f
def foldRight[A, B](v: Node[V, A], z: => B)(f: (A, => B) => B): B =
foldMap(v)((a: A) => (Endo.endo(f.curried(a)(_: B)))) apply z
}
implicit def fingerTreeFoldable[V]: Foldable[FingerTree[V, ?]] =
new Foldable[FingerTree[V, ?]] {
override def foldLeft[A, B](t: FingerTree[V, A], b: B)(f: (B, A) => B) = t.foldLeft(b)(f)
def foldMap[A, M: Monoid](t: FingerTree[V, A])(f: A => M): M = t foldMap(f)
override def foldRight[A, B](t: FingerTree[V, A], z: => B)(f: (A, => B) => B) = t.foldRight(z)(f)
}
implicit def fingerTreeMonoid[V, A](implicit m: Reducer[A, V]): Monoid[FingerTree[V, A]] =
new Monoid[FingerTree[V, A]] {
def append(f1: FingerTree[V, A], f2: => FingerTree[V, A]) = f1 <++> f2
def zero = empty
}
implicit def fingerTreeShow[V, A](implicit V: Show[V], A: Show[A]): Show[FingerTree[V,A]] =
new Show[FingerTree[V,A]] {
import std.iterable._
val AS = Show[List[A]]
import Cord._
override def show(t: FingerTree[V,A]) = t.fold(
empty = v => Cord(V.show(v), " []"),
single = (v, x) => Cord(V.show(v), " [", A.show(x), "]"),
deep = (v, pf, m, sf) => Cord(V.show(v), " [", AS.show(pf.toList), ", ?, ", AS.show(sf.toList), "]")
)
}
implicit def fingerTreeEqual[V, A : Equal]: Equal[FingerTree[V, A]] =
new Equal[FingerTree[V, A]] {
import std.stream._
def equal(x: FingerTree[V, A], y: FingerTree[V, A]) =
Equal[Stream[A]].equal(x.toStream, y.toStream)
}
}
object FingerTree extends FingerTreeInstances {
def Node2[V, A](v: V, a1: => A, a2: => A)(implicit r: Reducer[A, V]) =
new Node[V, A] {
def fold[B](two: (V, => A, => A) => B, three: (V, => A, => A, => A) => B) =
two(v, a1, a2)
val measure = v
}
def Node3[V, A](v: V, a1: => A, a2: => A, a3: => A)(implicit r: Reducer[A, V]) =
new Node[V, A] {
def fold[B](two: (V, => A, => A) => B, three: (V, => A, => A, => A) => B) =
three(v, a1, a2, a3)
val measure = v
}
def EmptyR[S[_], A]: ViewR[S, A] =
new ViewR[S, A] {
def fold[B](b: => B, f: (=> S[A], => A) => B) = b
}
def OnR[S[_], A](sa: => S[A], a: => A): ViewR[S, A] =
new ViewR[S, A] {
def fold[B](b: => B, f: (=> S[A], => A) => B) = f(sa, a)
}
def EmptyL[S[_], A]: ViewL[S, A] =
new ViewL[S, A] {
def fold[B](b: => B, f: (=> A, => S[A]) => B) = b
}
def OnL[S[_], A](a: => A, sa: => S[A]): ViewL[S, A] =
new ViewL[S, A] {
def fold[B](b: => B, f: (=> A, => S[A]) => B) = f(a, sa)
}
def one[V, A](a: A)(implicit measure: Reducer[A, V]) =
One(measure.unit(a), a)
def two[V, A](a1: A, a2: A)(implicit measure: Reducer[A, V]) =
Two(measure.snoc(measure.unit(a1), a2), a1, a2)
def three[V, A](a1: A, a2: A, a3: A)(implicit measure: Reducer[A, V]) =
Three(measure.snoc(measure.snoc(measure.unit(a1), a2), a3), a1, a2, a3)
def four[V, A](a1: A, a2: A, a3: A, a4: A)(implicit measure: Reducer[A, V]) =
