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+package scala.collection.mutable
+
+import scala.annotation.tailrec
+import scala.collection.Iterator
+
+/**
+ * An object containing the red-black tree implementation used by mutable `TreeMaps`.
+ *
+ * The trees implemented in this object are *not* thread safe.
+ *
+ * @author Rui Gonçalves
+ * @version 2.12
+ * @since 2.12
+ */
+private[collection] object RedBlackTree {
+
+ // ---- class structure ----
+
+ // For performance reasons, this implementation uses `null` references to represent leaves instead of a sentinel node.
+ // Currently, the internal nodes do not store their subtree size - only the tree object keeps track of their size.
+ // Therefore, while obtaining the size of the whole tree is O(1), knowing the number of entries inside a range is O(n)
+ // on the size of the range.
+
+ @SerialVersionUID(21575944040195605L)
+ final class Tree[A, B](var root: Node[A, B], var size: Int) extends Serializable
+
+ @SerialVersionUID(1950599696441054720L)
+ final class Node[A, B](var key: A, var value: B, var red: Boolean,
+ var left: Node[A, B], var right: Node[A, B], var parent: Node[A, B]) extends Serializable {
+
+ override def toString: String = "Node(" + key + ", " + value + ", " + red + ", " + left + ", " + right + ")"
+ }
+
+ object Tree {
+ def empty[A, B]: Tree[A, B] = new Tree(null, 0)
+ }
+
+ object Node {
+
+ @inline def apply[A, B](key: A, value: B, red: Boolean,
+ left: Node[A, B], right: Node[A, B], parent: Node[A, B]): Node[A, B] =
+ new Node(key, value, red, left, right, parent)
+
+ @inline def leaf[A, B](key: A, value: B, red: Boolean, parent: Node[A, B]): Node[A, B] =
+ new Node(key, value, red, null, null, parent)
+
+ def unapply[A, B](t: Node[A, B]) = Some((t.key, t.value, t.left, t.right, t.parent))
+ }
+
+ // ---- getters ----
+
+ def isRed(node: Node[_, _]) = (node ne null) && node.red
+ def isBlack(node: Node[_, _]) = (node eq null) || !node.red
+
+ // ---- size ----
+
+ def size(node: Node[_, _]): Int = if (node eq null) 0 else 1 + size(node.left) + size(node.right)
+ def size(tree: Tree[_, _]): Int = tree.size
+ def isEmpty(tree: Tree[_, _]) = tree.root eq null
+ def clear(tree: Tree[_, _]): Unit = { tree.root = null; tree.size = 0 }
+
+ // ---- search ----
+
+ def get[A: Ordering, B](tree: Tree[A, B], key: A): Option[B] = getNode(tree.root, key) match {
+ case null => None
+ case node => Some(node.value)
+ }
+
+ @tailrec private[this] def getNode[A, B](node: Node[A, B], key: A)(implicit ord: Ordering[A]): Node[A, B] =
+ if (node eq null) null
+ else {
+ val cmp = ord.compare(key, node.key)
+ if (cmp < 0) getNode(node.left, key)
+ else if (cmp > 0) getNode(node.right, key)
+ else node
+ }
+
+ def contains[A: Ordering](tree: Tree[A, _], key: A) = getNode(tree.root, key) ne null
+
+ def min[A, B](tree: Tree[A, B]): Option[(A, B)] = minNode(tree.root) match {
+ case null => None
+ case node => Some((node.key, node.value))
+ }
+
+ def minKey[A](tree: Tree[A, _]): Option[A] = minNode(tree.root) match {
+ case null => None
+ case node => Some(node.key)
+ }
+
+ private def minNode[A, B](node: Node[A, B]): Node[A, B] =
+ if (node eq null) null else minNodeNonNull(node)
+
+ @tailrec def minNodeNonNull[A, B](node: Node[A, B]): Node[A, B] =
+ if (node.left eq null) node else minNodeNonNull(node.left)
+
+ def max[A, B](tree: Tree[A, B]): Option[(A, B)] = maxNode(tree.root) match {
+ case null => None
+ case node => Some((node.key, node.value))
+ }
+
+ def maxKey[A](tree: Tree[A, _]): Option[A] = maxNode(tree.root) match {
+ case null => None
+ case node => Some(node.key)
+ }
+
+ private def maxNode[A, B](node: Node[A, B]): Node[A, B] =
+ if (node eq null) null else maxNodeNonNull(node)
+
+ @tailrec def maxNodeNonNull[A, B](node: Node[A, B]): Node[A, B] =
+ if (node.right eq null) node else maxNodeNonNull(node.right)
+
+ /**
+ * Returns the first (lowest) map entry with a key equal or greater than `key`. Returns `None` if there is no such
+ * node.
