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+/* $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $ */
+/* $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $ */
+/* $FreeBSD$ */
+
+/*-
+ * Copyright 2002 Niels Provos <provos@citi.umich.edu>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#pragma once
+
+/*
+ * This file defines data structures for red-black trees.
+ *
+ * A red-black tree is a binary search tree with the node color as an
+ * extra attribute. It fulfills a set of conditions:
+ * - every search path from the root to a leaf consists of the
+ * same number of black nodes,
+ * - each red node (except for the root) has a black parent,
+ * - each leaf node is black.
+ *
+ * Every operation on a red-black tree is bounded as O(lg n).
+ * The maximum height of a red-black tree is 2lg (n+1).
+ */
+
+namespace Common {
+template <typename T>
+class RBHead {
+public:
+ [[nodiscard]] T* Root() {
+ return rbh_root;
+ }
+
+ [[nodiscard]] const T* Root() const {
+ return rbh_root;
+ }
+
+ void SetRoot(T* root) {
+ rbh_root = root;
+ }
+
+ [[nodiscard]] bool IsEmpty() const {
+ return Root() == nullptr;
+ }
+
+private:
+ T* rbh_root = nullptr;
+};
+
+enum class EntryColor {
+ Black,
+ Red,
+};
+
+template <typename T>
+class RBEntry {
+public:
+ [[nodiscard]] T* Left() {
+ return rbe_left;
+ }
+
+ [[nodiscard]] const T* Left() const {
+ return rbe_left;
+ }
+
+ void SetLeft(T* left) {
+ rbe_left = left;
+ }
+
+ [[nodiscard]] T* Right() {
+ return rbe_right;
+ }
+
+ [[nodiscard]] const T* Right() const {
+ return rbe_right;
+ }
+
+ void SetRight(T* right) {
+ rbe_right = right;
+ }
+
+ [[nodiscard]] T* Parent() {
+ return rbe_parent;
+ }
+
+ [[nodiscard]] const T* Parent() const {
+ return rbe_parent;
+ }
+
+ void SetParent(T* parent) {
+ rbe_parent = parent;
+ }
+
+ [[nodiscard]] bool IsBlack() const {
+ return rbe_color == EntryColor::Black;
+ }
+
+ [[nodiscard]] bool IsRed() const {
+ return rbe_color == EntryColor::Red;
+ }
+
+ [[nodiscard]] EntryColor Color() const {
+ return rbe_color;
+ }
+
+ void SetColor(EntryColor color) {
+ rbe_color = color;
+ }
+
+private:
+ T* rbe_left = nullptr;
+ T* rbe_right = nullptr;
+ T* rbe_parent = nullptr;
+ EntryColor rbe_color{};
+};
+
+template <typename Node>
+[[nodiscard]] RBEntry<Node>& RB_ENTRY(Node* node) {
+ return node->GetEntry();
+}
+
+template <typename Node>
+[[nodiscard]] const RBEntry<Node>& RB_ENTRY(const Node* node) {
+ return node->GetEntry();
+}
+
+template <typename Node>
+[[nodiscard]] Node* RB_PARENT(Node* node) {
+ return RB_ENTRY(node).Parent();
+}
+
+template <typename Node>
+[[nodiscard]] const Node* RB_PARENT(const Node* node) {
+ return RB_ENTRY(node).Parent();
+}
+
+template <typename Node>
+void RB_SET_PARENT(Node* node, Node* parent) {