Four(measure.snoc(measure.snoc(measure.snoc(measure.unit(a1), a2), a3), a4), a1, a2, a3, a4)
def node2[V, A](a: A, b: A)(implicit measure: Reducer[A, V]) =
Node2[V, A](measure.snoc(measure.unit(a), b), a, b)
def node3[V, A](a: A, b: A, c: A)(implicit measure: Reducer[A, V]) =
Node3[V, A](measure.snoc(measure.snoc(measure.unit(a), b), c), a, b, c)
def mappendVal[V, A](v: V, t: FingerTree[V, A])(implicit measure: Reducer[A, V]) =
t.fold(x => v, (x, y) => fingerTreeMeasure[A, V].snoc(v, t), (x, p, m, s) => fingerTreeMeasure[A, V].snoc(v, t))
def empty[V, A](implicit ms: Reducer[A, V]) =
new FingerTree[V, A] {
def fold[B](b: V => B, s: (V, A) => B, d: (V, Finger[V, A], => FingerTree[V, Node[V, A]], Finger[V, A]) => B): B = b(ms.monoid.zero)
}
def single[V, A](a: A)(implicit ms: Reducer[A, V]): FingerTree[V, A] = single(ms.unit(a), a)
def single[V, A](v: V, a: => A)(implicit ms: Reducer[A, V]): FingerTree[V, A] =
new FingerTree[V, A] {
def fold[B](b: V => B, s: (V, A) => B, d: (V, Finger[V, A], => FingerTree[V, Node[V, A]], Finger[V, A]) => B): B = s(v, a)
}
def deep[V, A](pr: Finger[V, A], m: => FingerTree[V, Node[V, A]], sf: Finger[V, A])
(implicit ms: Reducer[A, V]): FingerTree[V, A] = {
val measure = fingerMeasure[A, V]
deep(measure.snoc(mappendVal(measure.unit(pr), m), sf), pr, m, sf)
}
def deep[V, A](v: V, pr: Finger[V, A], m: => FingerTree[V, Node[V, A]], sf: Finger[V, A])
(implicit ms: Reducer[A, V]): FingerTree[V, A] =
new FingerTree[V, A] {
implicit val nMeasure = nodeMeasure[A, V]
private[this] val mz = Need(m)
def fold[B](b: V => B, f: (V, A) => B, d: (V, Finger[V, A], => FingerTree[V, Node[V, A]], Finger[V, A]) => B): B =
d(v, pr, mz.value, sf)
}
def deepL[V, A](mpr: Option[Finger[V, A]], m: => FingerTree[V, Node[V, A]], sf: Finger[V, A])(implicit ms: Reducer[A, V]): FingerTree[V, A] =
mpr match {
case None => rotL(m, sf)
case Some(pr) => deep(pr, m, sf)
}
def deepR[V, A](pr: Finger[V, A], m: => FingerTree[V, Node[V, A]], msf: Option[Finger[V, A]])(implicit ms: Reducer[A, V]): FingerTree[V, A] =
msf match {
case None => rotR(pr, m)
case Some(sf) => deep(pr, m, sf)
}
def rotL[V, A](m: FingerTree[V, Node[V, A]], sf: Finger[V, A])(implicit ms: Reducer[A, V]): FingerTree[V, A] =
m.viewl.fold(
sf.toTree,
(a, mm) => deep(fingerMeasure[A, V].snoc(m.measure, sf), a.toDigit, mm, sf))
def rotR[V, A](pr: Finger[V, A], m: FingerTree[V, Node[V, A]])(implicit ms: Reducer[A, V]): FingerTree[V, A] =
m.viewr.fold(
pr.toTree,
(mm, a) => deep(mappendVal(pr.measure, m), pr, mm, a.toDigit))
}
/** Indexed sequences, based on [[scalaz.FingerTree]]
*
* The measure is the count of the preceding elements, provided by `UnitReducer((e: Int) => 1)`.
