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LeOS-Genesis/external/badvpn/structure/BAVL.h

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/**
* @file BAVL.h
* @author Ambroz Bizjak <ambrop7@gmail.com>
*
* @section LICENSE
*
* 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.
* 3. Neither the name of the author nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "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.
*
* @section DESCRIPTION
*
* AVL tree.
*/
#ifndef BADVPN_STRUCTURE_BAVL_H
#define BADVPN_STRUCTURE_BAVL_H
//#define BAVL_DEBUG
#include <stdint.h>
#include <stddef.h>
#include <misc/debug.h>
/**
* Handler function called by tree algorithms to compare two values.
* For any two values, the comparator must always return the same result.
* The <= relation defined by the comparator must be a total order.
* Values are obtained like that:
* - The value of a node in the tree, or a node that is being inserted is:
* (uint8_t *)node + offset.
* - The value being looked up is the same as given to the lookup function.
*
* @param user as in {@link BAVL_Init}
* @param val1 first value
* @param val2 second value
* @return -1 if val1 < val2, 0 if val1 = val2, 1 if val1 > val2
*/
typedef int (*BAVL_comparator) (void *user, void *val1, void *val2);
struct BAVLNode;
/**
* AVL tree.
*/
typedef struct {
int offset;
BAVL_comparator comparator;
void *user;
struct BAVLNode *root;
} BAVL;
/**
* AVL tree node.
*/
typedef struct BAVLNode {
struct BAVLNode *parent;
struct BAVLNode *link[2];
int8_t balance;
#ifdef BAVL_COUNT
uint64_t count;
#endif
} BAVLNode;
/**
* Initializes the tree.
*
* @param o tree to initialize
* @param offset offset of a value from its node
* @param comparator value comparator handler function
* @param user value to pass to comparator
*/
static void BAVL_Init (BAVL *o, int offset, BAVL_comparator comparator, void *user);
/**
* Inserts a node into the tree.
* Must not be called from comparator.
*
* @param o the tree
* @param node uninitialized node to insert. Must have a valid value (its value
* may be passed to the comparator during insertion).
* @param ref if not NULL, will return (regardless if insertion succeeded):
* - the greatest node lesser than the inserted value, or (not in order)
* - the smallest node greater than the inserted value, or
* - NULL meaning there were no nodes in the tree.
* @param 1 on success, 0 if an element with an equal value is already in the tree
*/
static int BAVL_Insert (BAVL *o, BAVLNode *node, BAVLNode **ref);
/**
* Removes a node from the tree.
* Must not be called from comparator.
*
* @param o the tree
* @param node node to remove
*/
static void BAVL_Remove (BAVL *o, BAVLNode *node);
/**
* Checks if the tree is empty.
* Must not be called from comparator.
*
* @param o the tree
* @return 1 if empty, 0 if not
*/
static int BAVL_IsEmpty (const BAVL *o);
/**
* Looks for a value in the tree.
* Must not be called from comparator.
*
* @param o the tree
* @param val value to look for
* @return If a node is in the thee with an equal value, that node.
* Else if the tree is not empty:
* - the greatest node lesser than the given value, or (not in order)
* - the smallest node greater than the given value.
* NULL if the tree is empty.
*/
static BAVLNode * BAVL_Lookup (const BAVL *o, void *val);
/**
* Looks for a value in the tree.
* Must not be called from comparator.
*
* @param o the tree
* @param val value to look for
* @return If a node is in the thee with an equal value, that node.
* Else NULL.
*/
static BAVLNode * BAVL_LookupExact (const BAVL *o, void *val);
/**
* Returns the smallest node in the tree, or NULL if the tree is empty.
*
* @param o the tree
* @return smallest node or NULL
*/
static BAVLNode * BAVL_GetFirst (const BAVL *o);
/**
* Returns the greatest node in the tree, or NULL if the tree is empty.