+ */
+ def minAfter[A, B](tree: Tree[A, B], key: A)(implicit ord: Ordering[A]): Option[(A, B)] =
+ minNodeAfter(tree.root, key) match {
+ case null => None
+ case node => Some((node.key, node.value))
+ }
+
+ def minKeyAfter[A](tree: Tree[A, _], key: A)(implicit ord: Ordering[A]): Option[A] =
+ minNodeAfter(tree.root, key) match {
+ case null => None
+ case node => Some(node.key)
+ }
+
+ private[this] def minNodeAfter[A, B](node: Node[A, B], key: A)(implicit ord: Ordering[A]): Node[A, B] = {
+ if (node eq null) null
+ else {
+ var y: Node[A, B] = null
+ var x = node
+ var cmp = 1
+ while ((x ne null) && cmp != 0) {
+ y = x
+ cmp = ord.compare(key, x.key)
+ x = if (cmp < 0) x.left else x.right
+ }
+ if (cmp <= 0) y else successor(y)
+ }
+ }
+
+ /**
+ * Returns the last (highest) map entry with a key smaller than `key`. Returns `None` if there is no such node.
+ */
+ def maxBefore[A, B](tree: Tree[A, B], key: A)(implicit ord: Ordering[A]): Option[(A, B)] =
+ maxNodeBefore(tree.root, key) match {
+ case null => None
+ case node => Some((node.key, node.value))
+ }
+
+ def maxKeyBefore[A](tree: Tree[A, _], key: A)(implicit ord: Ordering[A]): Option[A] =
+ maxNodeBefore(tree.root, key) match {
+ case null => None
+ case node => Some(node.key)
+ }
+
+ private[this] def maxNodeBefore[A, B](node: Node[A, B], key: A)(implicit ord: Ordering[A]): Node[A, B] = {
+ if (node eq null) null
+ else {
+ var y: Node[A, B] = null
+ var x = node
+ var cmp = 1
+ while ((x ne null) && cmp != 0) {
+ y = x
+ cmp = ord.compare(key, x.key)
+ x = if (cmp < 0) x.left else x.right
+ }
+ if (cmp > 0) y else predecessor(y)
+ }
+ }
+
+ // ---- insertion ----
+
+ def insert[A, B](tree: Tree[A, B], key: A, value: B)(implicit ord: Ordering[A]): Unit = {
+ var y: Node[A, B] = null
+ var x = tree.root
+ var cmp = 1
+ while ((x ne null) && cmp != 0) {
+ y = x
+ cmp = ord.compare(key, x.key)
+ x = if (cmp < 0) x.left else x.right
+ }
+
+ if (cmp == 0) y.value = value
+ else {
+ val z = Node.leaf(key, value, red = true, y)
+
+ if (y eq null) tree.root = z
+ else if (cmp < 0) y.left = z
+ else y.right = z
+
+ fixAfterInsert(tree, z)
+ tree.size += 1
+ }
+ }
+
+ private[this] def fixAfterInsert[A, B](tree: Tree[A, B], node: Node[A, B]): Unit = {
+ var z = node
+ while (isRed(z.parent)) {
+ if (z.parent eq z.parent.parent.left) {
+ val y = z.parent.parent.right
+ if (isRed(y)) {
+ z.parent.red = false
+ y.red = false
+ z.parent.parent.red = true
+ z = z.parent.parent
+ } else {
+ if (z eq z.parent.right) {
+ z = z.parent
+ rotateLeft(tree, z)
+ }
+ z.parent.red = false
+ z.parent.parent.red = true
+ rotateRight(tree, z.parent.parent)
+ }
+ } else { // symmetric cases
+ val y = z.parent.parent.left
+ if (isRed(y)) {
+ z.parent.red = false
+ y.red = false
+ z.parent.parent.red = true
+ z = z.parent.parent
+ } else {
+ if (z eq z.parent.left) {