+ return RB_ENTRY(node).SetParent(parent);
+}
+
+template <typename Node>
+[[nodiscard]] Node* RB_LEFT(Node* node) {
+ return RB_ENTRY(node).Left();
+}
+
+template <typename Node>
+[[nodiscard]] const Node* RB_LEFT(const Node* node) {
+ return RB_ENTRY(node).Left();
+}
+
+template <typename Node>
+void RB_SET_LEFT(Node* node, Node* left) {
+ return RB_ENTRY(node).SetLeft(left);
+}
+
+template <typename Node>
+[[nodiscard]] Node* RB_RIGHT(Node* node) {
+ return RB_ENTRY(node).Right();
+}
+
+template <typename Node>
+[[nodiscard]] const Node* RB_RIGHT(const Node* node) {
+ return RB_ENTRY(node).Right();
+}
+
+template <typename Node>
+void RB_SET_RIGHT(Node* node, Node* right) {
+ return RB_ENTRY(node).SetRight(right);
+}
+
+template <typename Node>
+[[nodiscard]] bool RB_IS_BLACK(const Node* node) {
+ return RB_ENTRY(node).IsBlack();
+}
+
+template <typename Node>
+[[nodiscard]] bool RB_IS_RED(const Node* node) {
+ return RB_ENTRY(node).IsRed();
+}
+
+template <typename Node>
+[[nodiscard]] EntryColor RB_COLOR(const Node* node) {
+ return RB_ENTRY(node).Color();
+}
+
+template <typename Node>
+void RB_SET_COLOR(Node* node, EntryColor color) {
+ return RB_ENTRY(node).SetColor(color);
+}
+
+template <typename Node>
+void RB_SET(Node* node, Node* parent) {
+ auto& entry = RB_ENTRY(node);
+ entry.SetParent(parent);
+ entry.SetLeft(nullptr);
+ entry.SetRight(nullptr);
+ entry.SetColor(EntryColor::Red);
+}
+
+template <typename Node>
+void RB_SET_BLACKRED(Node* black, Node* red) {
+ RB_SET_COLOR(black, EntryColor::Black);
+ RB_SET_COLOR(red, EntryColor::Red);
+}
+
+template <typename Node>
+void RB_ROTATE_LEFT(RBHead<Node>* head, Node* elm, Node*& tmp) {
+ tmp = RB_RIGHT(elm);
+ RB_SET_RIGHT(elm, RB_LEFT(tmp));
+ if (RB_RIGHT(elm) != nullptr) {
+ RB_SET_PARENT(RB_LEFT(tmp), elm);
+ }
+
+ RB_SET_PARENT(tmp, RB_PARENT(elm));
+ if (RB_PARENT(tmp) != nullptr) {
+ if (elm == RB_LEFT(RB_PARENT(elm))) {
+ RB_SET_LEFT(RB_PARENT(elm), tmp);
+ } else {
+ RB_SET_RIGHT(RB_PARENT(elm), tmp);
+ }
+ } else {
+ head->SetRoot(tmp);
+ }
+
+ RB_SET_LEFT(tmp, elm);
+ RB_SET_PARENT(elm, tmp);
+}
+
+template <typename Node>
+void RB_ROTATE_RIGHT(RBHead<Node>* head, Node* elm, Node*& tmp) {
+ tmp = RB_LEFT(elm);
+ RB_SET_LEFT(elm, RB_RIGHT(tmp));
+ if (RB_LEFT(elm) != nullptr) {
+ RB_SET_PARENT(RB_RIGHT(tmp), elm);
+ }
+
+ RB_SET_PARENT(tmp, RB_PARENT(elm));
+ if (RB_PARENT(tmp) != nullptr) {
+ if (elm == RB_LEFT(RB_PARENT(elm))) {
+ RB_SET_LEFT(RB_PARENT(elm), tmp);
+ } else {
+ RB_SET_RIGHT(RB_PARENT(elm), tmp);
+ }
+ } else {
+ head->SetRoot(tmp);
+ }
+
+ RB_SET_RIGHT(tmp, elm);
+ RB_SET_PARENT(elm, tmp);
+}
+
+template <typename Node>
+void RB_INSERT_COLOR(RBHead<Node>* head, Node* elm) {
+ Node* parent = nullptr;
