/* Produced by texiweb from libavl.w. */

/* libavl - library for manipulation of binary trees.
   Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software
   Foundation, Inc.

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 3 of the License, or (at your option) any later version.

   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA.
 */

/* Nov 2016, Markus Metz
 * from libavl-2.0.3
 * added safety checks and speed optimizations
 */

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "avl.h"

/* Creates and returns a new table
   with comparison function |compare| using parameter |param|
   and memory allocator |allocator|.
   Returns |NULL| if memory allocation failed. */
struct avl_table *avl_create(avl_comparison_func *compare, void *param,
                             struct libavl_allocator *allocator)
{
    struct avl_table *tree;

    assert(compare != NULL);

    if (allocator == NULL)
        allocator = &avl_allocator_default;

    tree = allocator->libavl_malloc(allocator, sizeof *tree);
    if (tree == NULL)
        return NULL;

    tree->avl_root = NULL;
    tree->avl_compare = compare;
    tree->avl_param = param;
    tree->avl_alloc = allocator;
    tree->avl_count = 0;
    tree->avl_generation = 0;

    return tree;
}

/* Search |tree| for an item matching |item|, and return it if found.
   Otherwise return |NULL|. */
void *avl_find(const struct avl_table *tree, const void *item)
{
    const struct avl_node *p;

    assert(tree != NULL && item != NULL);

    p = tree->avl_root;
    while (p != NULL) {
        int cmp = tree->avl_compare(item, p->avl_data, tree->avl_param);

        if (cmp == 0)
            return p->avl_data;

        p = p->avl_link[cmp > 0];
    }

    return NULL;
}

/* Inserts |item| into |tree| and returns a pointer to |item|'s address.
   If a duplicate item is found in the tree,
   returns a pointer to the duplicate without inserting |item|.
   Returns |NULL| in case of memory allocation failure. */
void **avl_probe(struct avl_table *tree, void *item)
{
    struct avl_node *y, *z; /* Top node to update balance factor, and parent. */
    struct avl_node *p, *q; /* Iterator, and parent. */
    struct avl_node *n;     /* Newly inserted node. */
    struct avl_node *w;     /* New root of rebalanced subtree. */
    int dir;                /* Direction to descend. */

    unsigned char da[AVL_MAX_HEIGHT]; /* Cached comparison results. */
    int k = 0;                        /* Number of cached results. */

    assert(tree != NULL && item != NULL);

    z = (struct avl_node *)&tree->avl_root;
    y = tree->avl_root;
    dir = 0;
    q = z, p = y;
    while (p != NULL) {
        int cmp = tree->avl_compare(item, p->avl_data, tree->avl_param);

        if (cmp == 0)
            return &p->avl_data;

        if (p->avl_balance != 0)
            z = q, y = p, k = 0;
        da[k++] = dir = cmp > 0;
        q = p, p = p->avl_link[dir];
    }

    n = tree->avl_alloc->libavl_malloc(tree->avl_alloc, sizeof *n);
    if (n == NULL)
        return NULL;

    tree->avl_count++;
    tree->avl_generation++;
    n->avl_link[0] = n->avl_link[1] = NULL;
    n->avl_data = item;
    n->avl_balance = 0;
    if (y == NULL) {
        tree->avl_root = n;

        return &n->avl_data;
    }
    q->avl_link[dir] = n;

    p = y, k = 0;
    while (p != n) {
        if (da[k] == 0)
            p->avl_balance--;
        else
            p->avl_balance++;
        p = p->avl_link[da[k]], k++;
    }

    if (y->avl_balance == -2) {
        struct avl_node *x = y->avl_link[0];

        if (x->avl_balance == -1) {
            w = x;
            y->avl_link[0] = x->avl_link[1];
            x->avl_link[1] = y;
            x->avl_balance = y->avl_balance = 0;
        }
        else {
            assert(x->avl_balance == +1);
            w = x->avl_link[1];
            x->avl_link[1] = w->avl_link[0];
            w->avl_link[0] = x;
            y->avl_link[0] = w->avl_link[1];
            w->avl_link[1] = y;
            if (w->avl_balance == -1)
                x->avl_balance = 0, y->avl_balance = +1;
            else if (w->avl_balance == 0)
                x->avl_balance = y->avl_balance = 0;
            else /* |w->avl_balance == +1| */
                x->avl_balance = -1, y->avl_balance = 0;
            w->avl_balance = 0;
        }
    }
    else if (y->avl_balance == +2) {
        struct avl_node *x = y->avl_link[1];

