Scala example source code file (Map.scala)
The Map.scala Scala example source code
package scalaz
/**
* @see [[http://hackage.haskell.org/package/containers-0.5.7.1/docs/mini_Data-Map-Strict.html]]
* @see [[https://github.com/haskell/containers/blob/v0.5.7.1/Data/Map/Base.hs]]
*/
import Ordering.{ EQ, LT, GT }
import std.anyVal._
import std.option._
import annotation.tailrec
/** An immutable map of key/value pairs implemented as a balanced binary tree
*
* Based on Haskell's Data.Map
*
* @since 7.0.3 */
sealed abstract class ==>>[A, B] {
import ==>>._
/** number of key/value pairs - O(1) */
val size: Int
/** returns `true` if this map contains no key/value pairs - O(1) */
def isEmpty: Boolean = this == empty
/** tupled form of [[insert]] */
def + (a: (A, B))(implicit o: Order[A]): A ==>> B =
insert(a._1, a._2)
/** inserts a new key/value - O(log n).
*
* If the key is already present, its value is replaced by the provided value. */
def insert(kx: A, x: B)(implicit n: Order[A]): A ==>> B =
this match {
case Tip() =>
singleton(kx, x)
case Bin(ky, y, l, r) =>
n.order(kx, ky) match {
case LT =>
balanceL(ky, y, l.insert(kx, x), r)
case GT =>
balanceR(ky, y, l, r.insert(kx, x))
case EQ =>
Bin(kx, x, l, r)
}
}
/** inserts a new key/value pair, resolving the conflict if the key already exists - O(log n)
*
* @param f function to resolve conflict with existing key:
* (insertedValue, existingValue) => resolvedValue
* @param kx key
* @param x value to insert if the key is not already present */
def insertWith(f: (B, B) => B, kx: A, x: B)(implicit o: Order[A]): A ==>> B =
insertWithKey((_, a, b) => f(a,b), kx, x)
/** inserts a new key/value pair, resolving the conflict if the key already exists - O(log n)
*
* @param f function to resolve conflict with existing key:
* (key, insertedValue, existingValue) => resolvedValue
* @param kx key
* @param x value to insert if the key is not already present */
def insertWithKey(f: (A, B, B) => B, kx: A, x: B)(implicit o: Order[A]): A ==>> B =
this match {
case Tip() =>
singleton(kx, x)
case Bin(ky, y, l, r) =>
o.order(kx, ky) match {
case LT =>
balanceL(ky, y, l.insertWithKey(f, kx, x), r)
case GT =>
balanceR(ky, y, l, r.insertWithKey(f, kx, x))
case EQ =>
Bin(kx, f(kx, x, y), l, r)
}
}
/** alias for [[delete]] */
def -(k: A)(implicit o: Order[A]): A ==>> B =
delete(k)
/** removes a key/value pair - O(log n) */
def delete(k: A)(implicit n: Order[A]): A ==>> B =
this match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
n.order(k, kx) match {
case LT =>
balanceR(kx, x, l.delete(k), r)
case EQ =>
glue(l, r)
case GT =>
balanceL(kx, x, l, r.delete(k))
}
}
/** if the key exists, transforms its value - O(log n) */
def adjust(k: A, f: B => B)(implicit o: Order[A]): A ==>> B =
adjustWithKey(k, (_, x) => f(x))
/** like [[adjust]] but with the key available in the transformation - O(log n) */
def adjustWithKey(k: A, f: (A, B) => B)(implicit o: Order[A]): A ==>> B =
updateWithKey(k, (a, b) => some(f(a, b)))
/** updates or removes a value - O(log n)
*
* if `f` returns `None`, then the key is removed from the map */
def update(k: A, f: B => Option[B])(implicit o: Order[A]): A ==>> B =
updateWithKey(k, (_, x) => f(x))
/** like [[update]] but with the key available in the update function - O(log n) */
def updateWithKey(k: A, f: (A, B) => Option[B])(implicit o: Order[A]): A ==>> B =
this match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
balanceR(kx, x, l.updateWithKey(k, f), r)
case GT =>
balanceL(kx, x, l, r.updateWithKey(k, f))
case EQ =>
f(kx, x) match {
case Some(v) =>
Bin(kx, v, l, r)
case None =>
glue(l, r)
}
}
}
/** looks up a key and updates its value - O(log n)
*
* Similar to [[updateWithKey]] but also returns the value. If the value was updated, returns the
* new value. If the value was deleted, returns the old value. */
def updateLookupWithKey(k: A, f: (A, B) => Option[B])(implicit o: Order[A]): (Option[B], A ==>> B) =
this match {
case Tip() =>
(none, empty)
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
val (found, ll) = l.updateLookupWithKey(k, f)
(found, balanceR(kx, x, ll, r))
case GT =>
val (found, rr) = r.updateLookupWithKey(k, f)
(found, balanceL(kx, x, l, rr))
case EQ =>
f(kx, x) match {
case Some(xx) =>
(some(xx), Bin(kx, xx, l, r))
case None =>
(some(x), glue(l, r))
}
}
}
def alter(k: A, f: Option[B] => Option[B])(implicit o: Order[A]): A ==>> B =
this match {
case Tip() =>
f(None) match {
case None =>
empty
case Some(x) =>
singleton(k, x)
}
case Bin(kx, x, l,r) =>
o.order(k, kx) match {
case LT =>
balance(kx, x, l.alter(k, f), r)
case GT =>
balance(kx, x, l, r.alter(k, f))
case EQ =>
f(some(x)) match {
case None =>
glue(l, r)
case Some(xx) =>
Bin(kx, xx, l, r)
}
}
}
@tailrec
final def lookup(k: A)(implicit n: Order[A]): Option[B] =
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
n.order(k, kx) match {
case LT =>
l.lookup(k)
case GT =>
r.lookup(k)
case EQ =>
some(x)
}
}
