/*
* Copyright (C) 2006 Jakub Jermar
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - 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.
* - The name of the author may not be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``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.
*/
/*
* This B-tree has the following properties:
* - it is a ballanced 2-3-4 tree (i.e. BTREE_M = 4)
* - values (i.e. pointers to values) are stored only in leaves
* - leaves are linked in a list
* - technically, it is a B+-tree (because of the previous properties)
*
* Be carefull when using these trees. They need to allocate
* and deallocate memory for their index nodes and as such
* can sleep.
*/
#include <adt/btree.h>
#include <adt/list.h>
#include <mm/slab.h>
#include <debug.h>
#include <panic.h>
#include <typedefs.h>
#include <print.h>
static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node);
static void node_initialize(btree_node_t *node);
static void node_insert_key_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static void node_insert_key_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median);
static void node_remove_key_left(btree_node_t *node, __native key);
static void node_remove_key_right(btree_node_t *node, __native key);
static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right);
static bool try_insert_by_left_rotation(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static bool try_insert_by_right_rotation(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
#define ROOT_NODE(n) (!(n)->parent)
#define INDEX_NODE(n) ((n)->subtree[0] != NULL)
#define LEAF_NODE(n) ((n)->subtree[0] == NULL)
#define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2)
#define MEDIAN_HIGH_INDEX(n) ((n)->keys/2)
#define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]);
#define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]);
/** Create empty B-tree.
*
* @param t B-tree.
*/
void btree_create(btree_t *t)
{
list_initialize(&t->leaf_head);
t
->root
= (btree_node_t
*) malloc(sizeof(btree_node_t
), 0); node_initialize(t->root);
list_append(&t->root->leaf_link, &t->leaf_head);
}
/** Destroy empty B-tree. */
void btree_destroy(btree_t *t)
{
ASSERT(!t->root->keys);
}
/** Insert key-value pair into B-tree.
*
* @param t B-tree.
* @param key Key to be inserted.
* @param value Value to be inserted.
* @param leaf_node Leaf node where the insertion should begin.
*/
void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node)
{
btree_node_t *lnode;
ASSERT(value);
lnode = leaf_node;
if (!lnode) {
if (btree_search(t, key, &lnode)) {
panic("B-tree %P already contains key %d\n", t, key);
}
}
_btree_insert(t, key, value, NULL, lnode);
}
/** Recursively insert into B-tree.
*
* @param t B-tree.
* @param key Key to be inserted.
* @param value Value to be inserted.
* @param rsubtree Right subtree of the inserted key.
* @param node Start inserting into this node.
*/
void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node)
{
if (node->keys < BTREE_MAX_KEYS) {
/*
* Node conatins enough space, the key can be stored immediately.
*/
node_insert_key_right(node, key, value, rsubtree);
} else if (try_insert_by_left_rotation(node, key, value, rsubtree)) {
/*
* The key-value-rsubtree triplet has been inserted because
* some keys could have been moved to the left sibling.
*/
} else if (try_insert_by_right_rotation(node, key, value, rsubtree)) {
/*
* The key-value-rsubtree triplet has been inserted because
* some keys could have been moved to the right sibling.
*/
} else {
btree_node_t *rnode;
__native median;
/*
* Node is full and both siblings (if both exist) are full too.
* Split the node and insert the smallest key from the node containing
* bigger keys (i.e. the new node) into its parent.
*/
rnode = node_split(node, key, value, rsubtree, &median);
if (LEAF_NODE(node)) {
list_append(&rnode->leaf_link, &node->leaf_link);
}
if (ROOT_NODE(node)) {
/*
* We split the root node. Create new root.
*/
t
->root
= (btree_node_t
*) malloc(sizeof(btree_node_t
), 0); node->parent = t->root;
rnode->parent = t->root;
node_initialize(t->root);
/*
* Left-hand side subtree will be the old root (i.e. node).
* Right-hand side subtree will be rnode.
*/
t->root->subtree[0] = node;
t->root->depth = node->depth + 1;
}
_btree_insert(t, median, NULL, rnode, node->parent);
}
}
/* TODO */
void btree_remove(btree_t *t, __native key)
{
}
/** Search key in a B-tree.
*
* @param t B-tree.