        if (x->avl_balance == +1) {
            w = x;
            y->avl_link[1] = x->avl_link[0];
            x->avl_link[0] = y;
            x->avl_balance = y->avl_balance = 0;
        }
        else {
            assert(x->avl_balance == -1);
            w = x->avl_link[0];
            x->avl_link[0] = w->avl_link[1];
            w->avl_link[1] = x;
            y->avl_link[1] = w->avl_link[0];
            w->avl_link[0] = y;
            if (w->avl_balance == +1)
                x->avl_balance = 0, y->avl_balance = -1;
            else if (w->avl_balance == 0)
                x->avl_balance = y->avl_balance = 0;
            else /* |w->avl_balance == -1| */
                x->avl_balance = +1, y->avl_balance = 0;
            w->avl_balance = 0;
        }
    }
    else
        return &n->avl_data;
    z->avl_link[y != z->avl_link[0]] = w;

    return &n->avl_data;
}

/* Inserts |item| into |table|.
   Returns |NULL| if |item| was successfully inserted
   or if a memory allocation error occurred.
   Otherwise, returns the duplicate item. */
void *avl_insert(struct avl_table *table, void *item)
{
    void **p = avl_probe(table, item);

    return p == NULL || *p == item ? NULL : *p;
}

/* Inserts |item| into |table|, replacing any duplicate item.
   Returns |NULL| if |item| was inserted without replacing a duplicate,
   or if a memory allocation error occurred.
   Otherwise, returns the item that was replaced. */
void *avl_replace(struct avl_table *table, void *item)
{
    void **p = avl_probe(table, item);

    if (p == NULL || *p == item)
        return NULL;
    else {
        void *r = *p;

        *p = item;

        return r;
    }
}

/* Deletes from |tree| and returns an item matching |item|.
   Returns a null pointer if no matching item found. */
void *avl_delete(struct avl_table *tree, const void *item)
{
    /* Stack of nodes. */
    struct avl_node *pa[AVL_MAX_HEIGHT]; /* Nodes. */
    unsigned char da[AVL_MAX_HEIGHT];    /* |avl_link[]| indexes. */
    int k;                               /* Stack pointer. */

    struct avl_node *p; /* Traverses tree to find node to delete. */
    int dir;            /* Side of |pa[k]| on which |p| is linked. */
    int cmp;            /* Result of comparison between |item| and |p|. */

    assert(tree != NULL && item != NULL);

    pa[0] = (struct avl_node *)&tree->avl_root;
    da[0] = 0;
    k = 1;
    p = tree->avl_root;
    while (p != NULL) {
        cmp = tree->avl_compare(item, p->avl_data, tree->avl_param);

        if (cmp == 0)
            break;

        dir = cmp > 0;

        pa[k] = p;
        da[k++] = dir;

        p = p->avl_link[dir];
    }
    if (p == NULL)
        return NULL;

    item = p->avl_data;

    if (p->avl_link[1] == NULL)
        pa[k - 1]->avl_link[da[k - 1]] = p->avl_link[0];
    else {
        struct avl_node *r = p->avl_link[1];

        if (r->avl_link[0] == NULL) {
            r->avl_link[0] = p->avl_link[0];
            r->avl_balance = p->avl_balance;
            pa[k - 1]->avl_link[da[k - 1]] = r;
            da[k] = 1;
            pa[k++] = r;
        }
        else {
            struct avl_node *s;
            int j = k++;

            while (r != NULL) {
                da[k] = 0;
                pa[k++] = r;
                s = r->avl_link[0];
                if (s->avl_link[0] == NULL)
                    break;

                r = s;
            }

            s->avl_link[0] = p->avl_link[0];
            r->avl_link[0] = s->avl_link[1];
            s->avl_link[1] = p->avl_link[1];
            s->avl_balance = p->avl_balance;