@tailrec
final def lookupAssoc(k: A)(implicit n: Order[A]): Option[(A, B)] =
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
n.order(k, kx) match {
case LT =>
l.lookupAssoc(k)
case GT =>
r.lookupAssoc(k)
case EQ =>
some((kx, x))
}
}
@tailrec
final def lookupLT(k: A)(implicit o: Order[A]): Option[(A, B)] = {
@tailrec
def goSome(kx: A, x: B, t: A ==>> B): Option[(A, B)] =
t match {
case Tip() =>
some((kx, x))
case Bin(ky, y, l, r) =>
if (o.lessThanOrEqual(k, ky)) goSome(kx, x, l) else goSome(ky, y, r)
}
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
if (o.lessThanOrEqual(k, kx)) l.lookupLT(k) else goSome(kx, x, r)
}
}
@tailrec
final def lookupGT(k: A)(implicit o: Order[A]): Option[(A, B)] = {
@tailrec
def goSome(kx: A, x: B, t: A ==>> B): Option[(A, B)] =
t match {
case Tip() =>
some((kx, x))
case Bin(ky, y, l, r) =>
if (o.greaterThanOrEqual(k, ky)) goSome(kx, x, r) else goSome(ky, y, l)
}
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
if (o.greaterThanOrEqual(k, kx)) r.lookupGT(k) else goSome(kx, x, l)
}
}
@tailrec
final def lookupLE(k: A)(implicit o: Order[A]): Option[(A, B)] = {
@tailrec
def goSome(kx: A, x: B, t: A ==>> B): Option[(A, B)] =
t match {
case Tip() =>
some((kx, x))
case Bin(ky, y, l, r) =>
o.order(k, ky) match {
case LT =>
goSome(kx, x, l)
case EQ =>
some((ky, y))
case GT =>
goSome(ky, y, r)
}
}
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
l.lookupLE(k)
case EQ =>
some((kx, x))
case GT =>
goSome(kx, x, r)
}
}
}
@tailrec
final def lookupGE(k: A)(implicit o: Order[A]): Option[(A, B)] = {
@tailrec
def goSome(kx: A, x: B, t: A ==>> B): Option[(A, B)] =
t match {
case Tip() =>
some((kx, x))
case Bin(ky, y, l, r) =>
o.order(k, ky) match {
case LT =>
goSome(ky, y, l)
case EQ =>
some((ky, y))
case GT =>
goSome(kx, x, r)
}
}
this match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
goSome(kx, x, l)
case EQ =>
some((kx, x))
case GT =>
r.lookupGE(k)
}
}
}
def values: List[B] =
foldrWithKey(List.empty[B])((_, x, xs) => x :: xs)
def keys: List[A] =
foldrWithKey(List.empty[A])((x, _, xs) => x :: xs)
def keySet: ISet[A] = this match {
case Tip() => ISet.Tip[A]
case Bin(k,v,l,r) => ISet.Bin(k,l.keySet,r.keySet)
}
def toList: List[(A, B)] =
toAscList
def toAscList: List[(A, B)] =
foldrWithKey(List.empty[(A, B)])((k, x, xs) => (k, x) :: xs)
def toDescList: List[(A, B)] =
foldlWithKey(List.empty[(A, B)])((xs, k, x) => (k, x) :: xs)
def member(k: A)(implicit n: Order[A]): Boolean =
lookup(k)(n).isDefined
def notMember(k: A)(implicit n: Order[A]): Boolean =
!member(k)
def lookupIndex(k: A)(implicit o: Order[A]): Option[Int] = {
@tailrec
def go(n: Int, m: A ==>> B): Option[Int] =
m match {
case Tip() =>
none
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
go(n, l)
case GT =>
go(n + l.size + 1, r)
case EQ =>
some((n + l.size))
}
}
go(0, this)
}
@tailrec
final def elemAt(i: Int): Option[(A, B)] =
this match {
case Tip() =>
none
case Bin(kx, x, l ,r) =>
implicitly[Order[Int]].order(i, l.size) match {
case LT =>
l.elemAt(i)
case GT =>
r.elemAt(i - l.size - 1)
case EQ =>
some((kx, x))
}
}
// TODO: This should be a total function
def updateAt(i: Int, f: (A, B) => Option[B]): A ==>> B =
this match {
case Tip() =>
sys.error("updateAt")
case Bin(kx, x, l, r) =>
implicitly[Order[Int]].order(i, l.size) match {
case LT =>
balanceR(kx, x, l.updateAt(i, f), r)
case GT =>
balanceL(kx, x, l, r.updateAt(i - l.size - 1, f))
case EQ =>
f(kx, x) match {
case Some(y) => Bin(kx, y, l, r)
case None => glue(l, r)
}
}
}
def deleteAt(i: Int): A ==>> B =
updateAt(i, (A, B) => None)
@tailrec
final def findMin: Option[(A, B)] =
this match {
case Bin(kx, x, Tip(), _) =>
some((kx, x))
case Bin(_, _, l, _) =>
l.findMin
case Tip() =>
none
}
@tailrec
final def findMax: Option[(A, B)] =
this match {
case Bin(kx, x, _, Tip()) =>
some((kx, x))
case Bin(_, _, _, r) =>
r.findMax
case Tip() =>
none
}
def deleteMin: A ==>> B =
this match {
case Bin(_, _, Tip(), r) =>
r
case Bin(kx, x, l, r) =>
balanceR(kx, x, l.deleteMin, r)
case Tip() =>
empty
}
def deleteMax: A ==>> B =
this match {
case Bin(_, _, l, Tip()) =>
l
case Bin(kx, x, l, r) =>
balanceL(kx, x, l, r.deleteMax)
case Tip() =>
empty
}
def updateMin(f: B => Option[B]): A ==>> B =
updateMinWithKey((_: A, b) => f(b))
def updateMinWithKey(f: (A, B) => Option[B]): A ==>> B =
this match {
case Bin(kx, x, Tip(), r) =>
f(kx, x) match {
case None =>
r
case Some(s) =>
Bin(kx, s, Tip(), r)
}
case Bin(kx, x, l, r) =>
balanceR(kx, x, l.updateMinWithKey(f), r)
case Tip() =>
empty
}
def updateMax(f: B => Option[B]): A ==>> B =
updateMaxWithKey((_: A, b) => f(b))
def updateMaxWithKey(f: (A, B) => Option[B]): A ==>> B =
this match {
case Bin(kx, x, l, Tip()) =>
f(kx, x) match {
case None =>
l
case Some(s) =>
Bin(kx, s, l, Tip())
}
case Bin(kx, x, l, r) =>
balanceL(kx, x, l, r.updateMaxWithKey(f))
case Tip() =>
empty
}
/**
* insert v into the map at k. If there is already a value for k,
