/* avl.c
*
* Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software
* Foundation, Inc.
* Copyright (C) 2014 Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program 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
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*
* This code is originally from GNU libavl. The memory management
* was slightly modified for use with preallocating GSL sparse matrices
*
* The allocator->libavl_malloc function is called only for creating
* a new avl_node (tree node). This allows GSL to preallocate some number
* of avl_node structs and then return pointers to them while the tree
* is being assembled, avoiding multiple malloc calls
*/
#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>
#include <string.h>
/* Function types. */
typedef int avl_comparison_func (const void *avl_a, const void *avl_b,
void *avl_param);
typedef void avl_item_func (void *avl_item, void *avl_param);
typedef void *avl_copy_func (void *avl_item, void *avl_param);
/* Memory allocator. */
struct libavl_allocator
{
void *(*libavl_malloc) (size_t libavl_size, void *param);
void (*libavl_free) (void *libavl_block, void *param);
};
/* Default memory allocator. */
static struct libavl_allocator avl_allocator_default;
static void *avl_malloc (size_t, void *param);
static void avl_free (void *, void *param);
/* Maximum AVL tree height. */
#ifndef AVL_MAX_HEIGHT
#define AVL_MAX_HEIGHT 92
#endif
/* An AVL tree node. */
struct avl_node
{
struct avl_node *avl_link[2]; /* Subtrees. */
void *avl_data; /* Pointer to data. */
signed char avl_balance; /* Balance factor. */
};
/* Tree data structure. */
struct avl_table
{
struct avl_node *avl_root; /* Tree's root. */
avl_comparison_func *avl_compare; /* Comparison function. */
void *avl_param; /* Extra argument to |avl_compare|. */
struct libavl_allocator *avl_alloc; /* Memory allocator. */
size_t avl_count; /* Number of items in tree. */
unsigned long avl_generation; /* Generation number. */
};
/* Table functions. */
static struct avl_table *avl_create (avl_comparison_func *, void *,
struct libavl_allocator *);
static struct avl_table *avl_copy (const struct avl_table *, avl_copy_func *,
avl_item_func *, struct libavl_allocator *);
static void avl_empty (struct avl_table *, avl_item_func *);
static void avl_destroy (struct avl_table *, avl_item_func *);
static void **avl_probe (struct avl_table *, void *);
static void *avl_insert (struct avl_table *, void *);
static void *avl_replace (struct avl_table *, void *);
static void *avl_delete (struct avl_table *, const void *);
static void *avl_find (const struct avl_table *, const void *);
/* Creates and returns a new table
with comparison function |compare| using parameter |param|
and memory allocator |allocator|.
Returns |NULL| if memory allocation failed. */
static struct avl_table *
avl_create (avl_comparison_func *compare, void *param,
struct libavl_allocator *allocator)
{
struct avl_table *tree;
if (allocator == NULL)
allocator = &avl_allocator_default;
/*tree = allocator->libavl_malloc (allocator, sizeof *tree);*/
tree = malloc(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|. */
static void *
avl_find (const struct avl_table *tree, const void *item)
{
const struct avl_node *p;
for (p = tree->avl_root; p != NULL; )
{
int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);
if (cmp < 0)
p = p->avl_link[0];
else if (cmp > 0)
p = p->avl_link[1];
else /* |cmp == 0| */
return p->avl_data;
}
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. */
static 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. */
z = (struct avl_node *) &tree->avl_root;
y = tree->avl_root;
dir = 0;
for (q = z, p = y; p != NULL; q = p, p = p->avl_link[dir])
{
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;
}
n = q->avl_link[dir] =
tree->avl_alloc->libavl_malloc (sizeof *n, tree->avl_param);
if (n == NULL)
return NULL;
tree->avl_count++;
n->avl_data = item;
n->avl_link[0] = n->avl_link[1] = NULL;
n->avl_balance = 0;
if (y == NULL)
return &n->avl_data;
for (p = y, k = 0; p != n; p = p->avl_link[da[k]], k++)
if (da[k] == 0)
p->avl_balance--;
else
p->avl_balance++;
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
{
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
{
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;
tree->avl_generation++;
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. */
static 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. */
static 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. */
static 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 cmp; /* Result of comparison between |item| and |p|. */
k = 0;
p = (struct avl_node *) &tree->avl_root;
for (cmp = -1; cmp != 0;
cmp = tree->avl_compare (item, p->avl_data, tree->avl_param))
{
int 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++;
for (;;)
{
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 (p, tree->avl_param);
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;
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;
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;
}
/* 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)
{
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. */
static 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;
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;
for (;;)
{
while (x->avl_link[0] != NULL)
{
y->avl_link[0] =
new->avl_alloc->libavl_malloc (sizeof *y->avl_link[0],
new->avl_param);
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 (sizeof *y->avl_link[1],
new->avl_param);
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];
}
}
}
/* empty tree (delete all nodes) but do not free the tree itself */
static void
avl_empty (struct avl_table *tree, avl_item_func *destroy)
{
struct avl_node *p, *q;
for (p = tree->avl_root; p != NULL; p = q)
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 (p, tree->avl_param);
}
else
{
q = p->avl_link[0];
p->avl_link[0] = q->avl_link[1];
q->avl_link[1] = p;
}
tree->avl_root = NULL;
tree->avl_count = 0;
tree->avl_generation = 0;
}
/* Frees storage allocated for |tree|.
If |destroy != NULL|, applies it to each data item in inorder. */
static void
avl_destroy (struct avl_table *tree, avl_item_func *destroy)
{
avl_empty(tree, destroy);
free(tree);
}
/* Allocates |size| bytes of space using |malloc()|.
Returns a null pointer if allocation fails. */
static void *
avl_malloc (size_t size, void *param)
{
(void)param; /* avoid unused parameter warning */
return malloc (size);
}
/* Frees |block|. */
static void
avl_free (void *block, void *param)
{
(void)param; /* avoid unused parameter warning */
free (block);
}
/* Default memory allocator that uses |malloc()| and |free()|. */
static struct libavl_allocator avl_allocator_default =
{
avl_malloc,
avl_free
};