            pa[j - 1]->avl_link[da[j - 1]] = s;
            da[j] = 1;
            pa[j] = s;
        }
    }

    tree->avl_alloc->libavl_free(tree->avl_alloc, p);

    assert(k > 0);
    while (--k > 0) {
        struct avl_node *y = pa[k];

        if (da[k] == 0) {
            y->avl_balance++;
            if (y->avl_balance == +1)
                break;
            else if (y->avl_balance == +2) {
                struct avl_node *x = y->avl_link[1];

                if (x->avl_balance == -1) {
                    struct avl_node *w;

                    assert(x->avl_balance == -1);
                    w = x->avl_link[0];
                    x->avl_link[0] = w->avl_link[1];
                    w->avl_link[1] = x;
                    y->avl_link[1] = w->avl_link[0];
                    w->avl_link[0] = y;
                    if (w->avl_balance == +1)
                        x->avl_balance = 0, y->avl_balance = -1;
                    else if (w->avl_balance == 0)
                        x->avl_balance = y->avl_balance = 0;
                    else /* |w->avl_balance == -1| */
                        x->avl_balance = +1, y->avl_balance = 0;
                    w->avl_balance = 0;
                    pa[k - 1]->avl_link[da[k - 1]] = w;
                }
                else {
                    y->avl_link[1] = x->avl_link[0];
                    x->avl_link[0] = y;
                    pa[k - 1]->avl_link[da[k - 1]] = x;
                    if (x->avl_balance == 0) {
                        x->avl_balance = -1;
                        y->avl_balance = +1;
                        break;
                    }
                    else
                        x->avl_balance = y->avl_balance = 0;
                }
            }
        }
        else {
            y->avl_balance--;
            if (y->avl_balance == -1)
                break;
            else if (y->avl_balance == -2) {
                struct avl_node *x = y->avl_link[0];

                if (x->avl_balance == +1) {
                    struct avl_node *w;

                    assert(x->avl_balance == +1);
                    w = x->avl_link[1];
                    x->avl_link[1] = w->avl_link[0];
                    w->avl_link[0] = x;
                    y->avl_link[0] = w->avl_link[1];
                    w->avl_link[1] = y;
                    if (w->avl_balance == -1)
                        x->avl_balance = 0, y->avl_balance = +1;
                    else if (w->avl_balance == 0)
                        x->avl_balance = y->avl_balance = 0;
                    else /* |w->avl_balance == +1| */
                        x->avl_balance = -1, y->avl_balance = 0;
                    w->avl_balance = 0;
                    pa[k - 1]->avl_link[da[k - 1]] = w;
                }
                else {
                    y->avl_link[0] = x->avl_link[1];
                    x->avl_link[1] = y;
                    pa[k - 1]->avl_link[da[k - 1]] = x;
                    if (x->avl_balance == 0) {
                        x->avl_balance = +1;
                        y->avl_balance = -1;
                        break;
                    }
                    else
                        x->avl_balance = y->avl_balance = 0;
                }
            }
        }
    }

    tree->avl_count--;
    tree->avl_generation++;

    return (void *)item;
}

/* Refreshes the stack of parent pointers in |trav|
   and updates its generation number. */
static void trav_refresh(struct avl_traverser *trav)
{
    assert(trav != NULL);

    trav->avl_generation = trav->avl_table->avl_generation;

    if (trav->avl_node != NULL) {
        avl_comparison_func *cmp = trav->avl_table->avl_compare;
        void *param = trav->avl_table->avl_param;
        struct avl_node *node = trav->avl_node;
        struct avl_node *i;

        trav->avl_height = 0;
        for (i = trav->avl_table->avl_root; i != node;) {
            assert(trav->avl_height < AVL_MAX_HEIGHT);
            assert(i != NULL);

            trav->avl_stack[trav->avl_height++] = i;
            i = i->avl_link[cmp(node->avl_data, i->avl_data, param) > 0];
        }
    }
}

/* Initializes |trav| for use with |tree|
   and selects the null node. */
void avl_t_init(struct avl_traverser *trav, struct avl_table *tree)
{
    trav->avl_table = tree;
    trav->avl_node = NULL;
    trav->avl_height = 0;
    trav->avl_generation = tree->avl_generation;
}