* append to the existing value using the Semigroup
*/
def updateAppend(k: A, v: B)(implicit o: Order[A], bsg: Semigroup[B]): A ==>> B =
alter(k, old ⇒ Some(old.map(bsg.append(_, v)).getOrElse(v)))
def minViewWithKey: Option[((A, B), A ==>> B)] =
this match {
case Tip() =>
none
case x @ Bin(_, _, _, _) =>
some(deleteFindMin(x))
}
def maxViewWithKey: Option[((A, B), A ==>> B)] =
this match {
case Tip() =>
none
case x @ Bin(_, _, _, _) =>
some(deleteFindMax(x))
}
def minView: Option[(B, A ==>> B)] =
this match {
case Tip() =>
none
case x @ Bin(_, _, _, _) =>
val r = deleteFindMin(x)
some((r._1._2, r._2))
}
def maxView: Option[(B, A ==>> B)] =
this match {
case Tip() =>
none
case x @ Bin(_, _, _, _) =>
val r = deleteFindMax(x)
some((r._1._2, r._2))
}
def deleteFindMax(t: Bin[A, B]): ((A, B), A ==>> B) =
t match {
case Bin(k, x, l, Tip()) =>
((k,x), l)
case Bin(k, x, l, r @ Bin(_, _, _, _)) =>
val (km, r2) = deleteFindMax(r)
(km, balanceL(k, x, l, r2))
}
def deleteFindMin(t: Bin[A, B]): ((A, B), A ==>> B) =
t match {
case Bin(k, x, Tip(), r) =>
((k, x), r)
case Bin(k, x, l @ Bin(_, _, _, _), r) =>
val (km, l2) = deleteFindMin(l)
(km, balanceR(k, x, l2, r))
}
/* Mappings */
def map[C](f: B => C): A ==>> C =
mapWithKey((_, x: B) => f(x))
def mapWithKey[C](f: (A, B) => C): A ==>> C =
this match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
Bin(kx, f(kx, x), l.mapWithKey(f), r.mapWithKey(f))
}
def traverseWithKey[F[_], C](f: (A, B) => F[C])(implicit G: Applicative[F]): F[A ==>> C] =
this match {
case Tip() =>
G.point(Tip())
case Bin(kx, x, Tip(), Tip()) =>
G.apply(f(kx, x)) { x2 =>
Bin(kx, x2, Tip(), Tip())
}
case Bin(kx, x, l, r) =>
G.apply3(l.traverseWithKey(f), f(kx, x), r.traverseWithKey(f)) {
(l2, x2, r2) => Bin(kx, x2, l2, r2)
}
}
def mapAccum[C](z: C)(f: (C, B) => (C, B)): (C, A ==>> B) =
mapAccumWithKey(z)((a2, _, x2) => f(a2, x2))
def mapAccumWithKey[C](z: C)(f: (C, A, B) => (C, B)): (C, A ==>> B) =
mapAccumL(z)(f)
def mapAccumL[C](a: C)(f: (C, A, B) => (C, B)): (C, A ==>> B) =
this match {
case Tip() =>
(a, empty)
case Bin(kx, x, l, r) =>
val (a1, l2) = l.mapAccumL(a)(f)
val (a2, x2) = f(a1, kx, x)
val (a3, r2) = r.mapAccumL(a2)(f)
(a3, Bin(kx, x2, l2, r2))
}
//def mapAccumRWithKey
def mapKeys[C](f: A => C)(implicit o: Order[C]): C ==>> B =
foldlWithKey(empty[C, B])((xs, k, x) => xs.insert(f(k), x))
def mapKeysWith[C](f: A => C, f2: (B, B) => B)(implicit o: Order[C]): C ==>> B =
fromListWith[C, B](toList.map(x => (f(x._1), x._2)))(f2)
/* Folds */
def fold[C](z: C)(f: (A, B, C) => C): C =
foldrWithKey(z)(f)
def foldlWithKey[C](z: C)(f: (C, A, B) => C): C =
this match {
case Tip() =>
z
case Bin(kx, x, l, r) =>
r.foldlWithKey(f(l.foldlWithKey(z)(f), kx, x))(f)
}
def foldrWithKey[C](z: C)(f: (A, B, C) => C): C =
this match {
case Tip() =>
z
case Bin(kx, x, l, r) =>
l.foldrWithKey(f(kx, x, r.foldrWithKey(z)(f)))(f)
}
def foldMapWithKey[C](f: (A, B) => C)(implicit F: Monoid[C]): C =
this match {
case Tip() =>
F.zero
case Bin(k, x, Tip(), Tip()) =>
f(k, x)
case Bin(k, x, l, r) =>
F.append(l.foldMapWithKey(f), F.append(f(k, x), r.foldMapWithKey(f)))
}
/* Unions */
def union(other: A ==>> B)(implicit k: Order[A]): A ==>> B = {
def hedgeUnion(blo: Option[A], bhi: Option[A], m1: A ==>> B, m2: A ==>> B): A ==>> B =
(m1, m2) match {
case (t1, Tip()) =>
t1
case (Tip(), Bin(kx, x, l, r)) =>
link(kx, x, l filterGt blo, r filterLt bhi)
case (t1, Bin(kx, x, Tip(), Tip())) =>
insertR(kx, x, t1)
case (Bin(kx, x, l, r), t2) =>
val bmi = Some(kx)
val nm1 = hedgeUnion(blo, bmi, l, ==>>.trim(blo, bmi, t2))
val nm2 = hedgeUnion(bmi, bhi, r, ==>>.trim(bmi, bhi, t2))
link(kx, x, nm1, nm2)
}
def insertR(kx: A, x: B, t: A ==>> B)(implicit o: Order[A]): A ==>> B = {
def go(kx: A, x: B, m: A ==>> B): A ==>> B =
m match {
case Tip() => singleton(kx, x)
case Bin(ky, y, l, r) =>
o.order(kx, ky) match {
case LT => balanceL(ky, y, go(kx, x, l), r)
case GT => balanceR(ky, y, l, go(kx, x, r))
case EQ => m
}
}
go(kx, x, t)
}
(this, other) match {
case (Tip(), t2) => t2
case (t1, Tip()) => t1
case (t1, t2) => hedgeUnion(None, None, t1, t2)
}
}
def unionWith(other: A ==>> B)(f: (B, B) => B)(implicit o: Order[A]): A ==>> B =
unionWithKey(other)((_, b, c) => f(b, c))
def unionWithKey(other: A ==>> B)(f: (A, B, B) => B)(implicit o: Order[A]): A ==>> B =
mergeWithKey(this, other)((a, b, c) => some(f(a, b, c)))(x => x, x => x)
// Difference functions
def \\[C](other: A ==>> C)(implicit o: Order[A]): A ==>> B =
difference(other)
def difference[C](other: A ==>> C)(implicit o: Order[A]): A ==>> B = {
def hedgeDiff(blo: Option[A], bhi: Option[A], a: A ==>> B, b: A ==>> C): A ==>> B =
(a, b) match {
case (Tip(), _) =>
empty
case (Bin(kx, x, l, r), Tip()) =>
link(kx, x, l filterGt blo, r filterLt bhi)
case (t, Bin(kx, _, l, r)) =>
val bmi = some(kx)
val aa = hedgeDiff(blo, bmi, ==>>.trim(blo, bmi, t), l)
val bb = hedgeDiff(bmi, bhi, ==>>.trim(bmi, bhi, t), r)
aa merge bb
}