+ z = z.parent
+ rotateRight(tree, z)
+ }
+ z.parent.red = false
+ z.parent.parent.red = true
+ rotateLeft(tree, z.parent.parent)
+ }
+ }
+ }
+ tree.root.red = false
+ }
+
+ // ---- deletion ----
+
+ def delete[A, B](tree: Tree[A, B], key: A)(implicit ord: Ordering[A]): Unit = {
+ val z = getNode(tree.root, key)
+ if (z ne null) {
+ var y = z
+ var yIsRed = y.red
+ var x: Node[A, B] = null
+ var xParent: Node[A, B] = null
+
+ if (z.left eq null) {
+ x = z.right
+ transplant(tree, z, z.right)
+ xParent = z.parent
+ }
+ else if (z.right eq null) {
+ x = z.left
+ transplant(tree, z, z.left)
+ xParent = z.parent
+ }
+ else {
+ y = minNodeNonNull(z.right)
+ yIsRed = y.red
+ x = y.right
+
+ if (y.parent eq z) xParent = y
+ else {
+ xParent = y.parent
+ transplant(tree, y, y.right)
+ y.right = z.right
+ y.right.parent = y
+ }
+ transplant(tree, z, y)
+ y.left = z.left
+ y.left.parent = y
+ y.red = z.red
+ }
+
+ if (!yIsRed) fixAfterDelete(tree, x, xParent)
+ tree.size -= 1
+ }
+ }
+
+ private[this] def fixAfterDelete[A, B](tree: Tree[A, B], node: Node[A, B], parent: Node[A, B]): Unit = {
+ var x = node
+ var xParent = parent
+ while ((x ne tree.root) && isBlack(x)) {
+ if (x eq xParent.left) {
+ var w = xParent.right
+ // assert(w ne null)
+
+ if (w.red) {
+ w.red = false
+ xParent.red = true
+ rotateLeft(tree, xParent)
+ w = xParent.right
+ }
+ if (isBlack(w.left) && isBlack(w.right)) {
+ w.red = true
+ x = xParent
+ } else {
+ if (isBlack(w.right)) {
+ w.left.red = false
+ w.red = true
+ rotateRight(tree, w)
+ w = xParent.right
+ }
+ w.red = xParent.red
+ xParent.red = false
+ w.right.red = false
+ rotateLeft(tree, xParent)
+ x = tree.root
+ }
+ } else { // symmetric cases
+ var w = xParent.left
+ // assert(w ne null)
+
+ if (w.red) {
+ w.red = false
+ xParent.red = true
+ rotateRight(tree, xParent)
+ w = xParent.left
+ }
+ if (isBlack(w.right) && isBlack(w.left)) {
+ w.red = true
+ x = xParent
+ } else {
+ if (isBlack(w.left)) {
+ w.right.red = false
+ w.red = true
+ rotateLeft(tree, w)
+ w = xParent.left
+ }
+ w.red = xParent.red
+ xParent.red = false
+ w.left.red = false
+ rotateRight(tree, xParent)
+ x = tree.root
+ }
+ }
+ xParent = x.parent
+ }
+ if (x ne null) x.red = false
+ }
+
+ // ---- helpers ----
+
+ /**
+ * Returns the node that follows `node` in an in-order tree traversal. If `node` has the maximum key (and is,
+ * therefore, the last node), this method returns `null`.
+ */
+ private[this] def successor[A, B](node: Node[A, B]): Node[A, B] = {
+ if (node.right ne null) minNodeNonNull(node.right)
+ else {
+ var x = node
+ var y = x.parent
+ while ((y ne null) && (x eq y.right)) {
+ x = y
+ y = y.parent
+ }
+ y
+ }
+ }
+
+ /**
+ * Returns the node that precedes `node` in an in-order tree traversal. If `node` has the minimum key (and is,
+ * therefore, the first node), this method returns `null`.