*
* @param o the tree
* @return greatest node or NULL
*/
static BAVLNode * BAVL_GetLast (const BAVL *o);
/**
* Returns the node that follows the given node, or NULL if it's the
* last node.
*
* @param o the tree
* @param n node
* @return next node, or NULL
*/
static BAVLNode * BAVL_GetNext (const BAVL *o, BAVLNode *n);
/**
* Returns the node that precedes the given node, or NULL if it's the
* first node.
*
* @param o the tree
* @param n node
* @return previous node, or NULL
*/
static BAVLNode * BAVL_GetPrev (const BAVL *o, BAVLNode *n);
#ifdef BAVL_COUNT
static uint64_t BAVL_Count (const BAVL *o);
static uint64_t BAVL_IndexOf (const BAVL *o, BAVLNode *n);
static BAVLNode * BAVL_GetAt (const BAVL *o, uint64_t index);
#endif
static void BAVL_Verify (BAVL *o);
#define BAVL_MAX(_a, _b) ((_a) > (_b) ? (_a) : (_b))
#define BAVL_OPTNEG(_a, _neg) ((_neg) ? -(_a) : (_a))
static void * _BAVL_node_value (const BAVL *o, BAVLNode *n)
{
return ((uint8_t *)n + o->offset);
}
static int _BAVL_compare_values (const BAVL *o, void *v1, void *v2)
{
int res = o->comparator(o->user, v1, v2);
ASSERT(res == -1 || res == 0 || res == 1)
return res;
}
static int _BAVL_compare_nodes (BAVL *o, BAVLNode *n1, BAVLNode *n2)
{
return _BAVL_compare_values(o, _BAVL_node_value(o, n1), _BAVL_node_value(o, n2));
}
#ifdef BAVL_AUTO_VERIFY
#define BAVL_ASSERT(_h) BAVL_Verify((_h));
#else
#define BAVL_ASSERT(_h)
#endif
static int _BAVL_assert_recurser (BAVL *o, BAVLNode *n)
{
ASSERT_FORCE(n->balance >= -1)
ASSERT_FORCE(n->balance <= 1)
int height_left = 0;
int height_right = 0;
#ifdef BAVL_COUNT
uint64_t count_left = 0;
uint64_t count_right = 0;
#endif
// check left subtree
if (n->link[0]) {
// check parent link
ASSERT_FORCE(n->link[0]->parent == n)
// check binary search tree
ASSERT_FORCE(_BAVL_compare_nodes(o, n->link[0], n) == -1)
// recursively calculate height
height_left = _BAVL_assert_recurser(o, n->link[0]);
#ifdef BAVL_COUNT
count_left = n->link[0]->count;
#endif
}
// check right subtree
if (n->link[1]) {
// check parent link
ASSERT_FORCE(n->link[1]->parent == n)
// check binary search tree
ASSERT_FORCE(_BAVL_compare_nodes(o, n->link[1], n) == 1)
// recursively calculate height
height_right = _BAVL_assert_recurser(o, n->link[1]);
#ifdef BAVL_COUNT
count_right = n->link[1]->count;
#endif
}
// check balance factor
ASSERT_FORCE(n->balance == height_right - height_left)
#ifdef BAVL_COUNT
// check count
ASSERT_FORCE(n->count == 1 + count_left + count_right)
#endif
return (BAVL_MAX(height_left, height_right) + 1);
}
#ifdef BAVL_COUNT
static void _BAVL_update_count_from_children (BAVLNode *n)
{
n->count = 1 + (n->link[0] ? n->link[0]->count : 0) + (n->link[1] ? n->link[1]->count : 0);
}
#endif
static void _BAVL_rotate (BAVL *tree, BAVLNode *r, uint8_t dir)
{
BAVLNode *nr = r->link[!dir];
r->link[!dir] = nr->link[dir];
if (r->link[!dir]) {
r->link[!dir]->parent = r;
}
nr->link[dir] = r;
nr->parent = r->parent;
if (nr->parent) {
nr->parent->link[r == r->parent->link[1]] = nr;
} else {
tree->root = nr;
}
r->parent = nr;
#ifdef BAVL_COUNT
// update counts
_BAVL_update_count_from_children(r); // first r!
