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Standard library for the Scala Programming Language
/*
* Scala (https://www.scala-lang.org)
*
* Copyright EPFL and Lightbend, Inc.
*
* Licensed under Apache License 2.0
* (http://www.apache.org/licenses/LICENSE-2.0).
*
* See the NOTICE file distributed with this work for
* additional information regarding copyright ownership.
*/
package scala
package util
import scala.reflect.ClassTag
import scala.math.Ordering
/** The `Sorting` object provides convenience wrappers for `java.util.Arrays.sort`.
* Methods that defer to `java.util.Arrays.sort` say that they do or under what
* conditions that they do.
*
* `Sorting` also implements a general-purpose quicksort and stable (merge) sort
* for those cases where `java.util.Arrays.sort` could only be used at the cost
* of a large memory penalty. If performance rather than memory usage is the
* primary concern, one may wish to find alternate strategies to use
* `java.util.Arrays.sort` directly e.g. by boxing primitives to use
* a custom ordering on them.
*
* `Sorting` provides methods where you can provide a comparison function, or
* can request a sort of items that are [[scala.math.Ordered]] or that
* otherwise have an implicit or explicit [[scala.math.Ordering]].
*
* Note also that high-performance non-default sorts for numeric types
* are not provided. If this is required, it is advisable to investigate
* other libraries that cover this use case.
*/
object Sorting {
/** Sort an array of Doubles using `java.util.Arrays.sort`. */
def quickSort(a: Array[Double]): Unit = java.util.Arrays.sort(a)
/** Sort an array of Ints using `java.util.Arrays.sort`. */
def quickSort(a: Array[Int]): Unit = java.util.Arrays.sort(a)
/** Sort an array of Floats using `java.util.Arrays.sort`. */
def quickSort(a: Array[Float]): Unit = java.util.Arrays.sort(a)
private final val qsortThreshold = 16
/** Sort array `a` with quicksort, using the Ordering on its elements.
* This algorithm sorts in place, so no additional memory is used aside from
* what might be required to box individual elements during comparison.
*/
def quickSort[K: Ordering](a: Array[K]): Unit = {
// Must have iN >= i0 or math will fail. Also, i0 >= 0.
def inner(a: Array[K], i0: Int, iN: Int, ord: Ordering[K]): Unit = {
if (iN - i0 < qsortThreshold) insertionSort(a, i0, iN, ord)
else {
val iK = (i0 + iN) >>> 1 // Unsigned div by 2
// Find index of median of first, central, and last elements
var pL =
if (ord.compare(a(i0), a(iN - 1)) <= 0)
if (ord.compare(a(i0), a(iK)) < 0)
if (ord.compare(a(iN - 1), a(iK)) < 0) iN - 1 else iK
else i0
else
if (ord.compare(a(i0), a(iK)) < 0) i0
else
if (ord.compare(a(iN - 1), a(iK)) <= 0) iN - 1
else iK
val pivot = a(pL)
// pL is the start of the pivot block; move it into the middle if needed
if (pL != iK) { a(pL) = a(iK); a(iK) = pivot; pL = iK }
// Elements equal to the pivot will be in range pL until pR
var pR = pL + 1
// Items known to be less than pivot are below iA (range i0 until iA)
var iA = i0
// Items known to be greater than pivot are at or above iB (range iB until iN)
var iB = iN
// Scan through everything in the buffer before the pivot(s)
while (pL - iA > 0) {
val current = a(iA)
ord.compare(current, pivot) match {
case 0 =>
// Swap current out with pivot block
a(iA) = a(pL - 1)
a(pL - 1) = current
pL -= 1
case x if x < 0 =>
// Already in place. Just update indices.
iA += 1
case _ if iB > pR =>
// Wrong side. There's room on the other side, so swap
a(iA) = a(iB - 1)
a(iB - 1) = current
iB -= 1
case _ =>
// Wrong side and there is no room. Swap by rotating pivot block.
a(iA) = a(pL - 1)
a(pL - 1) = a(pR - 1)
a(pR - 1) = current
pL -= 1
pR -= 1
iB -= 1
}
}
// Get anything remaining in buffer after the pivot(s)
while (iB - pR > 0) {
val current = a(iB - 1)
ord.compare(current, pivot) match {
case 0 =>
// Swap current out with pivot block
a(iB - 1) = a(pR)
a(pR) = current
pR += 1
case x if x > 0 =>
// Already in place. Just update indices.