* @param key Key to be searched.
* @param leaf_node Address where to put pointer to visited leaf node.
*
* @return Pointer to value or NULL if there is no such key.
*/
void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node)
{
btree_node_t *cur, *next;
/*
* Iteratively descend to the leaf that can contain the searched key.
*/
for (cur = t->root; cur; cur = next) {
/* Last iteration will set this with proper leaf node address. */
*leaf_node = cur;
/*
* The key can be in the leftmost subtree.
* Test it separately.
*/
if (key < cur->key[0]) {
next = cur->subtree[0];
continue;
} else {
void *val;
int i;
/*
* Now if the key is smaller than cur->key[i]
* it can only mean that the value is in cur->subtree[i]
* or it is not in the tree at all.
*/
for (i = 1; i < cur->keys; i++) {
if (key < cur->key[i]) {
next = cur->subtree[i];
val = cur->value[i - 1];
if (LEAF_NODE(cur))
return key == cur->key[i - 1] ? val : NULL;
goto descend;
}
}
/*
* Last possibility is that the key is in the rightmost subtree.
*/
next = cur->subtree[i];
val = cur->value[i - 1];
if (LEAF_NODE(cur))
return key == cur->key[i - 1] ? val : NULL;
}
descend:
;
}
/*
* The key was not found in the *leaf_node and is smaller than any of its keys.
*/
return NULL;
}
/** Get pointer to value with the smallest key within the node.
*
* Can be only used on leaf-level nodes.
*
* @param node B-tree node.
*
* @return Pointer to value assiciated with the smallest key.
*/
void *btree_node_min(btree_node_t *node)
{
ASSERT(LEAF_NODE(node));
ASSERT(node->keys);
return node->value[0];
}
/** Get pointer to value with the biggest key within the node.
*
* Can be only used on leaf-level nodes.
*
* @param node B-tree node.
*
* @return Pointer to value assiciated with the biggest key.
*/
void *btree_node_max(btree_node_t *node)
{
ASSERT(LEAF_NODE(node));
ASSERT(node->keys);
return node->value[node->keys - 1];
}
/** Initialize B-tree node.
*
* @param node B-tree node.
*/
void node_initialize(btree_node_t *node)
{
int i;
node->keys = 0;
/* Clean also space for the extra key. */
for (i = 0; i < BTREE_MAX_KEYS + 1; i++) {
node->key[i] = 0;
node->value[i] = NULL;
node->subtree[i] = NULL;
}
node->subtree[i] = NULL;
node->parent = NULL;
link_initialize(&node->leaf_link);
link_initialize(&node->bfs_link);
node->depth = 0;
}
/** Insert key-value-lsubtree triplet into B-tree node.
*
* It is actually possible to have more keys than BTREE_MAX_KEYS.
* This feature is used during insert by right rotation.
*
* @param node B-tree node into wich the new key is to be inserted.
* @param key The key to be inserted.
* @param value Pointer to value to be inserted.
* @param lsubtree Pointer to the left subtree.
*/
void node_insert_key_left(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree)
{
int i;
for (i = 0; i < node->keys; i++) {
if (key < node->key[i]) {
int j;
for (j = node->keys; j > i; j--) {
node->key[j] = node->key[j - 1];
node->value[j] = node->value[j - 1];
node->subtree[j + 1] = node->subtree[j];
}
node->subtree[j + 1] = node->subtree[j];
break;
}
}
node->key[i] = key;
node->value[i] = value;
node->subtree[i] = lsubtree;
node->keys++;
}
/** Insert key-value-rsubtree triplet into B-tree node.
*
* It is actually possible to have more keys than BTREE_MAX_KEYS.
* This feature is used during splitting the node when the
* number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation
* also makes use of this feature.
*
* @param node B-tree node into wich the new key is to be inserted.
* @param key The key to be inserted.
* @param value Pointer to value to be inserted.
* @param rsubtree Pointer to the right subtree.
*/
void node_insert_key_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree)
{
int i;
for (i = 0; i < node->keys; i++) {
if (key < node->key[i]) {
int j;
for (j = node->keys; j > i; j--) {
node->key[j] = node->key[j - 1];
node->value[j] = node->value[j - 1];
node->subtree[j + 1] = node->subtree[j];
}
break;
}
}
node->key[i] = key;
node->value[i] = value;
node->subtree[i + 1] = rsubtree;
node->keys++;
}
/** Split full B-tree node and insert new key-value-right-subtree triplet.