(this, other) match {
case (Tip(), _) =>
empty
case (t1, Tip()) =>
t1
case (t1, t2) =>
hedgeDiff(None, None, t1, t2)
}
}
def differenceWith[C](other: A ==>> C)(f: (B, C) => Option[B])(implicit o: Order[A]): A ==>> B =
differenceWithKey(other)((_, b, c) => f(b, c))
def differenceWithKey[C](other: A ==>> C)(f: (A, B, C) => Option[B])(implicit o: Order[A]): A ==>> B =
mergeWithKey(this, other)(f)(x => x, _ => empty)
// Intersections
def intersection[C](other: A ==>> C)(implicit o: Order[A]): A ==>> B = {
def hedgeInt(blo: Option[A], bhi: Option[A], a: A ==>> B, b: A ==>> C): A ==>> B =
(a, b) match {
case (_, Tip()) =>
empty
case (Tip(), _) =>
empty
case (Bin(kx, x, l, r), t2) =>
val bmi = some(kx)
val l2 = hedgeInt(blo, bmi, l, ==>>.trim(blo, bmi, t2))
val r2 = hedgeInt(bmi, bhi, r, ==>>.trim(bmi, bhi, t2))
if (t2 member kx) link(kx, x, l2, r2)
else l2 merge r2
}
(this, other) match {
case (Tip(), _) => empty
case (_, Tip()) => empty
case (t1, t2) => hedgeInt(None, None, t1, t2)
}
}
def intersectionWith[C, D](other: A ==>> C)(f: (B, C) => D)(implicit o: Order[A]): A ==>> D =
intersectionWithKey(other)((_, x, y) => f(x, y))
def intersectionWithKey[C, D](other: A ==>> C)(f: (A, B, C) => D)(implicit o: Order[A]): A ==>> D =
mergeWithKey(this, other)((a, b, c) => some(f(a, b, c)))(_ => empty, _ => empty)
// Submap
def isSubmapOf(a: A ==>> B)(implicit o: Order[A], e: Equal[B]): Boolean =
isSubmapOfBy(a, e.equal)
def isSubmapOfBy(a: A ==>> B, f: (B, B) => Boolean)(implicit o: Order[A]): Boolean =
size <= a.size && submap(a, f)
private[scalaz] def submap(a: A ==>> B, f: (B, B) => Boolean)(implicit o: Order[A]): Boolean =
(this, a) match {
case (Tip(), _) =>
true
case (_, Tip()) =>
false
case (Bin(kx, x, l, r), t) =>
val (lt, found, gt) = t splitLookup kx
found match {
case None =>
false
case Some(y) =>
f(x, y) && l.submap(lt, f) && r.submap(gt, f)
}
}
// Filter
def filter(p: B => Boolean)(implicit o: Order[A]): A ==>> B =
filterWithKey((_, x) => p(x))
def filterWithKey(p: (A, B) => Boolean)(implicit o: Order[A]): A ==>> B =
this match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
if (p(kx, x))
link(kx, x, l.filterWithKey(p), r.filterWithKey(p))
else
l.filterWithKey(p) merge r.filterWithKey(p)
}
// Partition
def partition(p: B => Boolean)(implicit o: Order[A]): (A ==>> B, A ==>> B) =
partitionWithKey((_, x) => p(x))
def partitionWithKey(p: (A, B) => Boolean)(implicit o: Order[A]): (A ==>> B, A ==>> B) =
this match {
case Tip() =>
(empty, empty)
case Bin(kx, x, l, r) =>
val (l1, l2) = l partitionWithKey p
val (r1, r2) = r partitionWithKey p
if (p(kx, x))
(link(kx, x, l1, r1), l2 merge r2)
else
(l1 merge r1, link(kx, x, l2, r2))
}
def mapOption[C](f: B => Option[C])(implicit o: Order[A]): A ==>> C =
mapOptionWithKey((_, x) => f(x))
def mapOptionWithKey[C](f: (A, B) => Option[C])(implicit o: Order[A]): A ==>> C =
this match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
f(kx, x) match {
case Some(y) =>
link(kx, y, l.mapOptionWithKey(f), r.mapOptionWithKey(f))
case None =>
l.mapOptionWithKey(f).merge(r.mapOptionWithKey(f))
}
}
def mapEither[C, D](f: B => C \/ D)(implicit o: Order[A]): (A ==>> C, A ==>> D) =
mapEitherWithKey((_, x) => f(x))
def mapEitherWithKey[C, D](f: (A, B) => C \/ D)(implicit o: Order[A]): (A ==>> C, A ==>> D) =
this match {
case Tip() =>
(empty, empty)
case Bin(kx, x, l, r) =>
val (l1, l2) = l.mapEitherWithKey(f)
val (r1, r2) = r.mapEitherWithKey(f)
f(kx, x) match {
case -\/(y) =>
(link(kx, y, l1, r1), l2 merge r2)
case \/-(z) =>
(l1 merge r1, link(kx, z, l2, r2))
}
}
// Split
def split(k: A)(implicit o: Order[A]): (A ==>> B, A ==>> B) =
this match {
case Tip() =>
(empty, empty)
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
val (lt, gt) = l.split(k)
(lt, link(kx, x, gt, r))
case GT =>
val (lt, gt) = r.split(k)
(link(kx, x, l, lt), gt)
case EQ =>
(l, r)
}
}
def splitLookup(k: A)(implicit o: Order[A]): (A ==>> B, Option[B], A ==>> B) =
this match {
case Tip() =>
(empty, none, empty)
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
val (lt, z, gt) = l splitLookup k
(lt, z, link(kx, x, gt, r))
case GT =>
val (lt, z, gt) = r splitLookup k
(link(kx, x, l, lt), z, gt)
case EQ =>
(l, some(x), r)
}
}
def splitLookupWithKey(k: A)(implicit o: Order[A]): (A ==>> B, Option[(A, B)], A ==>> B) =
this match {
case Tip() =>
(empty, none, empty)
case Bin(kx, x, l, r) =>
o.order(k, kx) match {
case LT =>
val (lt, z, gt) = l splitLookupWithKey k
(lt, z, link(kx, x, gt, r))
case GT =>
val (lt, z, gt) = r splitLookupWithKey k
(link(kx, x, l, lt), z, gt)
case EQ =>
(l, some((kx, x)), r)
}
}
def splitRoot: List[A ==>> B] =
this match {
case Tip() => List.empty[A ==>> B]
case Bin(k, x, l, r) => List(l, singleton(k, x), r)
}
// Utility functions
// Because the following functions depend on some public interface, such as deleteFindMax,
// they can't be moved to object ==>> unlike other utility functions, balance(...) for example.