_BAVL_update_count_from_children(nr);
#endif
}
static BAVLNode * _BAVL_subtree_max (BAVLNode *n)
{
ASSERT(n)
while (n->link[1]) {
n = n->link[1];
}
return n;
}
static void _BAVL_replace_subtree (BAVL *tree, BAVLNode *dest, BAVLNode *n)
{
ASSERT(dest)
if (dest->parent) {
dest->parent->link[dest == dest->parent->link[1]] = n;
} else {
tree->root = n;
}
if (n) {
n->parent = dest->parent;
}
#ifdef BAVL_COUNT
// update counts
for (BAVLNode *c = dest->parent; c; c = c->parent) {
ASSERT(c->count >= dest->count)
c->count -= dest->count;
if (n) {
ASSERT(n->count <= UINT64_MAX - c->count)
c->count += n->count;
}
}
#endif
}
static void _BAVL_swap_nodes (BAVL *tree, BAVLNode *n1, BAVLNode *n2)
{
if (n2->parent == n1 || n1->parent == n2) {
// when the nodes are directly connected we need special handling
// make sure n1 is above n2
if (n1->parent == n2) {
BAVLNode *t = n1;
n1 = n2;
n2 = t;
}
uint8_t side = (n2 == n1->link[1]);
BAVLNode *c = n1->link[!side];
if (n1->link[0] = n2->link[0]) {
n1->link[0]->parent = n1;
}
if (n1->link[1] = n2->link[1]) {
n1->link[1]->parent = n1;
}
if (n2->parent = n1->parent) {
n2->parent->link[n1 == n1->parent->link[1]] = n2;
} else {
tree->root = n2;
}
n2->link[side] = n1;
n1->parent = n2;
if (n2->link[!side] = c) {
c->parent = n2;
}
} else {
BAVLNode *temp;
// swap parents
temp = n1->parent;
if (n1->parent = n2->parent) {
n1->parent->link[n2 == n2->parent->link[1]] = n1;
} else {
tree->root = n1;
}
if (n2->parent = temp) {
n2->parent->link[n1 == temp->link[1]] = n2;
} else {
tree->root = n2;
}
// swap left children
temp = n1->link[0];
if (n1->link[0] = n2->link[0]) {
n1->link[0]->parent = n1;
}
if (n2->link[0] = temp) {
n2->link[0]->parent = n2;
}
// swap right children
temp = n1->link[1];
if (n1->link[1] = n2->link[1]) {
n1->link[1]->parent = n1;
}
if (n2->link[1] = temp) {
n2->link[1]->parent = n2;
}
}
// swap balance factors
int8_t b = n1->balance;
n1->balance = n2->balance;
n2->balance = b;
#ifdef BAVL_COUNT
// swap counts
uint64_t c = n1->count;
n1->count = n2->count;
n2->count = c;
#endif
}
static void _BAVL_rebalance (BAVL *o, BAVLNode *node, uint8_t side, int8_t deltac)
{
ASSERT(side == 0 || side == 1)
ASSERT(deltac >= -1 && deltac <= 1)
ASSERT(node->balance >= -1 && node->balance <= 1)
// if no subtree changed its height, no more rebalancing is needed
if (deltac == 0) {
return;
}
// calculate how much our height changed
int8_t delta = BAVL_MAX(deltac, BAVL_OPTNEG(node->balance, side)) - BAVL_MAX(0, BAVL_OPTNEG(node->balance, side));
ASSERT(delta >= -1 && delta <= 1)
// update our balance factor
node->balance -= BAVL_OPTNEG(deltac, side);
BAVLNode *child;
BAVLNode *gchild;
// perform transformations if the balance factor is wrong
if (node->balance == 2 || node->balance == -2) {
uint8_t bside;
int8_t bsidef;
if (node->balance == 2) {
bside = 1;
bsidef = 1;
} else {
bside = 0;
bsidef = -1;
}
ASSERT(node->link[bside])
child = node->link[bside];
switch (child->balance * bsidef) {
case 1:
_BAVL_rotate(o, node, !bside);
node->balance = 0;
child->balance = 0;
node = child;
delta -= 1;
break;
case 0:
_BAVL_rotate(o, node, !bside);
node->balance = 1 * bsidef;
child->balance = -1 * bsidef;
node = child;
break;
case -1:
ASSERT(child->link[!bside])
