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