// TODO: merge should be private as it's a utility function but not a public interface.
protected def merge(other: A ==>> B): A ==>> B =
(this, other) match {
case (Tip(), r) =>
r
case (l, Tip()) =>
l
case (l @ Bin(kx, x, lx, rx), r @ Bin(ky, y, ly, ry)) =>
if (delta * l.size < r.size) balanceL(ky, y, l.merge(ly), ry)
else if (delta * r.size < l.size) balanceR(kx, x, lx, rx.merge(r))
else glue(l, r)
}
private def glue(l: A ==>> B, r: A ==>> B): A ==>> B =
(l, r) match {
case (Tip(), r) => r
case (l, Tip()) => l
case (l @ Bin(_, _, _, _), r @ Bin(_, _, _, _)) => if (l.size > r.size) {
val ((km, m), l2) = deleteFindMax(l)
balanceR(km, m, l2, r)
}
else {
val ((km, m), r2) = deleteFindMin(r)
balanceL(km, m, l, r2)
}
}
@deprecated("trim is no longer a public function", "7.3")
@tailrec
final def trim(lo: A => Ordering, hi: A => Ordering): A ==>> B =
this match {
case Tip() =>
empty
case t @ Bin(kx, _, l, r) =>
lo(kx) match {
case LT => hi(kx) match {
case GT => t
case _ => l.trim(lo, hi)
}
case _ => r.trim(lo, hi)
}
}
@deprecated("trimLookupLo is no longer a public function", "7.3")
@tailrec
final def trimLookupLo(lo: A, cmphi: A => Ordering)(implicit o: Order[A]): (Option[(A, B)], A ==>> B) =
this match {
case Tip() =>
(none, empty)
case t @ Bin(kx, x, l, r) =>
o.order(lo, kx) match {
case LT =>
cmphi(kx) match {
case GT =>
(t lookupAssoc lo, t)
case _ =>
l.trimLookupLo(lo, cmphi)
}
case GT =>
r.trimLookupLo(lo, cmphi)
case EQ =>
(some((kx, x)), r.trim(a => o.order(lo, a), cmphi))
}
}
override final def equals(other: Any): Boolean =
other match {
case that: ==>>[A, B] =>
==>>.mapEqual[A, B](Equal.equalA, Equal.equalA).equal(this, that)
case _ =>
false
}
override final def hashCode: Int =
toAscList.hashCode
// filters on keys
private def filterGt(a: Option[A])(implicit o: Order[A]): A ==>> B = {
def filter(filteringKey: A, m: A ==>> B): A ==>> B =
m match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
o.order(filteringKey, kx) match {
case LT => link(kx, x, filter(filteringKey, l), r)
case EQ => r
case GT => filter(filteringKey, r)
}
}
cata(a)(filter(_, this), this)
}
private def filterLt(a: Option[A])(implicit o: Order[A]): A ==>> B = {
def filter(filteringKey: A, m: A ==>> B): A ==>> B =
m match {
case Tip() =>
empty
case Bin(kx, x, l, r) =>
o.order(kx, filteringKey) match {
case LT => link(kx, x, l, filter(filteringKey, r))
case EQ => l
case GT => filter(filteringKey, l)
}
}
cata(a)(filter(_, this), this)
}
@deprecated("join is no longer a protected function", "7.3")
protected def join(kx: A, x: B, other: A ==>> B)(implicit o: Order[A]): A ==>> B =
(this, other) match {
case (Tip(), r) =>
insertMin(kx, x, r)
case (l, Tip()) =>
insertMax(kx, x, l)
case (l @ Bin(ky, y, ly, ry), r @ Bin(kz, z, lz, rz)) =>
if (delta * l.size < r.size) balanceL(kz, z, link(kx, x, l, lz), rz)
else if (delta * r.size < l.size) balanceR(ky, y, ly, link(kx, x, ry, r))
else Bin(kx, x, l, r)
}
}
sealed abstract class MapInstances0 {
implicit def scalazMapInstance[S: Order]: Bind[S ==>> ?] with Align[S ==>> ?] with Zip[S ==>> ?] =
new Bind[S ==>> ?] with Align[S ==>> ?] with Zip[S ==>> ?] {
override def map[A, B](fa: S ==>> A)(f: A => B) =
fa map f
def bind[A, B](fa: S ==>> A)(f: A => (S ==>> B)) =
fa.mapOptionWithKey((k, v) => f(v).lookup(k))
import \&/._, ==>>.Tip
override def align[A, B](a: S ==>> A, b: S ==>> B) =
(a, b) match {
case (Tip(), Tip()) => Tip()
case (a , Tip()) => a.map(This(_))
case (Tip(), b ) => b.map(That(_))
case (a , b ) =>
a.map(This(_): A \&/ B).unionWith(b.map(That(_): A \&/ B)){
case (This(aa), That(bb)) => Both(aa, bb)
case _ => sys.error("==>> align")
}
}
override def alignWith[A, B, C](f: A \&/ B => C) = {
case (Tip(), Tip()) => Tip()
case (a , Tip()) => a.map(aa => f(This(aa)))
case (Tip(), b ) => b.map(bb => f(That(bb)))
case (a , b ) =>
a.map(This(_): A \&/ B).unionWith(b.map(That(_): A \&/ B)){
case (This(aa), That(bb)) => Both(aa, bb)
case _ => sys.error("==>> alignWith")
}.map(f)
}
def zip[A, B](a: => (S ==>> A), b: => (S ==>> B)) = {
val a0 = a
if(a0.isEmpty) ==>>.empty
else a0.intersectionWith(b)(Tuple2.apply)
}
override def zipWith[A, B, C](a: => (S ==>> A), b: => (S ==>> B))(f: (A, B) => C)(implicit F: Functor[S ==>> ?]) = {
val a0 = a
if(a0.isEmpty) ==>>.empty
else a0.intersectionWith(b)(f)
}
}
}
sealed abstract class MapInstances extends MapInstances0 {
import ==>>._
import std.list._
import std.tuple._
implicit def mapShow[A: Show, B: Show]: Show[==>>[A, B]] =
Contravariant[Show].contramap(Show[List[(A, B)]])(_.toAscList)
implicit def mapEqual[A: Equal, B: Equal]: Equal[A ==>> B] =
new MapEqual[A, B] {def A = implicitly; def B = implicitly}
implicit def mapOrder[A: Order, B: Order]: Order[A ==>> B] =
new Order[A ==>> B] with MapEqual[A, B] {
def A = implicitly
def B = implicitly
def order(o1: A ==>> B, o2: A ==>> B) =
Order[List[(A,B)]].order(o1.toAscList, o2.toAscList)
}
implicit def mapUnion[A, B](implicit A: Order[A], B: Semigroup[B]): Monoid[A ==>> B] =
Monoid.instance((l, r) => (l unionWith r)(B.append(_, _)), Tip())