iB -= 1
case _ =>
// Wrong side and we already know there is no room. Swap by rotating pivot block.
a(iB - 1) = a(pR)
a(pR) = a(pL)
a(pL) = current
iA += 1
pL += 1
pR += 1
}
}
// Use tail recursion on large half (Sedgewick's method) so we don't blow up the stack if pivots are poorly chosen
if (iA - i0 < iN - iB) {
inner(a, i0, iA, ord) // True recursion
inner(a, iB, iN, ord) // Should be tail recursion
}
else {
inner(a, iB, iN, ord) // True recursion
inner(a, i0, iA, ord) // Should be tail recursion
}
}
}
inner(a, 0, a.length, implicitly[Ordering[K]])
}
private final val mergeThreshold = 32
// Ordering[T] might be slow especially for boxed primitives, so use binary search variant of insertion sort
// Caller must pass iN >= i0 or math will fail. Also, i0 >= 0.
private def insertionSort[@specialized T](a: Array[T], i0: Int, iN: Int, ord: Ordering[T]): Unit = {
val n = iN - i0
if (n < 2) return
if (ord.compare(a(i0), a(i0+1)) > 0) {
val temp = a(i0)
a(i0) = a(i0+1)
a(i0+1) = temp
}
var m = 2
while (m < n) {
// Speed up already-sorted case by checking last element first
val next = a(i0 + m)
if (ord.compare(next, a(i0+m-1)) < 0) {
var iA = i0
var iB = i0 + m - 1
while (iB - iA > 1) {
val ix = (iA + iB) >>> 1 // Use bit shift to get unsigned div by 2
if (ord.compare(next, a(ix)) < 0) iB = ix
else iA = ix
}
val ix = iA + (if (ord.compare(next, a(iA)) < 0) 0 else 1)
var i = i0 + m
while (i > ix) {
a(i) = a(i-1)
i -= 1
}
a(ix) = next
}
m += 1
}
}
// Caller is required to pass iN >= i0, else math will fail. Also, i0 >= 0.
private def mergeSort[@specialized T: ClassTag](a: Array[T], i0: Int, iN: Int, ord: Ordering[T], scratch: Array[T] = null): Unit = {
if (iN - i0 < mergeThreshold) insertionSort(a, i0, iN, ord)
else {
val iK = (i0 + iN) >>> 1 // Bit shift equivalent to unsigned math, no overflow
val sc = if (scratch eq null) new Array[T](iK - i0) else scratch
mergeSort(a, i0, iK, ord, sc)
mergeSort(a, iK, iN, ord, sc)
mergeSorted(a, i0, iK, iN, ord, sc)
}
}
// Must have 0 <= i0 < iK < iN
private def mergeSorted[@specialized T](a: Array[T], i0: Int, iK: Int, iN: Int, ord: Ordering[T], scratch: Array[T]): Unit = {
// Check to make sure we're not already in order
if (ord.compare(a(iK-1), a(iK)) > 0) {
var i = i0
val jN = iK - i0
var j = 0
while (i < iK) {
scratch (j) = a(i)
i += 1
j += 1
}
var k = i0
j = 0
while (i < iN && j < jN) {
if (ord.compare(a(i), scratch(j)) < 0) { a(k) = a(i); i += 1 }
else { a(k) = scratch(j); j += 1 }
k += 1
}
while (j < jN) { a(k) = scratch(j); j += 1; k += 1 }
// Don't need to finish a(i) because it's already in place, k = i
}
}
// Why would you even do this?
private def booleanSort(a: Array[Boolean]): Unit = {
var i = 0
var n = 0
while (i < a.length) {
if (!a(i)) n += 1
i += 1
}
i = 0
while (i < n) {
a(i) = false
i += 1
}
while (i < a.length) {
a(i) = true
i += 1
}
}
// TODO: add upper bound: T <: AnyRef, propagate to callers below (not binary compatible)
// Maybe also rename all these methods to `sort`.