+ Node* tmp = nullptr;
+
+ while ((parent = RB_PARENT(elm)) != nullptr && RB_IS_RED(parent)) {
+ Node* gparent = RB_PARENT(parent);
+ if (parent == RB_LEFT(gparent)) {
+ tmp = RB_RIGHT(gparent);
+ if (tmp && RB_IS_RED(tmp)) {
+ RB_SET_COLOR(tmp, EntryColor::Black);
+ RB_SET_BLACKRED(parent, gparent);
+ elm = gparent;
+ continue;
+ }
+
+ if (RB_RIGHT(parent) == elm) {
+ RB_ROTATE_LEFT(head, parent, tmp);
+ tmp = parent;
+ parent = elm;
+ elm = tmp;
+ }
+
+ RB_SET_BLACKRED(parent, gparent);
+ RB_ROTATE_RIGHT(head, gparent, tmp);
+ } else {
+ tmp = RB_LEFT(gparent);
+ if (tmp && RB_IS_RED(tmp)) {
+ RB_SET_COLOR(tmp, EntryColor::Black);
+ RB_SET_BLACKRED(parent, gparent);
+ elm = gparent;
+ continue;
+ }
+
+ if (RB_LEFT(parent) == elm) {
+ RB_ROTATE_RIGHT(head, parent, tmp);
+ tmp = parent;
+ parent = elm;
+ elm = tmp;
+ }
+
+ RB_SET_BLACKRED(parent, gparent);
+ RB_ROTATE_LEFT(head, gparent, tmp);
+ }
+ }
+
+ RB_SET_COLOR(head->Root(), EntryColor::Black);
+}
+
+template <typename Node>
+void RB_REMOVE_COLOR(RBHead<Node>* head, Node* parent, Node* elm) {
+ Node* tmp;
+ while ((elm == nullptr || RB_IS_BLACK(elm)) && elm != head->Root()) {
+ if (RB_LEFT(parent) == elm) {
+ tmp = RB_RIGHT(parent);
+ if (RB_IS_RED(tmp)) {
+ RB_SET_BLACKRED(tmp, parent);
+ RB_ROTATE_LEFT(head, parent, tmp);
+ tmp = RB_RIGHT(parent);
+ }
+
+ if ((RB_LEFT(tmp) == nullptr || RB_IS_BLACK(RB_LEFT(tmp))) &&
+ (RB_RIGHT(tmp) == nullptr || RB_IS_BLACK(RB_RIGHT(tmp)))) {
+ RB_SET_COLOR(tmp, EntryColor::Red);
+ elm = parent;
+ parent = RB_PARENT(elm);
+ } else {
+ if (RB_RIGHT(tmp) == nullptr || RB_IS_BLACK(RB_RIGHT(tmp))) {
+ Node* oleft;
+ if ((oleft = RB_LEFT(tmp)) != nullptr) {
+ RB_SET_COLOR(oleft, EntryColor::Black);
+ }
+
+ RB_SET_COLOR(tmp, EntryColor::Red);
+ RB_ROTATE_RIGHT(head, tmp, oleft);
+ tmp = RB_RIGHT(parent);
+ }
+
+ RB_SET_COLOR(tmp, RB_COLOR(parent));
+ RB_SET_COLOR(parent, EntryColor::Black);
+ if (RB_RIGHT(tmp)) {
+ RB_SET_COLOR(RB_RIGHT(tmp), EntryColor::Black);
+ }
+
+ RB_ROTATE_LEFT(head, parent, tmp);
+ elm = head->Root();
+ break;
+ }
+ } else {
+ tmp = RB_LEFT(parent);
+ if (RB_IS_RED(tmp)) {
+ RB_SET_BLACKRED(tmp, parent);
+ RB_ROTATE_RIGHT(head, parent, tmp);
+ tmp = RB_LEFT(parent);
+ }
+
+ if ((RB_LEFT(tmp) == nullptr || RB_IS_BLACK(RB_LEFT(tmp))) &&
+ (RB_RIGHT(tmp) == nullptr || RB_IS_BLACK(RB_RIGHT(tmp)))) {
+ RB_SET_COLOR(tmp, EntryColor::Red);
+ elm = parent;
+ parent = RB_PARENT(elm);
+ } else {
+ if (RB_LEFT(tmp) == nullptr || RB_IS_BLACK(RB_LEFT(tmp))) {
+ Node* oright;
+ if ((oright = RB_RIGHT(tmp)) != nullptr) {
+ RB_SET_COLOR(oright, EntryColor::Black);
+ }
+
+ RB_SET_COLOR(tmp, EntryColor::Red);
+ RB_ROTATE_LEFT(head, tmp, oright);
+ tmp = RB_LEFT(parent);
+ }
+
+ RB_SET_COLOR(tmp, RB_COLOR(parent));