/* Initializes |trav| for |tree|
   and selects and returns a pointer to its least-valued item.
   Returns |NULL| if |tree| contains no nodes. */
void *avl_t_first(struct avl_traverser *trav, struct avl_table *tree)
{
    struct avl_node *x;

    assert(tree != NULL && trav != NULL);

    trav->avl_table = tree;
    trav->avl_height = 0;
    trav->avl_generation = tree->avl_generation;

    x = tree->avl_root;
    if (x != NULL)
        while (x->avl_link[0] != NULL) {
            assert(trav->avl_height < AVL_MAX_HEIGHT);
            trav->avl_stack[trav->avl_height++] = x;
            x = x->avl_link[0];
        }
    trav->avl_node = x;

    return x != NULL ? x->avl_data : NULL;
}

/* Initializes |trav| for |tree|
   and selects and returns a pointer to its greatest-valued item.
   Returns |NULL| if |tree| contains no nodes. */
void *avl_t_last(struct avl_traverser *trav, struct avl_table *tree)
{
    struct avl_node *x;

    assert(tree != NULL && trav != NULL);

    trav->avl_table = tree;
    trav->avl_height = 0;
    trav->avl_generation = tree->avl_generation;

    x = tree->avl_root;
    if (x != NULL)
        while (x->avl_link[1] != NULL) {
            assert(trav->avl_height < AVL_MAX_HEIGHT);
            trav->avl_stack[trav->avl_height++] = x;
            x = x->avl_link[1];
        }
    trav->avl_node = x;

    return x != NULL ? x->avl_data : NULL;
}

/* Searches for |item| in |tree|.
   If found, initializes |trav| to the item found and returns the item
   as well.
   If there is no matching item, initializes |trav| to the null item
   and returns |NULL|. */
void *avl_t_find(struct avl_traverser *trav, struct avl_table *tree, void *item)
{
    struct avl_node *p;

    assert(trav != NULL && tree != NULL && item != NULL);
    trav->avl_table = tree;
    trav->avl_height = 0;
    trav->avl_generation = tree->avl_generation;
    p = tree->avl_root;
    while (p != NULL) {
        int cmp = tree->avl_compare(item, p->avl_data, tree->avl_param);

        if (cmp == 0) {
            trav->avl_node = p;

            return p->avl_data;
        }

        assert(trav->avl_height < AVL_MAX_HEIGHT);
        trav->avl_stack[trav->avl_height++] = p;
        p = p->avl_link[cmp > 0];
    }

    trav->avl_height = 0;
    trav->avl_node = NULL;

    return NULL;
}

/* Attempts to insert |item| into |tree|.
   If |item| is inserted successfully, it is returned and |trav| is
   initialized to its location.
   If a duplicate is found, it is returned and |trav| is initialized to
   its location.  No replacement of the item occurs.
   If a memory allocation failure occurs, |NULL| is returned and |trav|
   is initialized to the null item. */
void *avl_t_insert(struct avl_traverser *trav, struct avl_table *tree,
                   void *item)
{
    void **p;

    assert(trav != NULL && tree != NULL && item != NULL);

    p = avl_probe(tree, item);
    if (p != NULL) {
        trav->avl_table = tree;
        trav->avl_node =
            ((struct avl_node *)((char *)p -
                                 offsetof(struct avl_node, avl_data)));

        trav->avl_generation = tree->avl_generation - 1;

        return *p;
    }
    else {
        avl_t_init(trav, tree);

        return NULL;
    }
}

/* Initializes |trav| to have the same current node as |src|. */
void *avl_t_copy(struct avl_traverser *trav, const struct avl_traverser *src)
{
    assert(trav != NULL && src != NULL);

    if (trav != src) {
        trav->avl_table = src->avl_table;
        trav->avl_node = src->avl_node;
        trav->avl_generation = src->avl_generation;
        if (trav->avl_generation == trav->avl_table->avl_generation) {
            trav->avl_height = src->avl_height;
            memcpy(trav->avl_stack, (const void *)src->avl_stack,
                   sizeof *trav->avl_stack * trav->avl_height);
        }
    }

