path: root/src/common/tree.h

/* $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::freebsd {

enum class RBColor {
    RB_BLACK = 0,
    RB_RED = 1,
};

#pragma pack(push, 4)
template <typename T>
class RBEntry {
public:
    constexpr RBEntry() = default;

    [[nodiscard]] constexpr T* Left() {
        return m_rbe_left;
    }
    [[nodiscard]] constexpr const T* Left() const {
        return m_rbe_left;
    }

    constexpr void SetLeft(T* e) {
        m_rbe_left = e;
    }

    [[nodiscard]] constexpr T* Right() {
        return m_rbe_right;
    }
    [[nodiscard]] constexpr const T* Right() const {
        return m_rbe_right;
    }

    constexpr void SetRight(T* e) {
        m_rbe_right = e;
    }

    [[nodiscard]] constexpr T* Parent() {
        return m_rbe_parent;
    }
    [[nodiscard]] constexpr const T* Parent() const {
        return m_rbe_parent;
    }

    constexpr void SetParent(T* e) {
        m_rbe_parent = e;
    }

    [[nodiscard]] constexpr bool IsBlack() const {
        return m_rbe_color == RBColor::RB_BLACK;
    }
    [[nodiscard]] constexpr bool IsRed() const {
        return m_rbe_color == RBColor::RB_RED;
    }
    [[nodiscard]] constexpr RBColor Color() const {
        return m_rbe_color;
    }

    constexpr void SetColor(RBColor c) {
        m_rbe_color = c;
    }

private:
    T* m_rbe_left{};
    T* m_rbe_right{};
    T* m_rbe_parent{};
    RBColor m_rbe_color{RBColor::RB_BLACK};
};
#pragma pack(pop)

template <typename T>
struct CheckRBEntry {
    static constexpr bool value = false;
};
template <typename T>
struct CheckRBEntry<RBEntry<T>> {
    static constexpr bool value = true;
};

template <typename T>
concept IsRBEntry = CheckRBEntry<T>::value;

template <typename T>
concept HasRBEntry = requires(T& t, const T& ct) {
    { t.GetRBEntry() } -> std::same_as<RBEntry<T>&>;
    { ct.GetRBEntry() } -> std::same_as<const RBEntry<T>&>;
};

template <typename T>
requires HasRBEntry<T>
class RBHead {
private:
    T* m_rbh_root = nullptr;

public:
    [[nodiscard]] constexpr T* Root() {
        return m_rbh_root;
    }
    [[nodiscard]] constexpr const T* Root() const {
        return m_rbh_root;
    }
    constexpr void SetRoot(T* root) {
        m_rbh_root = root;
    }

    [[nodiscard]] constexpr bool IsEmpty() const {
        return this->Root() == nullptr;
    }
};

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr RBEntry<T>& RB_ENTRY(T* t) {
    return t->GetRBEntry();
}
template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr const RBEntry<T>& RB_ENTRY(const T* t) {
    return t->GetRBEntry();
}

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr T* RB_LEFT(T* t) {
    return RB_ENTRY(t).Left();
}
template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr const T* RB_LEFT(const T* t) {
    return RB_ENTRY(t).Left();
}

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr T* RB_RIGHT(T* t) {
    return RB_ENTRY(t).Right();
}
template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr const T* RB_RIGHT(const T* t) {
    return RB_ENTRY(t).Right();
}

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr T* RB_PARENT(T* t) {
    return RB_ENTRY(t).Parent();
}
template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr const T* RB_PARENT(const T* t) {
    return RB_ENTRY(t).Parent();
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET_LEFT(T* t, T* e) {
    RB_ENTRY(t).SetLeft(e);
}
template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET_RIGHT(T* t, T* e) {
    RB_ENTRY(t).SetRight(e);
}
template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET_PARENT(T* t, T* e) {
    RB_ENTRY(t).SetParent(e);
}

