rb3ptr.c

/* rb3ptr  -- Intrusively linked 3-pointer Red-black tree implementation */

/* Copyright (C) 2019, Jens Stimpfle */

/*
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

#include <rb3ptr.h>
#include <stddef.h>  // offsetof()

enum {
        _RB3_DIR_BIT = 1 << 0,
        _RB3_COLOR_BIT = 1 << 1,
        _RB3_BLACK = 0,
        _RB3_RED = _RB3_COLOR_BIT,
};

static inline rb3_ptr rb3_child_ptr(struct rb3_head *head, int color)
{
        return (rb3_ptr) head | color;
}

static inline rb3_ptr rb3_parent_ptr(struct rb3_head *head, int dir)
{
        return (rb3_ptr) head | dir;
}

static inline struct rb3_head *rb3_get_black_child(struct rb3_head *head, int dir)
{
        return (struct rb3_head *) head->child[dir];
}

static inline int rb3_get_color_bit(struct rb3_head *head, int dir)
{
        return head->child[dir] & _RB3_COLOR_BIT;
}

static inline int rb3_is_red(struct rb3_head *head, int dir)
{
        return rb3_get_color_bit(head, dir) != 0;
}

static inline void rb3_set_red(struct rb3_head *head, int dir)
{
        head->child[dir] |= _RB3_COLOR_BIT;
}

static inline void rb3_set_black(struct rb3_head *head, int dir)
{
        head->child[dir] &= ~_RB3_COLOR_BIT;
}

static inline void rb3_connect(struct rb3_head *head, int dir, struct rb3_head *child, int color)
{
        head->child[dir] = rb3_child_ptr(child, color);
        child->parent = rb3_parent_ptr(head, dir);
}

static inline void rb3_connect_null(struct rb3_head *head, int dir, struct rb3_head *child, int color)
{
        head->child[dir] = rb3_child_ptr(child, color);
        if (child)
                child->parent = rb3_parent_ptr(head, dir);
}

struct rb3_tree *rb3_get_containing_tree(struct rb3_head *head)
{
        while (rb3_get_parent(head))
                head = rb3_get_parent(head);
        return (struct rb3_tree *) ((char *) head - (offsetof(struct rb3_head, child[0])));
}

static struct rb3_head *rb3_get_minmax_in_subtree(struct rb3_head *head, int dir)
{
        if (!head)
                return _RB3_NULL;
        while (rb3_has_child(head, dir))
                head = rb3_get_child(head, dir);
        return head;
}

struct rb3_head *rb3_get_minmax(struct rb3_tree *tree, int dir)
{
        return rb3_get_minmax_in_subtree(rb3_get_root(tree), dir);
}

struct rb3_head *rb3_get_prevnext_descendant(struct rb3_head *head, int dir)
{
        return rb3_get_minmax_in_subtree(rb3_get_child(head, dir), !dir);
}

struct rb3_head *rb3_get_prevnext_ancestor(struct rb3_head *head, int dir)
{
        /*
         * Note: the direction is "reversed" for our purposes here, since
         * the bit indicates the direction from the parent to `head`
         */
        while (head && rb3_get_parent_dir(head) == dir) {
                head = rb3_get_parent(head);
        }
        if (head) {
                head = rb3_get_parent(head);
                if (!head || rb3_is_base(head))
                        return _RB3_NULL;
                return head;
        }
        return _RB3_NULL;
}

struct rb3_head *rb3_get_prevnext(struct rb3_head *head, int dir)
{
        if (rb3_has_child(head, dir))
                return rb3_get_prevnext_descendant(head, dir);
        else
                return rb3_get_prevnext_ancestor(head, dir);
}

void rb3_update_augment(struct rb3_head *head, rb3_augment_func *augment)
{
        while (!rb3_is_base(head)) {
                augment(head);
                head = rb3_get_parent(head);
        }
}

static void rb3_rebalance_after_link(struct rb3_head *head, rb3_augment_func *augment)
{
        struct rb3_head *pnt;
        struct rb3_head *gpnt;
        struct rb3_head *ggpnt;
        int left;
        int right;
        int gdir;
        int ggdir;

        if (!rb3_get_parent(rb3_get_parent(head))) {
                rb3_set_black(rb3_get_parent(head), RB3_LEFT);
                if (augment)
                        augment(head);
                return;
        }

        if (!rb3_is_red(rb3_get_parent(rb3_get_parent(head)), rb3_get_parent_dir(rb3_get_parent(head)))) {
                /* parent is black */
                if (augment)
                        rb3_update_augment(head, augment);
                return;
        }