+ */
+ private[this] def predecessor[A, B](node: Node[A, B]): Node[A, B] = {
+ if (node.left ne null) maxNodeNonNull(node.left)
+ else {
+ var x = node
+ var y = x.parent
+ while ((y ne null) && (x eq y.left)) {
+ x = y
+ y = y.parent
+ }
+ y
+ }
+ }
+
+ private[this] def rotateLeft[A, B](tree: Tree[A, B], x: Node[A, B]): Unit = if (x ne null) {
+ // assert(x.right ne null)
+ val y = x.right
+ x.right = y.left
+
+ if (y.left ne null) y.left.parent = x
+ y.parent = x.parent
+
+ if (x.parent eq null) tree.root = y
+ else if (x eq x.parent.left) x.parent.left = y
+ else x.parent.right = y
+
+ y.left = x
+ x.parent = y
+ }
+
+ private[this] def rotateRight[A, B](tree: Tree[A, B], x: Node[A, B]): Unit = if (x ne null) {
+ // assert(x.left ne null)
+ val y = x.left
+ x.left = y.right
+
+ if (y.right ne null) y.right.parent = x
+ y.parent = x.parent
+
+ if (x.parent eq null) tree.root = y
+ else if (x eq x.parent.right) x.parent.right = y
+ else x.parent.left = y
+
+ y.right = x
+ x.parent = y
+ }
+
+ /**
+ * Transplant the node `from` to the place of node `to`. This is done by setting `from` as a child of `to`'s previous
+ * parent and setting `from`'s parent to the `to`'s previous parent. The children of `from` are left unchanged.
+ */
+ private[this] def transplant[A, B](tree: Tree[A, B], to: Node[A, B], from: Node[A, B]): Unit = {
+ if (to.parent eq null) tree.root = from
+ else if (to eq to.parent.left) to.parent.left = from
+ else to.parent.right = from
+
+ if (from ne null) from.parent = to.parent
+ }
+
+ // ---- tree traversal ----
+
+ def foreach[A, B, U](tree: Tree[A, B], f: ((A, B)) => U): Unit = foreachNode(tree.root, f)
+
+ private[this] def foreachNode[A, B, U](node: Node[A, B], f: ((A, B)) => U): Unit =
+ if (node ne null) foreachNodeNonNull(node, f)
+
+ private[this] def foreachNodeNonNull[A, B, U](node: Node[A, B], f: ((A, B)) => U): Unit = {
+ if (node.left ne null) foreachNodeNonNull(node.left, f)
+ f((node.key, node.value))
+ if (node.right ne null) foreachNodeNonNull(node.right, f)
+ }
+
+ def foreachKey[A, U](tree: Tree[A, _], f: A => U): Unit = foreachNodeKey(tree.root, f)
+
+ private[this] def foreachNodeKey[A, U](node: Node[A, _], f: A => U): Unit =
+ if (node ne null) foreachNodeKeyNonNull(node, f)
+
+ private[this] def foreachNodeKeyNonNull[A, U](node: Node[A, _], f: A => U): Unit = {
+ if (node.left ne null) foreachNodeKeyNonNull(node.left, f)
+ f(node.key)
+ if (node.right ne null) foreachNodeKeyNonNull(node.right, f)
+ }
+
+ def transform[A, B](tree: Tree[A, B], f: (A, B) => B): Unit = transformNode(tree.root, f)
+
+ private[this] def transformNode[A, B, U](node: Node[A, B], f: (A, B) => B): Unit =
+ if (node ne null) transformNodeNonNull(node, f)
+
+ private[this] def transformNodeNonNull[A, B, U](node: Node[A, B], f: (A, B) => B): Unit = {
+ if (node.left ne null) transformNodeNonNull(node.left, f)
+ node.value = f(node.key, node.value)
+ if (node.right ne null) transformNodeNonNull(node.right, f)
+ }
+
+ def iterator[A: Ordering, B](tree: Tree[A, B], start: Option[A] = None, end: Option[A] = None): Iterator[(A, B)] =
+ new EntriesIterator(tree, start, end)
+
+ def keysIterator[A: Ordering](tree: Tree[A, _], start: Option[A] = None, end: Option[A] = None): Iterator[A] =
+ new KeysIterator(tree, start, end)
+
+ def valuesIterator[A: Ordering, B](tree: Tree[A, B], start: Option[A] = None, end: Option[A] = None): Iterator[B] =
+ new ValuesIterator(tree, start, end)
+
+ private[this] abstract class TreeIterator[A, B, R](tree: Tree[A, B], start: Option[A], end: Option[A])
+ (implicit ord: Ordering[A]) extends Iterator[R] {
+