implicit def mapIntersection[A, B](implicit A: Order[A], B: Semigroup[B]
): Semigroup[(A ==>> B) @@ Tags.Conjunction] =
Tag.subst(Semigroup.instance((l, r) =>
(l intersectionWith r)(B.append(_, _))))
implicit def mapCovariant[S]: Traverse[S ==>> ?] =
new Traverse[S ==>> ?] {
override def findLeft[A](fa: S ==>> A)(f: A => Boolean): Option[A] =
fa match {
case Bin(_, x, l, r) =>
findLeft(l)(f) match {
case a @ Some(_) =>
a
case None =>
if (f(x))
Some(x)
else
findLeft(r)(f)
}
case Tip() =>
None
}
override def findRight[A](fa: S ==>> A)(f: A => Boolean): Option[A] =
fa match {
case Bin(_, x, l, r) =>
findRight(r)(f) match {
case a @ Some(_) =>
a
case None =>
if (f(x))
Some(x)
else
findRight(l)(f)
}
case Tip() =>
None
}
override def map[A, B](fa: S ==>> A)(f: A => B): S ==>> B =
fa map f
override def foldMap[A, B](fa: S ==>> A)(f: A => B)(implicit F: Monoid[B]): B =
fa match {
case Tip() =>
F.zero
case Bin(k, x, l, r) =>
F.append(foldMap(l)(f), F.append(f(x), foldMap(r)(f)))
}
override def foldRight[A, B](fa: S ==>> A, z: => B)(f: (A, => B) => B): B =
fa.foldrWithKey(z)((_, b, acc) => f(b, acc))
override def foldLeft[A, B](fa: S ==>> A, z: B)(f: (B, A) => B): B =
fa.foldlWithKey(z)((acc, _, b) => f(acc, b))
override def index[A](fa: S ==>> A, i: Int): Option[A] =
fa.elemAt(i).map(_._2)
def traverseImpl[F[_], A, B](fa: S ==>> A)(f: A => F[B])(implicit G: Applicative[F]): F[S ==>> B] =
fa match {
case Tip() =>
G.point(Tip())
case Bin(kx, x, l, r) =>
G.apply3(traverseImpl(l)(f), f(x), traverseImpl(r)(f)){
(l2, x2, r2) => Bin(kx, x2, l2, r2)
}
}
override def length[A](fa: S ==>> A): Int =
fa.size
override def any[A](fa: S ==>> A)(f: A => Boolean): Boolean =
fa match {
case Tip() => false
case Bin(_, x, l, r) =>
any(l)(f) || f(x) || any(r)(f)
}
override def all[A](fa: S ==>> A)(f: A => Boolean): Boolean =
fa match {
case Tip() => true
case Bin(_, x, l, r) =>
all(l)(f) && f(x) && all(r)(f)
}
}
implicit val mapBifoldable: Bifoldable[==>>] = new Bifoldable[==>>] {
def bifoldMap[A,B,M](fa: A ==>> B)(f: A => M)(g: B => M)(implicit F: Monoid[M]): M =
fa match {
case Tip() =>
F.zero
case Bin(k, x, l, r) =>
F.append(bifoldMap(l)(f)(g),
F.append(f(k), F.append(g(x), bifoldMap(r)(f)(g))))
}
def bifoldRight[A,B,C](fa: A ==>> B, z: => C)(f: (A, => C) => C)(g: (B, => C) => C): C =
fa.foldrWithKey(z)((a, b, c) => f(a, g(b, c)))
override def bifoldLeft[A,B,C](fa: A ==>> B, z: C)(f: (C, A) => C)(g: (C, B) => C): C =
fa.foldlWithKey(z)((c, a, b) => g(f(c, a), b))
}
}
private[scalaz] sealed trait MapEqual[A, B] extends Equal[A ==>> B] {
import std.list._
import std.tuple._
implicit def A: Equal[A]
implicit def B: Equal[B]
final override def equal(a1: A ==>> B, a2: A ==>> B): Boolean =
Equal[Int].equal(a1.size, a2.size) && Equal[List[(A, B)]].equal(a1.toAscList, a2.toAscList)
}
object ==>> extends MapInstances {
private[scalaz] case object Tip extends (Nothing ==>> Nothing) {
val size = 0
def unapply[A, B](a: A ==>> B): Boolean = a eq this
def apply[A, B](): A ==>> B = this.asInstanceOf[A ==>> B]
}
private[scalaz] final case class Bin[A, B](k: A, v: B, l: A ==>> B, r: A ==>> B) extends ==>>[A, B] {
val size = l.size + r.size + 1
}
final def apply[A: Order, B](x: (A, B)*): A ==>> B =
x.foldLeft(empty[A, B])((a, c) => a.insert(c._1, c._2))
final def empty[A, B]: A ==>> B =
Tip[A, B]()
final def singleton[A, B](k: A, x: B): A ==>> B =
Bin(k, x, Tip(), Tip())
/* List operations */
final def fromList[A: Order, B](l: List[(A, B)]): A ==>> B =
l.foldLeft(empty[A, B]) { (t, x) => t.insert(x._1, x._2) }
final def fromListWith[A: Order, B](l: List[(A, B)])(f: (B, B) => B): A ==>> B =
fromListWithKey(l)((_, x, y) => f(x, y))
final def fromListWithKey[A: Order, B](l: List[(A, B)])(f: (A, B, B) => B): A ==>> B =
l.foldLeft(empty[A, B])((a, c) => a.insertWithKey(f, c._1, c._2))
/* TODO: Ordered lists
, fromAscList
, fromAscListWith
, fromAscListWithKey
, fromDistinctAscList
*/
/* Foldable operations */
final def fromFoldable[F[_]: Foldable, A: Order, B](fa: F[(A, B)]): A ==>> B =
Foldable[F].foldLeft(fa, empty[A, B]) { (t, x) => t.insert(x._1, x._2) }
final def fromFoldableWith[F[_]: Foldable, A: Order, B](fa: F[(A, B)])(f: (B, B) => B): A ==>> B =
fromFoldableWithKey(fa)((_, x, y) => f(x, y))
final def fromFoldableWithKey[F[_]: Foldable, A: Order, B](fa: F[(A, B)])(f: (A, B, B) => B): A ==>> B =
Foldable[F].foldLeft(fa, empty[A, B])((a, c) => a.insertWithKey(f, c._1, c._2))
final def fromSet[A: Order, B](s: ISet[A])(f: A => B): A ==>> B =
s match {
case ISet.Tip() =>
empty
case ISet.Bin(x, l, r) =>
Bin(x, f(x), fromSet(l)(f), fromSet(r)(f))
}
final def unions[A: Order, B](xs: List[A ==>> B]): A ==>> B =
xs.foldLeft(empty[A, B])((a, c) => a.union(c))
final def unionsWith[A: Order, B](f: (B, B) => B)(xs: List[A ==>> B]): A ==>> B =
xs.foldLeft(empty[A, B])((a, c) => a.unionWith(c)(f))
private[scalaz] final val ratio = 2
private[scalaz] final val delta = 3
// Even though we have balanceL and balanceR, we need balance function
// as alter function still needs it.