+ RB_SET_COLOR(parent, EntryColor::Black);
+
+ if (RB_LEFT(tmp)) {
+ RB_SET_COLOR(RB_LEFT(tmp), EntryColor::Black);
+ }
+
+ RB_ROTATE_RIGHT(head, parent, tmp);
+ elm = head->Root();
+ break;
+ }
+ }
+ }
+
+ if (elm) {
+ RB_SET_COLOR(elm, EntryColor::Black);
+ }
+}
+
+template <typename Node>
+Node* RB_REMOVE(RBHead<Node>* head, Node* elm) {
+ Node* child = nullptr;
+ Node* parent = nullptr;
+ Node* old = elm;
+ EntryColor color{};
+
+ const auto finalize = [&] {
+ if (color == EntryColor::Black) {
+ RB_REMOVE_COLOR(head, parent, child);
+ }
+
+ return old;
+ };
+
+ if (RB_LEFT(elm) == nullptr) {
+ child = RB_RIGHT(elm);
+ } else if (RB_RIGHT(elm) == nullptr) {
+ child = RB_LEFT(elm);
+ } else {
+ Node* left;
+ elm = RB_RIGHT(elm);
+ while ((left = RB_LEFT(elm)) != nullptr) {
+ elm = left;
+ }
+
+ child = RB_RIGHT(elm);
+ parent = RB_PARENT(elm);
+ color = RB_COLOR(elm);
+
+ if (child) {
+ RB_SET_PARENT(child, parent);
+ }
+ if (parent) {
+ if (RB_LEFT(parent) == elm) {
+ RB_SET_LEFT(parent, child);
+ } else {
+ RB_SET_RIGHT(parent, child);
+ }
+ } else {
+ head->SetRoot(child);
+ }
+
+ if (RB_PARENT(elm) == old) {
+ parent = elm;
+ }
+
+ elm->SetEntry(old->GetEntry());
+
+ if (RB_PARENT(old)) {
+ if (RB_LEFT(RB_PARENT(old)) == old) {
+ RB_SET_LEFT(RB_PARENT(old), elm);
+ } else {
+ RB_SET_RIGHT(RB_PARENT(old), elm);
+ }
+ } else {
+ head->SetRoot(elm);
+ }
+ RB_SET_PARENT(RB_LEFT(old), elm);
+ if (RB_RIGHT(old)) {
+ RB_SET_PARENT(RB_RIGHT(old), elm);
+ }
+ if (parent) {
+ left = parent;
+ }
+
+ return finalize();
+ }
+
+ parent = RB_PARENT(elm);
+ color = RB_COLOR(elm);
+
+ if (child) {
+ RB_SET_PARENT(child, parent);
+ }
+ if (parent) {
+ if (RB_LEFT(parent) == elm) {
+ RB_SET_LEFT(parent, child);
+ } else {
+ RB_SET_RIGHT(parent, child);
+ }
+ } else {
+ head->SetRoot(child);
+ }
+
+ return finalize();
+}
+
+// Inserts a node into the RB tree
+template <typename Node, typename CompareFunction>
+Node* RB_INSERT(RBHead<Node>* head, Node* elm, CompareFunction cmp) {
+ Node* parent = nullptr;
+ Node* tmp = head->Root();
+ int comp = 0;
+
+ while (tmp) {
+ parent = tmp;
+ comp = cmp(elm, parent);
+ if (comp < 0) {
+ tmp = RB_LEFT(tmp);
+ } else if (comp > 0) {
+ tmp = RB_RIGHT(tmp);
+ } else {
+ return tmp;
+ }
+ }
+
+ RB_SET(elm, parent);
+
+ if (parent != nullptr) {
+ if (comp < 0) {
+ RB_SET_LEFT(parent, elm);
+ } else {
+ RB_SET_RIGHT(parent, elm);
+ }
+ } else {
+ head->SetRoot(elm);
+ }
+
+ RB_INSERT_COLOR(head, elm);
+ return nullptr;
+}
+
+// Finds the node with the same key as elm
+template <typename Node, typename CompareFunction>
+Node* RB_FIND(RBHead<Node>* head, Node* elm, CompareFunction cmp) {
+ Node* tmp = head->Root();
+
+ while (tmp) {
+ const int comp = cmp(elm, tmp);
+ if (comp < 0) {
+ tmp = RB_LEFT(tmp);
