/*
* 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 2-3-4-5 tree (i.e. BTREE_M = 5)
* - 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 _btree_remove(btree_t *t, __native key, btree_node_t *node);
static void node_initialize(btree_node_t *node);
static void node_insert_key_and_lsubtree(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree);
static void node_insert_key_and_rsubtree(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static void node_remove_key_and_lsubtree(btree_node_t *node, __native key);
static void node_remove_key_and_rsubtree(btree_node_t *node, __native key);
static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median);
static btree_node_t *node_combine(btree_node_t *node);
static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right);
static void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx);
static void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx);
static bool try_insert_by_rotation_to_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static bool try_insert_by_rotation_to_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static bool try_rotation_from_left(btree_node_t *rnode);
static bool try_rotation_from_right(btree_node_t *lnode);
#define ROOT_NODE(n) (!(n)->parent)
#define INDEX_NODE(n) ((n)->subtree[0] != NULL)
#define LEAF_NODE(n) ((n)->subtree[0] == NULL)
#define FILL_FACTOR ((BTREE_M-1)/2)
#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_and_rsubtree(node, key, value, rsubtree);
} else if (try_insert_by_rotation_to_left(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_rotation_to_right(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_prepend(&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);
}
}
/** Remove B-tree node.
*
* @param B-tree.
* @param key Key to be removed from the B-tree along with its associated value.
* @param leaf_node If not NULL, pointer to the leaf node where the key is found.
*/
void btree_remove(btree_t *t, __native key, btree_node_t *leaf_node)
{
btree_node_t *lnode;
lnode = leaf_node;
if (!lnode) {
if (!btree_search(t, key, &lnode)) {
panic("B-tree %P does not contain key %d\n", t, key);
}
}
_btree_remove(t, key, lnode);
}
/** Recursively remove B-tree node.
*
* @param B-tree.
* @param key Key to be removed from the B-tree along with its associated value.
* @param node Node where the key being removed resides.
*/
void _btree_remove(btree_t *t, __native key, btree_node_t *node)
{
if (ROOT_NODE(node)) {
if (node->keys == 1 && node->subtree[0]) {
/*
* Free the current root and set new root.
*/
t->root = node->subtree[0];
t->root->parent = NULL;
} else {
/*
* Remove the key from the root node.
* Note that the right subtree is removed because when
* combining two nodes, the left-side sibling is preserved
* and the right-side sibling is freed.
*/
node_remove_key_and_rsubtree(node, key);
}
return;
}
if (node->keys <= FILL_FACTOR) {
/*
* If the node is below the fill factor,
* try to borrow keys from left or right sibling.
*/
if (!try_rotation_from_left(node))
try_rotation_from_right(node);
}
if (node->keys > FILL_FACTOR) {
int i;
/*
* The key can be immediatelly removed.
*
* Note that the right subtree is removed because when
* combining two nodes, the left-side sibling is preserved
* and the right-side sibling is freed.
*/
node_remove_key_and_rsubtree(node, key);
for (i = 0; i < node->parent->keys; i++) {
if (node->parent->key[i] == key)
node->parent->key[i] = node->key[0];
}
} else {
index_t idx;
btree_node_t *rnode, *parent;
/*
* The node is below the fill factor as well as its left and right sibling.
* Resort to combining the node with one of its siblings.
* The node which is on the left is preserved and the node on the right is
* freed.
*/
parent = node->parent;
node_remove_key_and_rsubtree(node, key);
rnode = node_combine(node);
if (LEAF_NODE(rnode))
list_remove(&rnode->leaf_link);
idx = find_key_by_subtree(parent, rnode, true);
ASSERT((int) idx != -1);
_btree_remove(t, parent->key[idx], parent);
}
}
/** 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;
}
/** 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_and_lsubtree(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_and_rsubtree(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++;
}
/** 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_and_lsubtree(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_and_rsubtree(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);
}
/** 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_and_rsubtree(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;
}
/** Combine node with any of its siblings.
*
* The siblings are required to be below the fill factor.
*
* @param node Node to combine with one of its siblings.
*
* @return Pointer to the rightmost of the two nodes.