        /*
         * Since parent is red parent can't be the root.
         * So we have at least a grandparent node, and grand-grandparent
         * is either a real node or the base head.
         */
        pnt = rb3_get_parent(head);
        gpnt = rb3_get_parent(pnt);
        ggpnt = rb3_get_parent(gpnt);
        left = rb3_get_parent_dir(head);
        right = !rb3_get_parent_dir(head);
        gdir = rb3_get_parent_dir(pnt);
        ggdir = rb3_get_parent_dir(gpnt);

        if (rb3_is_red(gpnt, !gdir)) {
                /* uncle and parent are both red */
                rb3_set_red(ggpnt, ggdir);
                rb3_set_black(gpnt, RB3_LEFT);
                rb3_set_black(gpnt, RB3_RIGHT);
                if (augment)
                        rb3_update_augment(head, augment);
                rb3_rebalance_after_link(gpnt, augment);
        } else if (gdir == right) {
                rb3_connect_null(pnt, left, rb3_get_black_child(head, right), _RB3_BLACK);
                rb3_connect_null(gpnt, right, rb3_get_black_child(head, left), _RB3_BLACK);
                rb3_connect(head, left, gpnt, _RB3_RED);
                rb3_connect(head, right, pnt, _RB3_RED);
                rb3_connect(ggpnt, ggdir, head, _RB3_BLACK);
                if (augment) {
                        augment(pnt);
                        augment(gpnt);
                        rb3_update_augment(head, augment);
                }
        } else {
                rb3_connect_null(gpnt, left, rb3_get_black_child(pnt, right), _RB3_BLACK);
                rb3_connect(pnt, right, gpnt, _RB3_RED);
                rb3_connect(ggpnt, ggdir, pnt, _RB3_BLACK);
                if (augment) {
                        augment(gpnt);
                        rb3_update_augment(head, augment);
                }
        }
}

static void rb3_rebalance_after_unlink(struct rb3_head *pnt, int pdir, rb3_augment_func *augment)
{
        struct rb3_head *gpnt;
        struct rb3_head *sibling;
        struct rb3_head *sleft;
        struct rb3_head *sleftleft;
        struct rb3_head *sleftright;
        enum rb3_dir left;
        enum rb3_dir right;
        enum rb3_dir gdir;

        if (!rb3_get_parent(pnt))
                return;

        left = pdir;  // define "left" as the direction from parent to deleted node
        right = !pdir;
        gpnt = rb3_get_parent(pnt);
        gdir = rb3_get_parent_dir(pnt);
        sibling = rb3_get_child(pnt, right);
        sleft = rb3_get_child(sibling, left);

        if (rb3_is_red(pnt, right)) {
                /* sibling is red */
                rb3_connect(pnt, right, sleft, _RB3_BLACK);
                rb3_connect(sibling, left, pnt, _RB3_RED);
                rb3_connect(gpnt, gdir, sibling, _RB3_BLACK);
                if (augment)
                        augment(sleft);
                rb3_rebalance_after_unlink(pnt, pdir, augment);
        } else if (rb3_is_red(sibling, right)) {
                /* outer child of sibling is red */
                rb3_connect_null(pnt, right, sleft, rb3_get_color_bit(sibling, left));
                rb3_connect(sibling, left, pnt, _RB3_BLACK);
                rb3_connect(gpnt, gdir, sibling, rb3_get_color_bit(gpnt, gdir));
                if (augment) {
                        rb3_update_augment(pnt, augment);
                }
                rb3_set_black(sibling, right);
        } else if (rb3_is_red(sibling, left)) {
                /* inner child of sibling is red */
                sleftleft = rb3_get_child(sleft, left);
                sleftright = rb3_get_child(sleft, right);
                rb3_connect_null(pnt, right, sleftleft, _RB3_BLACK);
                rb3_connect_null(sibling, left, sleftright, _RB3_BLACK);
                rb3_connect(sleft, left, pnt, _RB3_BLACK);
                rb3_connect(sleft, right, sibling, _RB3_BLACK);
                rb3_connect(gpnt, gdir, sleft, rb3_get_color_bit(gpnt, gdir));
                if (augment) {
                        augment(sibling);
                        rb3_update_augment(pnt, augment);
                }
        } else if (rb3_is_red(gpnt, gdir)) {
                /* parent is red */
                rb3_set_red(pnt, right);
                rb3_set_black(gpnt, gdir);
                if (augment)
                        rb3_update_augment(pnt, augment);
        } else {
                /* all relevant nodes are black */
                rb3_set_red(pnt, right);
                if (augment)
                        augment(pnt);
                rb3_rebalance_after_unlink(gpnt, gdir, augment);
        }
}