+ } else if (comp > 0) {
+ tmp = RB_RIGHT(tmp);
+ } else {
+ return tmp;
+ }
+ }
+
+ return nullptr;
+}
+
+// Finds the first node greater than or equal to the search key
+template <typename Node, typename CompareFunction>
+Node* RB_NFIND(RBHead<Node>* head, Node* elm, CompareFunction cmp) {
+ Node* tmp = head->Root();
+ Node* res = nullptr;
+
+ while (tmp) {
+ const int comp = cmp(elm, tmp);
+ if (comp < 0) {
+ res = tmp;
+ tmp = RB_LEFT(tmp);
+ } else if (comp > 0) {
+ tmp = RB_RIGHT(tmp);
+ } else {
+ return tmp;
+ }
+ }
+
+ return res;
+}
+
+// Finds the node with the same key as lelm
+template <typename Node, typename CompareFunction>
+Node* RB_FIND_LIGHT(RBHead<Node>* head, const void* lelm, CompareFunction lcmp) {
+ Node* tmp = head->Root();
+
+ while (tmp) {
+ const int comp = lcmp(lelm, tmp);
+ if (comp < 0) {
+ tmp = RB_LEFT(tmp);
+ } else if (comp > 0) {
+ tmp = RB_RIGHT(tmp);
+ } else {
+ return tmp;
+ }
+ }
+
+ return nullptr;
+}
+
+// Finds the first node greater than or equal to the search key
+template <typename Node, typename CompareFunction>
+Node* RB_NFIND_LIGHT(RBHead<Node>* head, const void* lelm, CompareFunction lcmp) {
+ Node* tmp = head->Root();
+ Node* res = nullptr;
+
+ while (tmp) {
+ const int comp = lcmp(lelm, tmp);
+ if (comp < 0) {
+ res = tmp;
+ tmp = RB_LEFT(tmp);
+ } else if (comp > 0) {
+ tmp = RB_RIGHT(tmp);
+ } else {
+ return tmp;
+ }
+ }
+
+ return res;
+}
+
+template <typename Node>
+Node* RB_NEXT(Node* elm) {
+ if (RB_RIGHT(elm)) {
+ elm = RB_RIGHT(elm);
+ while (RB_LEFT(elm)) {
+ elm = RB_LEFT(elm);
+ }
+ } else {
+ if (RB_PARENT(elm) && (elm == RB_LEFT(RB_PARENT(elm)))) {
+ elm = RB_PARENT(elm);
+ } else {
+ while (RB_PARENT(elm) && (elm == RB_RIGHT(RB_PARENT(elm)))) {
+ elm = RB_PARENT(elm);
+ }
+ elm = RB_PARENT(elm);
+ }
+ }
+ return elm;
+}
+
+template <typename Node>
+Node* RB_PREV(Node* elm) {
+ if (RB_LEFT(elm)) {
+ elm = RB_LEFT(elm);
+ while (RB_RIGHT(elm)) {
+ elm = RB_RIGHT(elm);
+ }
+ } else {
+ if (RB_PARENT(elm) && (elm == RB_RIGHT(RB_PARENT(elm)))) {
+ elm = RB_PARENT(elm);
+ } else {
+ while (RB_PARENT(elm) && (elm == RB_LEFT(RB_PARENT(elm)))) {
+ elm = RB_PARENT(elm);
+ }
+ elm = RB_PARENT(elm);
+ }
+ }
+ return elm;
+}
+
+template <typename Node>
+Node* RB_MINMAX(RBHead<Node>* head, bool is_min) {
+ Node* tmp = head->Root();
+ Node* parent = nullptr;
+
+ while (tmp) {
+ parent = tmp;
+ if (is_min) {
+ tmp = RB_LEFT(tmp);
+ } else {
+ tmp = RB_RIGHT(tmp);
+ }
+ }
+
+ return parent;
+}
+
+template <typename Node>
+Node* RB_MIN(RBHead<Node>* head) {
+ return RB_MINMAX(head, true);
+}
+
+template <typename Node>
+Node* RB_MAX(RBHead<Node>* head) {
+ return RB_MINMAX(head, false);
+}
+} // namespace Common
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