gchild = child->link[!bside];
_BAVL_rotate(o, child, bside);
_BAVL_rotate(o, node, !bside);
node->balance = -BAVL_MAX(0, gchild->balance * bsidef) * bsidef;
child->balance = BAVL_MAX(0, -gchild->balance * bsidef) * bsidef;
gchild->balance = 0;
node = gchild;
delta -= 1;
break;
default:
ASSERT(0);
}
}
ASSERT(delta >= -1 && delta <= 1)
// Transformations above preserve this. Proof:
// - if a child subtree gained 1 height and rebalancing was needed,
// it was the heavier subtree. Then delta was was originally 1, because
// the heaviest subtree gained one height. If the transformation reduces
// delta by one, it becomes 0.
// - if a child subtree lost 1 height and rebalancing was needed, it
// was the lighter subtree. Then delta was originally 0, because
// the height of the heaviest subtree was unchanged. If the transformation
// reduces delta by one, it becomes -1.
if (node->parent) {
_BAVL_rebalance(o, node->parent, node == node->parent->link[1], delta);
}
}
void BAVL_Init (BAVL *o, int offset, BAVL_comparator comparator, void *user)
{
o->offset = offset;
o->comparator = comparator;
o->user = user;
o->root = NULL;
BAVL_ASSERT(o)
}
int BAVL_Insert (BAVL *o, BAVLNode *node, BAVLNode **ref)
{
// insert to root?
if (!o->root) {
o->root = node;
node->parent = NULL;
node->link[0] = NULL;
node->link[1] = NULL;
node->balance = 0;
#ifdef BAVL_COUNT
node->count = 1;
#endif
BAVL_ASSERT(o)
if (ref) {
*ref = NULL;
}
return 1;
}
// find node to insert to
BAVLNode *c = o->root;
int side;
while (1) {
// compare
int comp = _BAVL_compare_nodes(o, node, c);
// have we found a node that compares equal?
if (comp == 0) {
if (ref) {
*ref = c;
}
return 0;
}
side = (comp == 1);
// have we reached a leaf?
if (!c->link[side]) {
break;
}
c = c->link[side];
}
// insert
c->link[side] = node;
node->parent = c;
node->link[0] = NULL;
node->link[1] = NULL;
node->balance = 0;
#ifdef BAVL_COUNT
node->count = 1;
#endif
#ifdef BAVL_COUNT
// update counts
for (BAVLNode *p = c; p; p = p->parent) {
ASSERT(p->count < UINT64_MAX)
p->count++;
}
#endif
// rebalance
_BAVL_rebalance(o, c, side, 1);
BAVL_ASSERT(o)
if (ref) {
*ref = c;
}
return 1;
}
void BAVL_Remove (BAVL *o, BAVLNode *node)
{
// if we have both subtrees, swap the node and the largest node
// in the left subtree, so we have at most one subtree
if (node->link[0] && node->link[1]) {
// find the largest node in the left subtree
BAVLNode *max = _BAVL_subtree_max(node->link[0]);
// swap the nodes
_BAVL_swap_nodes(o, node, max);
}
// have at most one child now
ASSERT(!(node->link[0] && node->link[1]))
BAVLNode *parent = node->parent;
BAVLNode *child = (node->link[0] ? node->link[0] : node->link[1]);
if (parent) {
// remember on which side node is
int side = (node == parent->link[1]);
// replace node with child
_BAVL_replace_subtree(o, node, child);
// rebalance
_BAVL_rebalance(o, parent, side, -1);
} else {
// replace node with child
_BAVL_replace_subtree(o, node, child);
}
BAVL_ASSERT(o)
}
int BAVL_IsEmpty (const BAVL *o)
{
return (!o->root);
}
BAVLNode * BAVL_Lookup (const BAVL *o, void *val)
{
if (!o->root) {
return NULL;
}
BAVLNode *c = o->root;
while (1) {
// compare
int comp = _BAVL_compare_values(o, val, _BAVL_node_value(o, c));
// have we found a node that compares equal?