*
* This function will split a node and return pointer to a newly created
* node containing keys greater than or equal to the greater of medians
* (or median) of the old keys and the newly added key. It will also write
* the median key to a memory address supplied by the caller.
*
* If the node being split is an index node, the median will not be
* included in the new node. If the node is a leaf node,
* the median will be copied there.
*
* @param node B-tree node wich is going to be split.
* @param key The key to be inserted.
* @param value Pointer to the value to be inserted.
* @param rsubtree Pointer to the right subtree of the key being added.
* @param median Address in memory, where the median key will be stored.
*
* @return Newly created right sibling of node.
*/
btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median)
{
btree_node_t *rnode;
int i, j;
ASSERT(median);
ASSERT(node->keys == BTREE_MAX_KEYS);
/*
* Use the extra space to store the extra node.
*/
node_insert_key_right(node, key, value, rsubtree);
/*
* Compute median of keys.
*/
*median = MEDIAN_HIGH(node);
/*
* Allocate and initialize new right sibling.
*/
rnode
= (btree_node_t
*) malloc(sizeof(btree_node_t
), 0); node_initialize(rnode);
rnode->parent = node->parent;
rnode->depth = node->depth;
/*
* Copy big keys, values and subtree pointers to the new right sibling.
* If this is an index node, do not copy the median.
*/
i = (int) INDEX_NODE(node);
for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) {
rnode->key[j] = node->key[i];
rnode->value[j] = node->value[i];
rnode->subtree[j] = node->subtree[i];
/*
* Fix parent links in subtrees.
*/
if (rnode->subtree[j])
rnode->subtree[j]->parent = rnode;
}
rnode->subtree[j] = node->subtree[i];
if (rnode->subtree[j])
rnode->subtree[j]->parent = rnode;
rnode->keys = j; /* Set number of keys of the new node. */
node->keys /= 2; /* Shrink the old node. */
return rnode;
}
/** Remove key and its left subtree pointer from B-tree node.
*
* Remove the key and eliminate gaps in node->key array.
* Note that the value pointer and the left subtree pointer
* is removed from the node as well.
*
* @param node B-tree node.
* @param key Key to be removed.
*/
void node_remove_key_left(btree_node_t *node, __native key)
{
int i, j;
for (i = 0; i < node->keys; i++) {
if (key == node->key[i]) {
for (j = i + 1; j < node->keys; j++) {
node->key[j - 1] = node->key[j];
node->value[j - 1] = node->value[j];
node->subtree[j - 1] = node->subtree[j];
}
node->subtree[j - 1] = node->subtree[j];
node->keys--;
return;
}
}
panic("node %P does not contain key %d\n", node, key);
}
/** Remove key and its right subtree pointer from B-tree node.
*
* Remove the key and eliminate gaps in node->key array.
* Note that the value pointer and the right subtree pointer
* is removed from the node as well.
*
* @param node B-tree node.
* @param key Key to be removed.
*/
void node_remove_key_right(btree_node_t *node, __native key)
{
int i, j;
for (i = 0; i < node->keys; i++) {
if (key == node->key[i]) {
for (j = i + 1; j < node->keys; j++) {
node->key[j - 1] = node->key[j];
node->value[j - 1] = node->value[j];
node->subtree[j] = node->subtree[j + 1];
}
node->keys--;
return;
}
}
panic("node %P does not contain key %d\n", node, key);
}
/** Find key by its left or right subtree.
*
* @param node B-tree node.
* @param subtree Left or right subtree of a key found in node.
* @param right If true, subtree is a right subtree. If false, subtree is a left subtree.
*
* @return Index of the key associated with the subtree.
*/
index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right)
{
int i;
for (i = 0; i < node->keys + 1; i++) {
if (subtree == node->subtree[i])
return i - (int) (right != false);
}
panic("node %P does not contain subtree %P\n", node, subtree);
}
/** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done.
*
* Left sibling of the node (if it exists) is checked for free space.