void rb3_link_and_rebalance_and_maybe_augment(struct rb3_head *head, struct rb3_head *parent, int dir, rb3_augment_func *augment)
{
        _RB3_ASSERT(dir == RB3_LEFT || dir == RB3_RIGHT);
        _RB3_ASSERT(!rb3_has_child(parent, dir));

        parent->child[dir] = rb3_child_ptr(head, _RB3_RED);
        head->parent = rb3_parent_ptr(parent, dir);
        head->child[RB3_LEFT] = rb3_child_ptr(_RB3_NULL, _RB3_BLACK);
        head->child[RB3_RIGHT] = rb3_child_ptr(_RB3_NULL, _RB3_BLACK);
        rb3_rebalance_after_link(head, augment);
}

void rb3_replace_and_maybe_augment(struct rb3_head *head, struct rb3_head *newhead, rb3_augment_func *augment)
{
        struct rb3_head *left;
        struct rb3_head *right;
        struct rb3_head *parent;
        int pdir;
        int pcol;

        *newhead = *head;

        left = rb3_get_child(head, RB3_LEFT);
        right = rb3_get_child(head, RB3_RIGHT);
        parent = rb3_get_parent(head);
        pdir = rb3_get_parent_dir(head);
        pcol = rb3_get_color_bit(parent, pdir);

        if (left)
                left->parent = rb3_parent_ptr(newhead, RB3_LEFT);
        if (right)
                right->parent = rb3_parent_ptr(newhead, RB3_RIGHT);
        parent->child[pdir] = rb3_child_ptr(newhead, pcol);

        if (augment)
                rb3_update_augment(newhead, augment);
}

static void rb3_unlink_noninternal_and_rebalance_and_maybe_augment(struct rb3_head *head, rb3_augment_func *augment)
{
        struct rb3_head *pnt;
        struct rb3_head *cld;
        int pdir;
        int dir;

        dir = rb3_get_child(head, RB3_RIGHT) ? RB3_RIGHT : RB3_LEFT;
        pnt = rb3_get_parent(head);
        cld = rb3_get_child(head, dir);
        pdir = rb3_get_parent_dir(head);

        int mustRebalance = !rb3_is_red(pnt, pdir) && !rb3_is_red(head, dir);

        /* since we added the possibility for augmentation,
        we need to remove `head` *before* the rebalancing that we do below.
        (Otherwise the augmentation function would still see the to-be-deleted child). */
        rb3_connect_null(pnt, pdir, cld, _RB3_BLACK);

        if (mustRebalance)
                /* To be deleted node is black (and child cannot be repainted)
                 * => height decreased */
                rb3_rebalance_after_unlink(pnt, pdir, augment);
        else if (augment)
                /* the augment wasn't done since we didn't rebalance. So we need to do it separately.
                TODO: Could we restrict the augmentation done during rebalancing to just the
                nodes that aren't not be augmented by a regular rb3_augment_ancestors(pnt, augment)? */
                rb3_update_augment(pnt, augment);
}

static void rb3_unlink_internal_and_rebalance_and_maybe_augment(struct rb3_head *head, rb3_augment_func *augment)
{
        struct rb3_head *subst;

        subst = rb3_get_next_descendant(head);
        rb3_unlink_noninternal_and_rebalance_and_maybe_augment(subst, augment);
        rb3_replace_and_maybe_augment(head, subst, augment);
}

void rb3_unlink_and_rebalance_and_maybe_augment(struct rb3_head *head, rb3_augment_func *augment)
{
        if (rb3_has_child(head, RB3_LEFT) && rb3_has_child(head, RB3_RIGHT))
                rb3_unlink_internal_and_rebalance_and_maybe_augment(head, augment);
        else
                rb3_unlink_noninternal_and_rebalance_and_maybe_augment(head, augment);
}

struct rb3_head *rb3_find_parent_in_subtree(struct rb3_head *parent, int dir, rb3_cmp cmp, void *data, struct rb3_head **parent_out, int *dir_out)
{
        return rb3_INLINE_find(parent, dir, cmp, data, parent_out, dir_out);
}

struct rb3_head *rb3_insert(struct rb3_tree *tree, struct rb3_head *head, rb3_cmp cmp, void *data)
{
        struct rb3_head *found;
        struct rb3_head *parent;
        int dir;