    return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL;
}

/* Returns the next data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *avl_t_next(struct avl_traverser *trav)
{
    struct avl_node *x;

    assert(trav != NULL);

    if (trav->avl_generation != trav->avl_table->avl_generation)
        trav_refresh(trav);

    x = trav->avl_node;
    if (x == NULL) {
        return avl_t_first(trav, trav->avl_table);
    }
    else if (x->avl_link[1] != NULL) {
        assert(trav->avl_height < AVL_MAX_HEIGHT);
        trav->avl_stack[trav->avl_height++] = x;
        x = x->avl_link[1];

        while (x->avl_link[0] != NULL) {
            assert(trav->avl_height < AVL_MAX_HEIGHT);
            trav->avl_stack[trav->avl_height++] = x;
            x = x->avl_link[0];
        }
    }
    else {
        struct avl_node *y;

        do {
            if (trav->avl_height == 0) {
                trav->avl_node = NULL;
                return NULL;
            }

            y = x;
            x = trav->avl_stack[--trav->avl_height];
        } while (y == x->avl_link[1]);
    }
    trav->avl_node = x;

    return x->avl_data;
}

/* Returns the previous data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *avl_t_prev(struct avl_traverser *trav)
{
    struct avl_node *x;

    assert(trav != NULL);

    if (trav->avl_generation != trav->avl_table->avl_generation)
        trav_refresh(trav);

    x = trav->avl_node;
    if (x == NULL) {
        return avl_t_last(trav, trav->avl_table);
    }
    else if (x->avl_link[0] != NULL) {
        assert(trav->avl_height < AVL_MAX_HEIGHT);
        trav->avl_stack[trav->avl_height++] = x;
        x = x->avl_link[0];

        while (x->avl_link[1] != NULL) {
            assert(trav->avl_height < AVL_MAX_HEIGHT);
            trav->avl_stack[trav->avl_height++] = x;
            x = x->avl_link[1];
        }
    }
    else {
        struct avl_node *y;

        do {
            if (trav->avl_height == 0) {
                trav->avl_node = NULL;
                return NULL;
            }

            y = x;
            x = trav->avl_stack[--trav->avl_height];
        } while (y == x->avl_link[0]);
    }
    trav->avl_node = x;

    return x->avl_data;
}

/* Returns |trav|'s current item. */
void *avl_t_cur(struct avl_traverser *trav)
{
    assert(trav != NULL);

    return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL;
}

/* Replaces the current item in |trav| by |new| and returns the item replaced.
   |trav| must not have the null item selected.
   The new item must not upset the ordering of the tree. */
void *avl_t_replace(struct avl_traverser *trav, void *new)
{
    void *old;

    assert(trav != NULL && trav->avl_node != NULL && new != NULL);
    old = trav->avl_node->avl_data;
    trav->avl_node->avl_data = new;

    return old;
}

/* Destroys |new| with |avl_destroy (new, destroy)|,
   first setting right links of nodes in |stack| within |new|
   to null pointers to avoid touching uninitialized data. */
static void copy_error_recovery(struct avl_node **stack, int height,
                                struct avl_table *new, avl_item_func *destroy)
{
    assert(stack != NULL && height >= 0 && new != NULL);

    for (; height > 2; height -= 2)
        stack[height - 1]->avl_link[1] = NULL;
    avl_destroy(new, destroy);
}

/* Copies |org| to a newly created tree, which is returned.
   If |copy != NULL|, each data item in |org| is first passed to |copy|,
   and the return values are inserted into the tree,
   with |NULL| return values taken as indications of failure.
   On failure, destroys the partially created new tree,
   applying |destroy|, if non-null, to each item in the new tree so far,
   and returns |NULL|.
   If |allocator != NULL|, it is used for allocation in the new tree.
   Otherwise, the same allocator used for |org| is used. */
struct avl_table *avl_copy(const struct avl_table *org, avl_copy_func *copy,
                           avl_item_func *destroy,
                           struct libavl_allocator *allocator)
{
    struct avl_node *stack[2 * (AVL_MAX_HEIGHT + 1)];
    int height = 0;

