suyu/src/common/tree.h

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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).
*/
#include "common/assert.h"
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() && parent != nullptr) {
if (RB_LEFT(parent) == elm) {
tmp = RB_RIGHT(parent);
if (!tmp) {
ASSERT_MSG(false, "tmp is invalid!");
break;
}
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 (!tmp) {
ASSERT_MSG(false, "tmp is invalid!");
break;
}
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