private[scalaz] def balance[A, B](k: A, x: B, l: A ==>> B, r: A ==>> B): A ==>> B =
l match {
case Tip() =>
r match {
case Tip() =>
singleton(k, x)
case Bin(_, _, Tip(), Tip()) =>
Bin(k, x, Tip(), r)
case Bin(rk, rx, Tip(), rr@Bin(_, _, _, _)) =>
Bin(rk, rx, singleton(k, x), rr)
case Bin(rk, rx, Bin(rlk, rlx, _, _), Tip()) =>
Bin(rlk, rlx, singleton(k, x), singleton(rk, rx))
case Bin(rk, rx, rl@Bin(rlk, rlx, rll, rlr), rr@Bin(_, _, _, _)) =>
if (rl.size < ratio*rr.size) Bin(rk, rx, Bin(k, x, Tip(), rl), rr)
else Bin(rlk, rlx, Bin(k, x, Tip(), rll), Bin(rk, rx, rlr, rr))
}
case Bin(lk, lx, ll, lr) =>
r match {
case Tip() => (ll, lr) match {
case (Tip(), Tip()) =>
Bin(k, x, l, Tip())
case (Tip(), Bin(lrk, lrx, _, _)) =>
Bin(lrk, lrx, singleton(lk, lx), singleton(k, x))
case (Bin(_, _, _, _), Tip()) =>
Bin(lk, lx, ll, singleton(k, x))
case (Bin(_, _, _, _), Bin(lrk, lrx, lrl, lrr)) =>
if (lr.size < ratio*ll.size) Bin(lk, lx, ll, Bin(k, x, lr, Tip()))
else Bin(lrk, lrx, Bin(lk, lx, ll, lrl), Bin(k, x, lrr, Tip()))
}
case Bin(rk, rx, rl, rr) =>
if (r.size > delta*l.size) {
(rl, rr) match {
case (Bin(rlk, rlx, rll, rlr), Bin(_, _, _, _)) =>
if (rl.size < ratio*rr.size) Bin(rk, rx, Bin(k, x, l, rl), rr)
else Bin(rlk, rlx, Bin(k, x, l, rll), Bin(rk, rx, rlr, rr))
case _ =>
sys.error("Failure in Map.balance")
}
}
else if (l.size > delta*r.size) {
(ll, lr) match {
case (Bin(_, _, _, _), Bin(lrk, lrx, lrl, lrr)) =>
if (lr.size < ratio*ll.size) Bin(lk, lx, ll, Bin(k, x, lr, r))
else Bin(lrk, lrx, Bin(lk, lx, ll, lrl), Bin(k, x, lrr, r))
case _ =>
sys.error("Failure in Map.balance")
}
}
else Bin(k, x, l, r)
}
}
// balanceL is used to balance a tree when an element might have been inserted to
// a left subtree, or when an element might have been deleted from a right subtree.
private[scalaz] def balanceL[A, B](k: A, x: B, l: A ==>> B, r: A ==>> B): A ==>> B =
r match {
case Tip() =>
l match {
case Tip() =>
singleton(k, x)
case Bin(_, _, Tip(), Tip()) =>
Bin(k, x, l, Tip())
case Bin(lk, lx, Tip(), Bin(lrk, lrx, _, _)) =>
Bin(lrk, lrx, singleton(lk, lx), singleton(k, x))
case Bin(lk, lx, ll@Bin(_, _, _, _), Tip()) =>
Bin(lk, lx, ll, singleton(k, x))
case Bin(lk, lx, ll@Bin(_, _, _, _), lr@Bin(lrk, lrx, lrl, lrr)) =>
if (lr.size < ratio*ll.size) Bin(lk, lx, ll, Bin(k, x, lr, Tip()))
else Bin(lrk, lrx, Bin(lk, lx, ll, lrl), Bin(k, x, lrr, Tip()))
}
case Bin(_, _, _, _) =>
l match {
case Tip() =>
Bin(k, x, Tip(), r)
case Bin(lk, lx, ll, lr) =>
if (l.size > delta*r.size) {
(ll, lr) match {
case (Bin(_, _, _, _), Bin(lrk, lrx, lrl, lrr)) =>
if (lr.size < ratio*ll.size) Bin(lk, lx, ll, Bin(k, x, lr, r))
else Bin(lrk, lrx, Bin(lk, lx, ll, lrl), Bin(k, x, lrr, r))
case _ => sys.error("Failure in Map.balanceL")
}
} else Bin(k, x, l, r)
}
}
// balanceR is used to balance a tree when a key-value might have been inserted to
// a right subtree, or when a key-value might have been deleted from a left subtree.
private[scalaz] def balanceR[A, B](k: A, x: B, l: A ==>> B, r: A ==>> B): A ==>> B =
l match {
case Tip() =>
r match {
case Tip() =>
singleton(k, x)
case Bin(_, _, Tip(), Tip()) =>
Bin(k, x, Tip(), r)
case Bin(rk, rx, Tip(), rr@Bin(_, _, _, _)) =>
Bin(rk, rx, singleton(k, x), rr)
case Bin(rk, rx, Bin(rlk, rlx, _, _), Tip()) =>
Bin(rlk, rlx, singleton(k, x), singleton(rk, rx))
case Bin(rk, rx, rl@Bin(rlk, rlx, rll, rlr), rr@Bin(_, _, _, _)) =>
if (rl.size < ratio*rr.size) Bin(rk, rx, Bin(k, x, Tip(), rl), rr)
else Bin(rlk, rlx, Bin(k, x, Tip(), rll), Bin(rk, rx, rlr, rr))
}
case Bin(_, _, _, _) =>
r match {
case Tip() =>
Bin(k, x, l, Tip())
case Bin(rk, rx, rl, rr) =>
if (r.size > delta*l.size) {
(rl, rr) match {
case (Bin(rlk, rlx, rll, rlr), Bin(_, _, _, _)) =>
if (rl.size < ratio*rr.size) Bin(rk, rx, Bin(k, x, l, rl), rr)
else Bin(rlk, rlx, Bin(k, x, l, rll), Bin(rk, rx, rlr, rr))
case _ => sys.error("Failure in Map.balanceR")
}
} else Bin(k, x, l, r)
}
}
private[scalaz] def link[A, B](kx: A, x: B, l: A ==>> B, r: A ==>> B): A ==>> B =
(l, r) match {
case (Tip(), r) =>
insertMin(kx, x, r)
case (l, Tip()) =>
insertMax(kx, x, l)
case (Bin(ky, y, ly, ry), Bin(kz, z, lz, rz)) =>
if (delta * l.size < r.size) balanceL(kz, z, link(kx, x, l, lz), rz)
else if (delta * r.size < l.size) balanceR(ky, y, ly, link(kx, x, ry, r))
else Bin(kx, x, l, r)
}
// insertMax and insertMin are only used for link(...)