@inline private def sort[T](a: Array[T], from: Int, until: Int, ord: Ordering[T]): Unit = (a: @unchecked) match {
case _: Array[AnyRef] =>
// Note that runtime matches are covariant, so could actually be any Array[T] s.t. T is not primitive (even boxed value classes)
if (a.length > 1 && (ord eq null)) throw new NullPointerException("Ordering")
java.util.Arrays.sort(a, from, until, ord)
case a: Array[Int] => if (ord eq Ordering.Int) java.util.Arrays.sort(a) else mergeSort[Int](a, from, until, ord)
case a: Array[Double] => mergeSort[Double](a, from, until, ord) // Because not all NaNs are identical, stability is meaningful!
case a: Array[Long] => if (ord eq Ordering.Long) java.util.Arrays.sort(a) else mergeSort[Long](a, from, until, ord)
case a: Array[Float] => mergeSort[Float](a, from, until, ord) // Because not all NaNs are identical, stability is meaningful!
case a: Array[Char] => if (ord eq Ordering.Char) java.util.Arrays.sort(a) else mergeSort[Char](a, from, until, ord)
case a: Array[Byte] => if (ord eq Ordering.Byte) java.util.Arrays.sort(a) else mergeSort[Byte](a, from, until, ord)
case a: Array[Short] => if (ord eq Ordering.Short) java.util.Arrays.sort(a) else mergeSort[Short](a, from, until, ord)
case a: Array[Boolean] => if (ord eq Ordering.Boolean) booleanSort(a) else mergeSort[Boolean](a, from, until, ord)
// Array[Unit] is matched as an Array[AnyRef] due to covariance in runtime matching. Not worth catching it as a special case.
case null => throw new NullPointerException
}
/** Sort array `a` using the Ordering on its elements, preserving the original ordering where possible.
* Uses `java.util.Arrays.sort` unless `K` is a primitive type. This is the same as `stableSort(a, 0, a.length)`. */
@`inline` def stableSort[K: Ordering](a: Array[K]): Unit = stableSort(a, 0, a.length)
/** Sort array `a` or a part of it using the Ordering on its elements, preserving the original ordering where possible.
* Uses `java.util.Arrays.sort` unless `K` is a primitive type.
*
* @param a The array to sort
* @param from The first index in the array to sort
* @param until The last index (exclusive) in the array to sort
*/
def stableSort[K: Ordering](a: Array[K], from: Int, until: Int): Unit = sort(a, from, until, Ordering[K])
/** Sort array `a` using function `f` that computes the less-than relation for each element.
* Uses `java.util.Arrays.sort` unless `K` is a primitive type. This is the same as `stableSort(a, f, 0, a.length)`. */
@`inline` def stableSort[K](a: Array[K], f: (K, K) => Boolean): Unit = stableSort(a, f, 0, a.length)
// TODO: make this fast for primitive K (could be specialized if it didn't go through Ordering)
/** Sort array `a` or a part of it using function `f` that computes the less-than relation for each element.
* Uses `java.util.Arrays.sort` unless `K` is a primitive type.
*
* @param a The array to sort
* @param f A function that computes the less-than relation for each element
* @param from The first index in the array to sort
* @param until The last index (exclusive) in the array to sort
*/
def stableSort[K](a: Array[K], f: (K, K) => Boolean, from: Int, until: Int): Unit = sort(a, from, until, Ordering fromLessThan f)
/** A sorted Array, using the Ordering for the elements in the sequence `a`. Uses `java.util.Arrays.sort` unless `K` is a primitive type. */
def stableSort[K: ClassTag: Ordering](a: scala.collection.Seq[K]): Array[K] = {
val ret = a.toArray
sort(ret, 0, ret.length, Ordering[K])
ret
}
// TODO: make this fast for primitive K (could be specialized if it didn't go through Ordering)
/** A sorted Array, given a function `f` that computes the less-than relation for each item in the sequence `a`. Uses `java.util.Arrays.sort` unless `K` is a primitive type. */
def stableSort[K: ClassTag](a: scala.collection.Seq[K], f: (K, K) => Boolean): Array[K] = {
val ret = a.toArray
sort(ret, 0, ret.length, Ordering fromLessThan f)
ret
}
/** A sorted Array, given an extraction function `f` that returns an ordered key for each item in the sequence `a`. Uses `java.util.Arrays.sort` unless `K` is a primitive type. */
def stableSort[K: ClassTag, M: Ordering](a: scala.collection.Seq[K], f: K => M): Array[K] = {
val ret = a.toArray
sort(ret, 0, ret.length, Ordering[M] on f)
ret
}
}