*/
final class IndSeq[A](val self: FingerTree[Int, A]) {
import std.anyVal._
import IndSeq.indSeq
implicit def sizer[A] = UnitReducer((a: A) => 1)
def apply(i: Int): A =
self.split(_ > i)._2.viewl.headOption.getOrElse(sys.error("Index " + i + " > " + self.measure))
def replace(i: Int, a: => A): IndSeq[A] = {
val (l, r) = self.split(_ > i)
indSeq(l <++> (a |-: r))
}
def split(i: Int): (IndSeq[A], IndSeq[A]) = {
val (l, r) = self.split(_ > i)
(indSeq(l), indSeq(r))
}
def ++(xs: IndSeq[A]): IndSeq[A] = indSeq(self <++> xs.self)
def :+(x: => A): IndSeq[A] = indSeq(self :+ x)
def +:(x: => A): IndSeq[A] = indSeq(x +: self)
def length: Int = self.measure
def tail: IndSeq[A] = indSeq(self.tail)
def init: IndSeq[A] = indSeq(self.init)
def drop(n: Int): IndSeq[A] = split(n)._2
def take(n: Int): IndSeq[A] = split(n)._1
def map[B](f: A => B): IndSeq[B] = indSeq(self map f)
import FingerTree.fingerTreeFoldable
def flatMap[B](f: A => IndSeq[B]): IndSeq[B] = indSeq(fingerTreeFoldable.foldLeft(self, empty[Int, B])((ys, x) => ys <++> f(x).self))
}
object IndSeq extends IndSeqInstances {
private def indSeq[A](v: FingerTree[Int, A]): IndSeq[A] = new IndSeq(v)
import std.anyVal._
def apply[A](as: A*) = fromSeq(as)
def fromSeq[A](as: Seq[A]) = indSeq(as.foldLeft(empty[Int, A](UnitReducer(a => 1)))((x, y) => x :+ y))
}
sealed abstract class IndSeqInstances {
implicit def indSeqEqual[A: Equal]: Equal[IndSeq[A]] =
Equal.equalBy(_.self)
implicit val indSeqInstance: MonadPlus[IndSeq] with Traverse[IndSeq] with IsEmpty[IndSeq] =
new MonadPlus[IndSeq] with Traverse[IndSeq] with IsEmpty[IndSeq] with IsomorphismFoldable[IndSeq, FingerTree[Int, ?]]{
def G = implicitly
override val naturalTrans = new (IndSeq ~> FingerTree[Int, ?]) {
def apply[A](a: IndSeq[A]) =
a.self
}
def traverseImpl[G[_], A, B](fa: IndSeq[A])(f: A => G[B])(implicit G: Applicative[G]) = {
import std.anyVal._
implicit val r = UnitReducer((_: B) => 1)
G.map(fa.self.traverseTree(f))(new IndSeq(_))
}
override def length[A](fa: IndSeq[A]) =
fa.length
override def index[A](fa: IndSeq[A], i: Int) =
if(0 <= i && i < fa.length) Some(fa(i)) else None
override def isEmpty[A](fa: IndSeq[A]) =
fa.self.isEmpty
override def empty[A](fa: IndSeq[A]) =
fa.self.isEmpty
def point[A](a: => A) =
IndSeq(a)
def bind[A, B](fa: IndSeq[A])(f: A => IndSeq[B]) =
fa flatMap f
override def map[A, B](fa: IndSeq[A])(f: A => B) =
fa map f
def plus[A](a: IndSeq[A], b: => IndSeq[A]) =
a ++ b
def empty[A] =
IndSeq.apply()
}
}
/** Ordered sequences, based on [[scalaz.FingerTree]]
*
* `a` has a higher priority than `b` if `Order[A].greaterThan(a, b)`.
*
* `insert` and `++` maintains the ordering.
*
* The measure is calculated with a `Monoid[Option[A] @@ Last]`, whose `append`
* operation favours the first argument. Accordingly, the measuer of a node is the
* item with the highest priority contained recursively below that node.
*/
sealed abstract class OrdSeq[A] extends Ops[FingerTree[LastOption[A], A]] {
import std.function._
import std.option._
implicit val ord: Order[A]
/**
* @return (higher, lowerOrEqual) The sub-sequences that contain elements of higher and of lower-than-or-equal
* priority than `a`, and of lower or equal priority respectively.
*/
def partition(a: A): (OrdSeq[A], OrdSeq[A]) =
function1Instance.product(OrdSeq.ordSeq[A](_: FingerTree[LastOption[A], A]))(self.split(a1 =>
Order[LastOption[A]].greaterThanOrEqual(a1, Tags.Last(some(a)))))
/** Insert `a` at a the first point that all elements to the left are of higher priority */
def insert(a: A): OrdSeq[A] = partition(a) match {
case (l, r) => OrdSeq.ordSeq(l <++> (a +: r))
}
/** Append `xs` to this sequence, reordering elements to */
def ++(xs: OrdSeq[A]): OrdSeq[A] = xs.self.toList.foldLeft(this)(_ insert _)
}
object OrdSeq {
private def ordSeq[A: Order](t: FingerTree[LastOption[A], A]): OrdSeq[A] = new OrdSeq[A] {
val self = t
val ord = Order[A]
}
implicit def unwrap[A](t: OrdSeq[A]): FingerTree[LastOption[A], A] = t.self
def apply[A: Order](as: A*): OrdSeq[A] = {
val z: OrdSeq[A] = {
val keyer: Reducer[A, LastOption[A]] = UnitReducer((a: A) => Tags.Last(some(a)))
ordSeq(empty[LastOption[A], A](keyer))
}
as.foldLeft(z)((x, y) => x insert y)
}
}
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