if (comp == 0) {
return c;
}
int side = (comp == 1);
// have we reached a leaf?
if (!c->link[side]) {
return c;
}
c = c->link[side];
}
}
BAVLNode * BAVL_LookupExact (const BAVL *o, void *val)
{
if (!o->root) {
return NULL;
}
BAVLNode *c = o->root;
while (1) {
// compare
int comp = _BAVL_compare_values(o, val, _BAVL_node_value(o, c));
// have we found a node that compares equal?
if (comp == 0) {
return c;
}
int side = (comp == 1);
// have we reached a leaf?
if (!c->link[side]) {
return NULL;
}
c = c->link[side];
}
}
BAVLNode * BAVL_GetFirst (const BAVL *o)
{
if (!o->root) {
return NULL;
}
BAVLNode *n = o->root;
while (n->link[0]) {
n = n->link[0];
}
return n;
}
BAVLNode * BAVL_GetLast (const BAVL *o)
{
if (!o->root) {
return NULL;
}
BAVLNode *n = o->root;
while (n->link[1]) {
n = n->link[1];
}
return n;
}
BAVLNode * BAVL_GetNext (const BAVL *o, BAVLNode *n)
{
if (n->link[1]) {
n = n->link[1];
while (n->link[0]) {
n = n->link[0];
}
} else {
while (n->parent && n == n->parent->link[1]) {
n = n->parent;
}
n = n->parent;
}
return n;
}
BAVLNode * BAVL_GetPrev (const BAVL *o, BAVLNode *n)
{
if (n->link[0]) {
n = n->link[0];
while (n->link[1]) {
n = n->link[1];
}
} else {
while (n->parent && n == n->parent->link[0]) {
n = n->parent;
}
n = n->parent;
}
return n;
}
#ifdef BAVL_COUNT
static uint64_t BAVL_Count (const BAVL *o)
{
return (o->root ? o->root->count : 0);
}
static uint64_t BAVL_IndexOf (const BAVL *o, BAVLNode *n)
{
uint64_t index = (n->link[0] ? n->link[0]->count : 0);
for (BAVLNode *c = n; c->parent; c = c->parent) {
if (c == c->parent->link[1]) {
ASSERT(c->parent->count > c->count)
ASSERT(c->parent->count - c->count <= UINT64_MAX - index)
index += c->parent->count - c->count;
}
}
return index;
}
static BAVLNode * BAVL_GetAt (const BAVL *o, uint64_t index)
{
if (index >= BAVL_Count(o)) {
return NULL;
}
BAVLNode *c = o->root;
while (1) {
ASSERT(c)
ASSERT(index < c->count)
uint64_t left_count = (c->link[0] ? c->link[0]->count : 0);
if (index == left_count) {
return c;
}
if (index < left_count) {
c = c->link[0];
} else {
c = c->link[1];
index -= left_count + 1;
}
}
}
#endif
static void BAVL_Verify (BAVL *o)
{
if (o->root) {
ASSERT(!o->root->parent)
_BAVL_assert_recurser(o, o->root);
}
}
#endif
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