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr bool RB_IS_BLACK(const T* t) {
    return RB_ENTRY(t).IsBlack();
}
template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr bool RB_IS_RED(const T* t) {
    return RB_ENTRY(t).IsRed();
}

template <typename T>
requires HasRBEntry<T>
[[nodiscard]] constexpr RBColor RB_COLOR(const T* t) {
    return RB_ENTRY(t).Color();
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET_COLOR(T* t, RBColor c) {
    RB_ENTRY(t).SetColor(c);
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET(T* elm, T* parent) {
    auto& rb_entry = RB_ENTRY(elm);
    rb_entry.SetParent(parent);
    rb_entry.SetLeft(nullptr);
    rb_entry.SetRight(nullptr);
    rb_entry.SetColor(RBColor::RB_RED);
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_SET_BLACKRED(T* black, T* red) {
    RB_SET_COLOR(black, RBColor::RB_BLACK);
    RB_SET_COLOR(red, RBColor::RB_RED);
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_ROTATE_LEFT(RBHead<T>& head, T* elm, T*& tmp) {
    tmp = RB_RIGHT(elm);
    if (RB_SET_RIGHT(elm, RB_LEFT(tmp)); RB_RIGHT(elm) != nullptr) {
        RB_SET_PARENT(RB_LEFT(tmp), elm);
    }

    if (RB_SET_PARENT(tmp, RB_PARENT(elm)); 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 T>
requires HasRBEntry<T>
constexpr void RB_ROTATE_RIGHT(RBHead<T>& head, T* elm, T*& tmp) {
    tmp = RB_LEFT(elm);
    if (RB_SET_LEFT(elm, RB_RIGHT(tmp)); RB_LEFT(elm) != nullptr) {
        RB_SET_PARENT(RB_RIGHT(tmp), elm);
    }

    if (RB_SET_PARENT(tmp, RB_PARENT(elm)); 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 T>
requires HasRBEntry<T>
constexpr void RB_REMOVE_COLOR(RBHead<T>& head, T* parent, T* elm) {
    T* 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, RBColor::RB_RED);
                elm = parent;
                parent = RB_PARENT(elm);
            } else {
                if (RB_RIGHT(tmp) == nullptr || RB_IS_BLACK(RB_RIGHT(tmp))) {
                    T* oleft;
                    if ((oleft = RB_LEFT(tmp)) != nullptr) {
                        RB_SET_COLOR(oleft, RBColor::RB_BLACK);
                    }

                    RB_SET_COLOR(tmp, RBColor::RB_RED);
                    RB_ROTATE_RIGHT(head, tmp, oleft);
                    tmp = RB_RIGHT(parent);
                }

                RB_SET_COLOR(tmp, RB_COLOR(parent));
                RB_SET_COLOR(parent, RBColor::RB_BLACK);
                if (RB_RIGHT(tmp)) {
                    RB_SET_COLOR(RB_RIGHT(tmp), RBColor::RB_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, RBColor::RB_RED);
                elm = parent;
                parent = RB_PARENT(elm);
            } else {
                if (RB_LEFT(tmp) == nullptr || RB_IS_BLACK(RB_LEFT(tmp))) {
                    T* oright;
                    if ((oright = RB_RIGHT(tmp)) != nullptr) {
                        RB_SET_COLOR(oright, RBColor::RB_BLACK);
                    }

                    RB_SET_COLOR(tmp, RBColor::RB_RED);
                    RB_ROTATE_LEFT(head, tmp, oright);
                    tmp = RB_LEFT(parent);
                }

                RB_SET_COLOR(tmp, RB_COLOR(parent));
                RB_SET_COLOR(parent, RBColor::RB_BLACK);

                if (RB_LEFT(tmp)) {
                    RB_SET_COLOR(RB_LEFT(tmp), RBColor::RB_BLACK);
                }

                RB_ROTATE_RIGHT(head, parent, tmp);
                elm = head.Root();
                break;
            }
        }
    }

    if (elm) {
        RB_SET_COLOR(elm, RBColor::RB_BLACK);
    }
}

template <typename T>
requires HasRBEntry<T>
constexpr T* RB_REMOVE(RBHead<T>& head, T* elm) {
    T* child = nullptr;
    T* parent = nullptr;
    T* old = elm;
    RBColor color = RBColor::RB_BLACK;

    if (RB_LEFT(elm) == nullptr) {
        child = RB_RIGHT(elm);
    } else if (RB_RIGHT(elm) == nullptr) {
        child = RB_LEFT(elm);
    } else {
        T* 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->SetRBEntry(old->GetRBEntry());

