lean2/src/util/rb_tree.h

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#pragma once
#include <utility>
#include <algorithm>
#include "util/rc.h"
#include "util/debug.h"
#include "util/buffer.h"
#include "util/optional.h"
#include "util/memory_pool.h"

namespace lean {
/**
   \brief Left-leaning Red-Black Trees

   It uses a O(1) copy operation. Different trees can share nodes.
   The sharing is thread-safe.

   \c CMP is a functional object for comparing values of type T.
   It must have a method
   <code>
         int operator()(T const & v1, T const & v2) const;
   </code>
   The method must return
   - -1 if <tt>v1 < v2</tt>,
   - 0  if <tt>v1 == v2</tt>,
   - 1  if <tt>v1 > v2</tt>
*/
template<typename T, typename CMP>
class rb_tree : public CMP {
    struct node_cell;
    struct node {
        node_cell * m_ptr;
        node():m_ptr(nullptr) {}
        node(node_cell * ptr):m_ptr(ptr) { if (m_ptr) ptr->inc_ref(); }
        node(node const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
        node(node && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
        ~node() { if (m_ptr) m_ptr->dec_ref(); }
        node & operator=(node const & n) { LEAN_COPY_REF(n); }
        node & operator=(node&& n) { LEAN_MOVE_REF(n); }
        operator bool() const { return m_ptr != nullptr; }
        bool is_shared() const { return m_ptr && m_ptr->get_rc() > 1; }
        bool is_red() const { return m_ptr && m_ptr->m_red; }
        bool is_black() const { return !is_red(); }
        node_cell * operator->() const { lean_assert(m_ptr); return m_ptr; }
        friend bool is_eqp(node const & n1, node const & n2) { return n1.m_ptr == n2.m_ptr; }
        friend void swap(node & n1, node & n2) { std::swap(n1.m_ptr, n2.m_ptr); }
        node steal() { node r; swap(r, *this); return r; }
    };

    struct node_cell {
        node m_left;
        node m_right;
        T    m_value;
        bool m_red;
        MK_LEAN_RC();
        void dealloc();
        node_cell(T const & v):m_value(v), m_red(true), m_rc(0) {}
        node_cell(node_cell const & s):m_left(s.m_left), m_right(s.m_right), m_value(s.m_value), m_red(s.m_red), m_rc(0) {}
    };

    int cmp(T const & v1, T const & v2) const {
        return CMP::operator()(v1, v2);
    }

    static node ensure_unshared(node && n) {
        if (n.is_shared()) {
            return node(new node_cell(*n.m_ptr));
        } else {
            return n;
        }
    }

    static node set_black(node && n) {
        if (n.is_black())
            return n;
        node r = ensure_unshared(n.steal());
        r->m_red = false;
        return r;
    }

    static node rotate_left(node && h) {
        lean_assert(!h.is_shared());
        node x = ensure_unshared(h->m_right.steal());
        lean_assert(!h->m_right); // x stole the ownership of h->m_right
        h->m_right = x->m_left;
        x->m_left  = h;
        x->m_red   = h->m_red;
        h->m_red   = true;
        return x;
    }

    static node rotate_right(node && h) {
        lean_assert(!h.is_shared());
        node x = ensure_unshared(h->m_left.steal());
        lean_assert(!h->m_left); // x stole the ownership of h->m_left
        h->m_left  = x->m_right;
        x->m_right = h;
        x->m_red   = h->m_red;
        h->m_red   = true;
        return x;
    }

    static node flip_colors(node && h) {
        lean_assert(!h.is_shared());
        h->m_red = !h->m_red;
        h->m_left  = ensure_unshared(h->m_left.steal());
        h->m_right = ensure_unshared(h->m_right.steal());
        h->m_left->m_red  = !h->m_left->m_red;
        h->m_right->m_red = !h->m_right->m_red;
        return h;
    }

    static node fixup(node && h) {
        lean_assert(!h.is_shared());
        if (h->m_right.is_red() && !h->m_left.is_red())
            h = rotate_left(h.steal());
        if (h->m_left.is_red() && h->m_left->m_left.is_red())
            h = rotate_right(h.steal());
        if (h->m_left.is_red() && h->m_right.is_red())
            h = flip_colors(h.steal());
        return h;
    }