        parent = rb3_get_base(tree);
        dir = RB3_LEFT;
        found = rb3_find_parent_in_subtree(parent, dir, cmp, data, &parent, &dir);
        if (found)
                return found;
        rb3_link_and_rebalance(head, parent, dir);
        return _RB3_NULL;
}

struct rb3_head *rb3_delete(struct rb3_tree *tree, rb3_cmp cmp, void *data)
{
        struct rb3_head *found;

        found = rb3_find(tree, cmp, data);
        if (found) {
                rb3_unlink_and_rebalance(found);
                return found;
        }
        return _RB3_NULL;
}

struct rb3_head *rb3_find_parent(struct rb3_tree *tree, rb3_cmp cmp, void *data, struct rb3_head **parent_out, int *dir_out)
{
        return rb3_find_parent_in_subtree(rb3_get_base(tree), RB3_LEFT, cmp, data, parent_out, dir_out);
}

struct rb3_head *rb3_find(struct rb3_tree *tree, rb3_cmp cmp, void *data)
{
        return rb3_find_parent_in_subtree(rb3_get_base(tree), RB3_LEFT, cmp, data, _RB3_NULL, _RB3_NULL);
}

void rb3_link_and_rebalance(struct rb3_head *head, struct rb3_head *parent, int dir)
{
        rb3_link_and_rebalance_and_maybe_augment(head, parent, dir, _RB3_NULL);
}

void rb3_unlink_and_rebalance(struct rb3_head *head)
{
        rb3_unlink_and_rebalance_and_maybe_augment(head, _RB3_NULL);
}

void rb3_replace(struct rb3_head *head, struct rb3_head *newhead)
{
        rb3_replace_and_maybe_augment(head, newhead, _RB3_NULL);
}

void rb3_link_and_rebalance_and_augment(struct rb3_head *head, struct rb3_head *parent, int dir, rb3_augment_func *augment)
{
        rb3_link_and_rebalance_and_maybe_augment(head, parent, dir, augment);
}

void rb3_unlink_and_rebalance_and_augment(struct rb3_head *head, rb3_augment_func *augment)
{
        rb3_unlink_and_rebalance_and_maybe_augment(head, augment);
}

void rb3_replace_and_augment(struct rb3_head *head, struct rb3_head *newhead, rb3_augment_func *augment)
{
        rb3_replace_and_maybe_augment(head, newhead, augment);
}


/* DEBUG STUFF */

#include <stdio.h>
static void visit_inorder_helper(struct rb3_head *head, int isred)
{
        if (!head)
                return;
        printf(" (");
        visit_inorder_helper(rb3_get_child(head, RB3_LEFT), rb3_is_red(head, RB3_LEFT));
        printf("%s", isred ? "R" : "B");
        visit_inorder_helper(rb3_get_child(head, RB3_RIGHT), rb3_is_red(head, RB3_RIGHT));
        printf(")");
}

static void visit_inorder(struct rb3_tree *tree)
{
        visit_inorder_helper(rb3_get_root(tree), 0);
        printf("\n");
}

static int rb3_is_valid_tree_helper(struct rb3_head *head, int isred, int dir, int *depth)
{
        int i;
        int depths[2] = { 1,1 };

        *depth = 1;

        if (!head) {
                if (isred) {
                        printf("red leaf child!\n");
                        return 0;
                }
                return 1;
        }

        if (rb3_get_parent_dir(head) != dir) {
                printf("Directions messed up!\n");
                return 0;
        }

        for (i = 0; i < 2; i++) {
                if (isred && rb3_get_color_bit(head, i)) {
                        printf("two red in a row!\n");
                        return 0;
                }
                if (!rb3_is_valid_tree_helper(rb3_get_child(head, i),
                        rb3_is_red(head, i), i, &depths[i]))
                        return 0;
        }
        if (depths[0] != depths[1]) {
                printf("Unbalanced tree! got %d and %d\n", depths[0], depths[1]);
                return 0;
        }
        *depth = depths[0] + !isred;

        return 1;
}

int rb3_check_tree(struct rb3_tree *tree)
{
        int depth;
        int valid;

        if (rb3_is_red(&tree->base, RB3_LEFT)) {
                printf("Error! root is red.\n");
                return 0;
        }

        valid = rb3_is_valid_tree_helper(rb3_get_root(tree), 0, 0, &depth);
        if (!valid)
                visit_inorder(tree);
        return valid;
}