private def insertMax[A, B](kx: A, x: B, t: A ==>> B): A ==>> B =
t match {
case Tip() =>
singleton(kx, x)
case Bin(ky, y, l, r) =>
balanceR(ky, y, l, insertMax(kx, x, r))
}
private def insertMin[A, B](kx: A, x: B, t: A ==>> B): A ==>> B =
t match {
case Tip() =>
singleton(kx, x)
case Bin(ky, y, l, r) =>
balanceL(ky, y, insertMin(kx, x, l), r)
}
private[scalaz] def trim[A, B](lo: Option[A], hi: Option[A], t: A ==>> B)(implicit o: Order[A]): A ==>> B =
(lo, hi) match {
case (None, None) =>
t
case (Some(lk), None) =>
@tailrec
def greater(lo: A, m: A ==>> B): A ==>> B =
m match {
case Bin(kx, _, _, r) if o.lessThanOrEqual(kx, lo) =>
greater(lo, r)
case _ =>
m
}
greater(lk, t)
case (None, Some(hk)) =>
@tailrec
def lesser(hi: A, m: A ==>> B): A ==>> B =
m match {
case Bin(kx, _, l, _) if o.greaterThanOrEqual(kx, hi) =>
lesser(hi, l)
case _ =>
m
}
lesser(hk, t)
case (Some(lk), Some(hk)) =>
@tailrec
def middle(lo: A, hi: A, m: A ==>> B): A ==>> B =
m match {
case Bin(kx, _, _, r) if o.lessThanOrEqual(kx, lo) =>
middle(lo, hi, r)
case Bin(kx, _, l, _) if o.greaterThanOrEqual(kx, hi) =>
middle(lo, hi, l)
case _ => m
}
middle(lk, hk, t)
}
private[scalaz] def trimLookupLo[A, B](lk: A, hkOption: Option[A], t: A ==>> B)(implicit o: Order[A]): (Option[B], A ==>> B) =
hkOption match {
case None =>
@tailrec
def greater(lo: A, m: A ==>> B): (Option[B], A ==>> B) =
m match {
case Tip() =>
(none, Tip())
case Bin(kx, x, l, r) =>
o.order(lo, kx) match {
case LT =>
(l.lookup(lo), m)
case EQ =>
(some(x), r)
case GT =>
greater(lo, r)
}
}
greater(lk, t)
case Some(hk) =>
@tailrec
def middle(lo: A, hi: A, m: A ==>> B): (Option[B], A ==>> B) =
m match {
case Tip() =>
(none, Tip())
case Bin(kx, x, l, r) =>
o.order(lo, kx) match {
case LT if o.order(kx, hi) == LT =>
(l.lookup(lo), m)
case LT =>
middle(lo, hi, l)
case EQ =>
(some(x), lesser(hi, r))
case GT =>
middle(lo, hi, r)
}
}
@tailrec
def lesser(hi: A, m: A ==>> B): A ==>> B =
m match {
case Bin(k, _, l, _) if o.greaterThanOrEqual(k, hi) =>
lesser(hi, l)
case _ =>
m
}
middle(lk, hk, t)
}
/*
* The documentation below is partially copied from haskell/containers Map.
* Please refer to the full documentation if necessary.
* @see [[https://github.com/haskell/containers/blob/v0.5.7.1/Data/Map/Base.hs#L1402-L1440]]
*
-- | /O(n+m)/. A high-performance universal combining function. This function
-- is used to define 'unionWith', 'unionWithKey', 'differenceWith',
-- 'differenceWithKey', 'intersectionWith', 'intersectionWithKey' and can be
-- used to define other custom combine functions.
-- When calling mergeWithKey(a, b)(f)(g1, g2), a function combining two
-- 'Map's is created, such that
--
-- * if a key is present in both maps, it is passed with both corresponding
-- values to the combine @f@ function. Depending on the result, the key is either
-- present in the result with specified value, or is left out;
--
-- * a nonempty subtree present only in the first map is passed to @g1@ and
-- the output is added to the result;
--
-- * a nonempty subtree present only in the second map is passed to @g2@ and
-- the output is added to the result.
*
* @param a first map
* @param b second map
* @param f combine function used to define `XxxWithKey`
* @param g1 function applied to a nonempty subtree present only in the first map a
* @param g2 function applied to a nonempty subtree present only in the second map b
*/
def mergeWithKey[A: Order, B, C, D](a: A ==>> B, b: A ==>> C)
(f: (A, B, C) => Option[D])
(g1: (A ==>> B) => (A ==>> D), g2: (A ==>> C) => (A ==>> D))
(implicit o: Order[A]): A ==>> D = {
def hedgeMerge(blo: Option[A], bhi: Option[A], a: A ==>> B, b: A ==>> C): A ==>> D = {
(a, b) match {
case (t1, Tip()) => g1(t1)
case (Tip(), Bin(kx, x, l, r)) =>
val t2 = link(kx, x, l.filterGt(blo)(o), r.filterLt(bhi)(o))
g2(t2)
case (Bin(kx, x, l, r), t2) =>
val bmi = some(kx)
val l2 = hedgeMerge(blo, bmi, l, trim(blo, bmi, t2)(o))
val (found, trim_t2) = trimLookupLo(kx, bhi, t2)(o)
val r2 = hedgeMerge(bmi, bhi, r, trim_t2)
found match {
case None =>
g1(singleton(kx, x)) match {
case Tip() =>
l2 merge r2
case Bin(_, x2, Tip(), Tip()) =>
link(kx, x2, l2, r2)
case _ =>
sys.error("mergeWithKey: Given function g1 does not fulfil required conditions (see documentation)")
}
case Some(x2) =>
f(kx, x, x2) match {
case None =>
l2 merge r2
case Some(xx) =>
link(kx, xx, l2, r2)
}
}
}
}
(a, b) match {
case (Tip(), t2) => g2(t2)
case (t1, Tip()) => g1(t1)
case (t1, t2) => hedgeMerge(None, None, t1, t2)
}
}
}
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