    node insert(node && n, T const & v) {
        if (!n) {
            return node(new node_cell(v));
        }
        node h = ensure_unshared(n.steal());

        int c = cmp(v, h->m_value);
        if (c == 0)
            h->m_value = v;
        else if (c < 0)
            h->m_left  = insert(h->m_left.steal(), v);
        else
            h->m_right = insert(h->m_right.steal(), v);
        return fixup(h.steal());
    }

    static node move_red_left(node && h) {
        lean_assert(!h.is_shared());
        h = flip_colors(h.steal());
        if (h->m_right && h->m_right->m_left.is_red()) {
            h->m_right = rotate_right(h->m_right.steal());
            h          = rotate_left(h.steal());
            return flip_colors(h.steal());
        } else {
            return h;
        }
    }

    static node move_red_right(node && h) {
        lean_assert(!h.is_shared());
        h = flip_colors(h.steal());
        if (h->m_left && h->m_left->m_left.is_red()) {
            h          = rotate_right(h.steal());
            return flip_colors(h.steal());
        } else {
            return h;
        }
    }

    static node erase_min(node && n) {
        if (!n->m_left)
            return node();
        node h = ensure_unshared(n.steal());
        if (!h->m_left.is_red() && !h->m_left->m_left.is_red())
            h = move_red_left(h.steal());
        h->m_left = erase_min(h->m_left.steal());
        return fixup(h.steal());
    }

    static T const * min(node const & n) {
        node_cell const * it = n.m_ptr;
        if (!it)
            return nullptr;
        while (it->m_left)
            it = it->m_left.m_ptr;
        return &it->m_value;
    }

    static T const * max(node const & n) {
        node_cell const * it = n.m_ptr;
        if (!it)
            return nullptr;
        while (it->m_right)
            it = it->m_right.m_ptr;
        return &it->m_value;
    }

    node erase(node && n, T const & v) {
        lean_assert(n);
        node h = ensure_unshared(n.steal());
        if (cmp(v, h->m_value) < 0) {
            lean_assert(h->m_left); // the tree contains v
            if (!h->m_left.is_red() && !h->m_left->m_left.is_red())
                h = move_red_left(h.steal());
            h->m_left = erase(h->m_left.steal(), v);
        } else {
            if (h->m_left.is_red())
                h = rotate_right(h.steal());
            if (cmp(v, h->m_value) == 0 && !h->m_right)
                return node();
            lean_assert(h->m_right);
            if (!h->m_right.is_red() && !h->m_right->m_left.is_red())
                h = move_red_right(h.steal());
            if (cmp(v, h->m_value) == 0) {
                h->m_value = *min(h->m_right);
                h->m_right = erase_min(h->m_right.steal());
            } else {
                h->m_right = erase(h->m_right.steal(), v);
            }
        }
        return fixup(h.steal());
    }

    template<typename F>
    static void for_each(F && f, node_cell const * n) {
        if (n) {
            for_each(f, n->m_left.m_ptr);
            f(n->m_value);
            for_each(f, n->m_right.m_ptr);
        }
    }

    static void display(std::ostream & out, node_cell const * n) {
        if (n) {
            out << "(";
            if (n->m_red)
                out << "*";
            out << n->m_value << " ";
            display(out, n->m_left.m_ptr);
            out << " ";
            display(out, n->m_right.m_ptr);
            out << ")";
        } else {
            out << "nil";
        }
    }

    static unsigned get_depth(node_cell const * n) {
        if (n)
            return std::max(get_depth(n->m_left.m_ptr), get_depth(n->m_right.m_ptr)) + 1;
        else
            return 0;
    }

    static void to_buffer(node_cell const * n, buffer<T> & r) {
        if (n) {
            to_buffer(n->m_left.m_ptr, r);
            r.push_back(n->m_value);
            to_buffer(n->m_right.m_ptr, r);
        }
    }