    struct avl_table *new;
    const struct avl_node *x;
    struct avl_node *y;

    assert(org != NULL);
    new = avl_create(org->avl_compare, org->avl_param,
                     allocator != NULL ? allocator : org->avl_alloc);
    if (new == NULL)
        return NULL;

    new->avl_count = org->avl_count;
    if (new->avl_count == 0)
        return new;

    x = (const struct avl_node *)&org->avl_root;
    y = (struct avl_node *)&new->avl_root;
    while (x != NULL) {
        while (x->avl_link[0] != NULL) {
            assert(height < 2 * (AVL_MAX_HEIGHT + 1));

            y->avl_link[0] = new->avl_alloc->libavl_malloc(
                new->avl_alloc, sizeof *y->avl_link[0]);
            if (y->avl_link[0] == NULL) {
                if (y != (struct avl_node *)&new->avl_root) {
                    y->avl_data = NULL;
                    y->avl_link[1] = NULL;
                }

                copy_error_recovery(stack, height, new, destroy);
                return NULL;
            }

            stack[height++] = (struct avl_node *)x;
            stack[height++] = y;
            x = x->avl_link[0];
            y = y->avl_link[0];
        }
        y->avl_link[0] = NULL;

        for (;;) {
            y->avl_balance = x->avl_balance;
            if (copy == NULL)
                y->avl_data = x->avl_data;
            else {
                y->avl_data = copy(x->avl_data, org->avl_param);
                if (y->avl_data == NULL) {
                    y->avl_link[1] = NULL;
                    copy_error_recovery(stack, height, new, destroy);
                    return NULL;
                }
            }

            if (x->avl_link[1] != NULL) {
                y->avl_link[1] = new->avl_alloc->libavl_malloc(
                    new->avl_alloc, sizeof *y->avl_link[1]);
                if (y->avl_link[1] == NULL) {
                    copy_error_recovery(stack, height, new, destroy);
                    return NULL;
                }

                x = x->avl_link[1];
                y = y->avl_link[1];
                break;
            }
            else
                y->avl_link[1] = NULL;

            if (height <= 2)
                return new;

            y = stack[--height];
            x = stack[--height];
        }
    }

    return new;
}

/* Frees storage allocated for |tree|.
   If |destroy != NULL|, applies it to each data item in inorder. */
void avl_destroy(struct avl_table *tree, avl_item_func *destroy)
{
    struct avl_node *p, *q;

    assert(tree != NULL);

    p = tree->avl_root;
    while (p != NULL) {
        if (p->avl_link[0] == NULL) {
            q = p->avl_link[1];
            if (destroy != NULL && p->avl_data != NULL)
                destroy(p->avl_data, tree->avl_param);
            tree->avl_alloc->libavl_free(tree->avl_alloc, p);
        }
        else {
            q = p->avl_link[0];
            p->avl_link[0] = q->avl_link[1];
            q->avl_link[1] = p;
        }
        p = q;
    }

    tree->avl_alloc->libavl_free(tree->avl_alloc, tree);
}

/* Allocates |size| bytes of space using |malloc()|.
   Returns a null pointer if allocation fails. */
void *avl_malloc(struct libavl_allocator *allocator, size_t size)
{
    assert(allocator != NULL && size > 0);

    return malloc(size);
}

/* Frees |block|. */
void avl_free(struct libavl_allocator *allocator, void *block)
{
    assert(allocator != NULL && block != NULL);
    free(block);
}

/* Default memory allocator that uses |malloc()| and |free()|. */
struct libavl_allocator avl_allocator_default = {avl_malloc, avl_free};

#undef NDEBUG
#include <assert.h>

/* Asserts that |avl_insert()| succeeds at inserting |item| into |table|. */
void(avl_assert_insert)(struct avl_table *table, void *item)
{
    void **p = avl_probe(table, item);

    assert(p != NULL && *p == item);
}

/* Asserts that |avl_delete()| really removes |item| from |table|,
   and returns the removed item. */
void *(avl_assert_delete)(struct avl_table *table, void *item)
{
    void *p = avl_delete(table, item);

    assert(p != NULL);

    return p;
}