        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;
        }

        if (color == RBColor::RB_BLACK) {
            RB_REMOVE_COLOR(head, parent, child);
        }

        return old;
    }

    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 (color == RBColor::RB_BLACK) {
        RB_REMOVE_COLOR(head, parent, child);
    }

    return old;
}

template <typename T>
requires HasRBEntry<T>
constexpr void RB_INSERT_COLOR(RBHead<T>& head, T* elm) {
    T *parent = nullptr, *tmp = nullptr;
    while ((parent = RB_PARENT(elm)) != nullptr && RB_IS_RED(parent)) {
        T* gparent = RB_PARENT(parent);
        if (parent == RB_LEFT(gparent)) {
            tmp = RB_RIGHT(gparent);
            if (tmp && RB_IS_RED(tmp)) {
                RB_SET_COLOR(tmp, RBColor::RB_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, RBColor::RB_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(), RBColor::RB_BLACK);
}

template <typename T, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_INSERT(RBHead<T>& head, T* elm, Compare cmp) {
    T* parent = nullptr;
    T* 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;
}

template <typename T, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_FIND(RBHead<T>& head, T* elm, Compare cmp) {
    T* 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;
}

template <typename T, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_NFIND(RBHead<T>& head, T* elm, Compare cmp) {
    T* tmp = head.Root();
    T* 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;
}

template <typename T, typename U, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_FIND_KEY(RBHead<T>& head, const U& key, Compare cmp) {
    T* tmp = head.Root();

    while (tmp) {
        const int comp = cmp(key, tmp);
        if (comp < 0) {
            tmp = RB_LEFT(tmp);
        } else if (comp > 0) {
            tmp = RB_RIGHT(tmp);
        } else {
            return tmp;
        }
    }

    return nullptr;
}

template <typename T, typename U, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_NFIND_KEY(RBHead<T>& head, const U& key, Compare cmp) {
    T* tmp = head.Root();
    T* res = nullptr;

    while (tmp) {
        const int comp = cmp(key, 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 T, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_FIND_EXISTING(RBHead<T>& head, T* elm, Compare cmp) {
    T* tmp = head.Root();

    while (true) {
        const int comp = cmp(elm, tmp);
        if (comp < 0) {
            tmp = RB_LEFT(tmp);
        } else if (comp > 0) {
            tmp = RB_RIGHT(tmp);
        } else {
            return tmp;
        }
    }
}

template <typename T, typename U, typename Compare>
requires HasRBEntry<T>
constexpr T* RB_FIND_EXISTING_KEY(RBHead<T>& head, const U& key, Compare cmp) {
    T* tmp = head.Root();

    while (true) {
        const int comp = cmp(key, tmp);
        if (comp < 0) {
            tmp = RB_LEFT(tmp);
        } else if (comp > 0) {
            tmp = RB_RIGHT(tmp);
        } else {
            return tmp;
        }
    }
}

template <typename T>
requires HasRBEntry<T>
constexpr T* RB_NEXT(T* 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 T>
requires HasRBEntry<T>
constexpr T* RB_PREV(T* 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 T>
requires HasRBEntry<T>
constexpr T* RB_MIN(RBHead<T>& head) {
    T* tmp = head.Root();
    T* parent = nullptr;

    while (tmp) {
        parent = tmp;
        tmp = RB_LEFT(tmp);
    }

    return parent;
}

template <typename T>
requires HasRBEntry<T>
constexpr T* RB_MAX(RBHead<T>& head) {
    T* tmp = head.Root();
    T* parent = nullptr;

    while (tmp) {
        parent = tmp;
        tmp = RB_RIGHT(tmp);
    }

    return parent;
}

} // namespace Common::freebsd