+ protected[this] def nextResult(node: Node[A, B]): R
+
+ def hasNext: Boolean = nextNode ne null
+
+ def next(): R = nextNode match {
+ case null => throw new NoSuchElementException("next on empty iterator")
+ case node =>
+ nextNode = successor(node)
+ setNullIfAfterEnd()
+ nextResult(node)
+ }
+
+ private[this] var nextNode: Node[A, B] = start match {
+ case None => minNode(tree.root)
+ case Some(from) => minNodeAfter(tree.root, from)
+ }
+
+ private[this] def setNullIfAfterEnd(): Unit =
+ if (end.isDefined && (nextNode ne null) && ord.compare(nextNode.key, end.get) >= 0)
+ nextNode = null
+
+ setNullIfAfterEnd()
+ }
+
+ private[this] final class EntriesIterator[A: Ordering, B](tree: Tree[A, B], start: Option[A], end: Option[A])
+ extends TreeIterator[A, B, (A, B)](tree, start, end) {
+
+ def nextResult(node: Node[A, B]) = (node.key, node.value)
+ }
+
+ private[this] final class KeysIterator[A: Ordering, B](tree: Tree[A, B], start: Option[A], end: Option[A])
+ extends TreeIterator[A, B, A](tree, start, end) {
+
+ def nextResult(node: Node[A, B]) = node.key
+ }
+
+ private[this] final class ValuesIterator[A: Ordering, B](tree: Tree[A, B], start: Option[A], end: Option[A])
+ extends TreeIterator[A, B, B](tree, start, end) {
+
+ def nextResult(node: Node[A, B]) = node.value
+ }
+
+ // ---- debugging ----
+
+ /**
+ * Checks if the tree is in a valid state. That happens if:
+ * - It is a valid binary search tree;
+ * - All red-black properties are satisfied;
+ * - All non-null nodes have their `parent` reference correct;
+ * - The size variable in `tree` corresponds to the actual size of the tree.
+ */
+ def isValid[A: Ordering, B](tree: Tree[A, B]): Boolean =
+ isValidBST(tree.root) && hasProperParentRefs(tree) && isValidRedBlackTree(tree) && size(tree.root) == tree.size
+
+ /**
+ * Returns true if all non-null nodes have their `parent` reference correct.
+ */
+ private[this] def hasProperParentRefs[A, B](tree: Tree[A, B]): Boolean = {
+
+ def hasProperParentRefs(node: Node[A, B]): Boolean = {
+ if (node eq null) true
+ else {
+ if ((node.left ne null) && (node.left.parent ne node) ||
+ (node.right ne null) && (node.right.parent ne node)) false
+ else hasProperParentRefs(node.left) && hasProperParentRefs(node.right)
+ }
+ }
+
+ if(tree.root eq null) true
+ else (tree.root.parent eq null) && hasProperParentRefs(tree.root)
+ }
+
+ /**
+ * Returns true if this node follows the properties of a binary search tree.
+ */
+ private[this] def isValidBST[A, B](node: Node[A, B])(implicit ord: Ordering[A]): Boolean = {
+ if (node eq null) true
+ else {
+ if ((node.left ne null) && (ord.compare(node.key, node.left.key) <= 0) ||
+ (node.right ne null) && (ord.compare(node.key, node.right.key) >= 0)) false
+ else isValidBST(node.left) && isValidBST(node.right)
+ }
+ }
+
+ /**
+ * Returns true if the tree has all the red-black tree properties: if the root node is black, if all children of red
+ * nodes are black and if the path from any node to any of its null children has the same number of black nodes.
+ */
+ private[this] def isValidRedBlackTree[A, B](tree: Tree[A, B]): Boolean = {
+
+ def noRedAfterRed(node: Node[A, B]): Boolean = {
+ if (node eq null) true
+ else if (node.red && (isRed(node.left) || isRed(node.right))) false
+ else noRedAfterRed(node.left) && noRedAfterRed(node.right)
+ }
+
+ def blackHeight(node: Node[A, B]): Int = {
+ if (node eq null) 1
+ else {
+ val lh = blackHeight(node.left)
+ val rh = blackHeight(node.right)
+
+ if (lh == -1 || lh != rh) -1
+ else if (isRed(node)) lh
+ else lh + 1
+ }
+ }
+
+ isBlack(tree.root) && noRedAfterRed(tree.root) && blackHeight(tree.root) >= 0
+ }
+}