    bool check_invariant(node_cell const * n, unsigned curr_black, optional<unsigned> & num_black) const {
        // We check:
        //  1) the nodes are really ordered, that is, left->value < n->value < right->value
        //  2) there are no two consecutive red nodes
        //  3) every path has the same number of black nodes
        if (n) {
            if (!n->m_red)
                curr_black++;
            if (n->m_left) {
                lean_assert(!n->m_red || !n->m_left.is_red());
                check_invariant(n->m_left.m_ptr, curr_black, num_black);
                lean_assert(cmp(n->m_left->m_value, n->m_value) < 0);
            }
            if (n->m_right) {
                lean_assert(!n->m_red || !n->m_right.is_red());
                check_invariant(n->m_right.m_ptr, curr_black, num_black);
                lean_assert(cmp(n->m_value, n->m_right->m_value) < 0);
            }
        } else {
            // end of a path
            if (num_black) {
                lean_assert(curr_black == *num_black);
            } else {
                num_black = curr_black;
            }
        }
        return true;
    }

    node m_root;

public:
    rb_tree(CMP const & cmp = CMP()):CMP(cmp) {}
    rb_tree(rb_tree const & s):CMP(s), m_root(s.m_root) {}
    rb_tree(rb_tree && s):CMP(s), m_root(s.m_root) {}

    rb_tree & operator=(rb_tree const & s) { m_root = s.m_root; return *this; }
    rb_tree & operator=(rb_tree && s) { m_root = s.m_root; return *this; }

    unsigned get_rc() const { return m_root ? m_root->get_rc() : 0; }

    void insert(T const & v) {
        m_root = set_black(insert(m_root.steal(), v));
        lean_assert(check_invariant());
    }

    void erase_min() {
        m_root = set_black(erase_min(m_root.steal()));
        lean_assert(check_invariant());
    }

    void erase_core(T const & v) {
        lean_assert(contains(v));
        m_root = set_black(erase(m_root.steal(), v));
        lean_assert(check_invariant());
    }

    void erase(T const & v) {
        if (contains(v))
            erase_core(v);
    }

    T const * find(T const & v) const {
        node_cell const * h = m_root.m_ptr;
        while (h) {
            int c = cmp(v, h->m_value);
            if (c == 0)
                return &(h->m_value);
            else if (c < 0)
                h = h->m_left.m_ptr;
            else
                h = h->m_right.m_ptr;
        }
        return nullptr;
    }

    T const * min() const { return min(m_root); }
    T const * max() const { return max(m_root); }
    bool contains(T const & v) const { return find(v) != nullptr; }

    template<typename F>
    void for_each(F && f) const { for_each(f, m_root.m_ptr); }

    // For debugging purposes
    void display(std::ostream & out) const { display(out, m_root.m_ptr); }

    unsigned get_depth() const { return get_depth(m_root.m_ptr); }

    unsigned size() const {
        unsigned r = 0;
        for_each([&](T const & ){ r = r + 1; });
        return r;
    }

    bool empty() const { return m_root.m_ptr == nullptr; }

    void clear() { m_root = node(); }

    friend std::ostream & operator<<(std::ostream & out, rb_tree const & t) {
        t.display(out);
        return out;
    }

    bool check_invariant() const {
        optional<unsigned> num_black;
        return check_invariant(m_root.m_ptr, 0, num_black);
    }

    /**
        \brief Copy the contents of this tree to the given buffer.
        The elements will be stored in increasing order.
    */
    void to_buffer(buffer<T> & r) const {
        to_buffer(m_root.m_ptr, r);
    }
};

template<typename T, typename CMP>
void rb_tree<T, CMP>::node_cell::dealloc() {
    delete this;
}

template<typename T, typename CMP>
rb_tree<T, CMP> insert(rb_tree<T, CMP> const & t, T const & v) { rb_tree<T, CMP> r(t); r.insert(v); return r; }
template<typename T, typename CMP>
rb_tree<T, CMP> erase(rb_tree<T, CMP> const & t, T const & v) { rb_tree<T, CMP> r(t); r.erase(v); return r; }

struct unsigned_cmp {
    int operator()(unsigned i1, unsigned i2) const { return i1 < i2 ? -1 : (i1 == i2 ? 0 : 1); }
};
struct int_cmp {
    int operator()(int i1, int i2) const { return i1 < i2 ? -1 : (i1 == i2 ? 0 : 1); }
};
}