* If there is free space, the key is inserted and the smallest key of
* the node is moved there. The index node which is the parent of both
* nodes is fixed.
*
* @param node B-tree node.
* @param inskey Key to be inserted.
* @param insvalue Value to be inserted.
* @param rsubtree Right subtree of inskey.
*
* @return True if the rotation was performed, false otherwise.
*/
bool try_insert_by_left_rotation(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree)
{
index_t idx;
btree_node_t *lnode;
/*
* If this is root node, the rotation can not be done.
*/
if (ROOT_NODE(node))
return false;
idx = find_key_by_subtree(node->parent, node, true);
if ((int) idx == -1) {
/*
* If this node is the leftmost subtree of its parent,
* the rotation can not be done.
*/
return false;
}
lnode = node->parent->subtree[idx];
if (lnode->keys < BTREE_MAX_KEYS) {
__native key;
/*
* The rotaion can be done. The left sibling has free space.
*/
node_insert_key_right(node, inskey, insvalue, rsubtree);
key = node->key[0];
if (LEAF_NODE(node)) {
void *value;
value = node->value[0];
node_remove_key_left(node, key);
node_insert_key_right(lnode, key, value, NULL);
node->parent->key[idx] = node->key[0];
} else {
btree_node_t *lsubtree;
lsubtree = node->subtree[0];
node_remove_key_left(node, key);
node_insert_key_right(lnode, node->parent->key[idx], NULL, lsubtree);
node->parent->key[idx] = key;
/* Fix parent link of the reconnected left subtree. */
lsubtree->parent = lnode;
}
return true;
}
return false;
}
/** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done.
*
* Right sibling of the node (if it exists) is checked for free space.
* If there is free space, the key is inserted and the biggest key of
* the node is moved there. The index node which is the parent of both
* nodes is fixed.
*
* @param node B-tree node.
* @param inskey Key to be inserted.
* @param insvalue Value to be inserted.
* @param rsubtree Right subtree of inskey.
*
* @return True if the rotation was performed, false otherwise.
*/
bool try_insert_by_right_rotation(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree)
{
index_t idx;
btree_node_t *rnode;
/*
* If this is root node, the rotation can not be done.
*/
if (ROOT_NODE(node))
return false;
idx = find_key_by_subtree(node->parent, node, false);
if (idx == node->parent->keys) {
/*
* If this node is the rightmost subtree of its parent,
* the rotation can not be done.
*/
return false;
}
rnode = node->parent->subtree[idx + 1];
if (rnode->keys < BTREE_MAX_KEYS) {
__native key;
/*
* The rotaion can be done. The right sibling has free space.
*/
node_insert_key_right(node, inskey, insvalue, rsubtree);
key = node->key[node->keys - 1];
if (LEAF_NODE(node)) {
void *value;
value = node->value[node->keys - 1];
node_remove_key_right(node, key);
node_insert_key_left(rnode, key, value, NULL);
node->parent->key[idx] = key;
} else {
btree_node_t *rsubt;
rsubt = node->subtree[node->keys];
node_remove_key_right(node, key);
node_insert_key_left(rnode, node->parent->key[idx], NULL, rsubt);
node->parent->key[idx] = key;
/* Fix parent link of the reconnected right subtree. */
rsubt->parent = rnode;
}
return true;
}
return false;
}
/** Print B-tree.
*
* @param t Print out B-tree.
*/
void btree_print(btree_t *t)
{
int i, depth = t->root->depth;
link_t head;
list_initialize(&head);
list_append(&t->root->bfs_link, &head);
/*
* Use BFS search to print out the tree.
* Levels are distinguished from one another by node->depth.
*/
while (!list_empty(&head)) {
link_t *hlp;
btree_node_t *node;
hlp = head.next;
ASSERT(hlp != &head);
node = list_get_instance(hlp, btree_node_t, bfs_link);
list_remove(hlp);
ASSERT(node);
if (node->depth != depth) {
depth = node->depth;
}
for (i = 0; i < node->keys; i++) {
if (node->depth && node->subtree[i]) {
list_append(&node->subtree[i]->bfs_link, &head);
}
}
if (node->depth && node->subtree[i]) {
list_append(&node->subtree[i]->bfs_link, &head);
}
}
}