*/
btree_node_t *node_combine(btree_node_t *node)
{
index_t idx;
btree_node_t *rnode;
int i;
ASSERT(!ROOT_NODE(node));
idx = find_key_by_subtree(node->parent, node, false);
if (idx == node->parent->keys) {
/*
* Rightmost subtree of its parent, combine with the left sibling.
*/
idx--;
rnode = node;
node = node->parent->subtree[idx];
} else {
rnode = node->parent->subtree[idx + 1];
}
/* Index nodes need to insert parent node key in between left and right node. */
if (INDEX_NODE(node))
node->key[node->keys++] = node->parent->key[idx];
/* Copy the key-value-subtree triplets from the right node. */
for (i = 0; i < rnode->keys; i++) {
node->key[node->keys + i] = rnode->key[i];
node->value[node->keys + i] = rnode->value[i];
if (INDEX_NODE(node)) {
node->subtree[node->keys + i] = rnode->subtree[i];
rnode->subtree[i]->parent = node;
}
}
if (INDEX_NODE(node)) {
node->subtree[node->keys + i] = rnode->subtree[i];
rnode->subtree[i]->parent = node;
}
node->keys += rnode->keys;
return rnode;
}
/** 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);
}
/** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling.
*
* The biggest key and its value and right subtree is rotated from the left node
* to the right. If the node is an index node, than the parent node key belonging to
* the left node takes part in the rotation.
*
* @param lnode Left sibling.
* @param rnode Right sibling.
* @param idx Index of the parent node key that is taking part in the rotation.
*/
void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx)
{
__native key;
key = lnode->key[lnode->keys - 1];
if (LEAF_NODE(lnode)) {
void *value;
value = lnode->value[lnode->keys - 1];
node_remove_key_and_rsubtree(lnode, key);
node_insert_key_and_lsubtree(rnode, key, value, NULL);
lnode->parent->key[idx] = key;
} else {
btree_node_t *rsubtree;
rsubtree = lnode->subtree[lnode->keys];
node_remove_key_and_rsubtree(lnode, key);
node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree);
lnode->parent->key[idx] = key;
/* Fix parent link of the reconnected right subtree. */
rsubtree->parent = rnode;
}
}
/** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling.
*
* The smallest key and its value and left subtree is rotated from the right node
* to the left. If the node is an index node, than the parent node key belonging to
* the right node takes part in the rotation.
*
* @param lnode Left sibling.
* @param rnode Right sibling.
* @param idx Index of the parent node key that is taking part in the rotation.
*/
void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx)
{
__native key;
key = rnode->key[0];
if (LEAF_NODE(rnode)) {
void *value;
value = rnode->value[0];
node_remove_key_and_lsubtree(rnode, key);
node_insert_key_and_rsubtree(lnode, key, value, NULL);
rnode->parent->key[idx] = rnode->key[0];
} else {
btree_node_t *lsubtree;
lsubtree = rnode->subtree[0];
node_remove_key_and_lsubtree(rnode, key);
node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree);
rnode->parent->key[idx] = key;
/* Fix parent link of the reconnected left subtree. */
lsubtree->parent = lnode;
}
}
/** 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_rotation_to_left(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) {
/*
* The rotaion can be done. The left sibling has free space.
*/
node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree);
rotate_from_right(lnode, node, idx);
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_rotation_to_right(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) {
/*
* The rotaion can be done. The right sibling has free space.
*/
node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree);
rotate_from_left(node, rnode, idx);
return true;
}
return false;
}
/** Rotate in a key from the left sibling or from the index node, if this operation can be done.
*
* @param rnode Node into which to add key from its left sibling or from the index node.
*
* @return True if the rotation was performed, false otherwise.
*/
bool try_rotation_from_left(btree_node_t *rnode)
{
index_t idx;
btree_node_t *lnode;
/*
* If this is root node, the rotation can not be done.
*/
if (ROOT_NODE(rnode))
return false;
idx = find_key_by_subtree(rnode->parent, rnode, true);
if ((int) idx == -1) {
/*
* If this node is the leftmost subtree of its parent,
* the rotation can not be done.
*/
return false;
}
lnode = rnode->parent->subtree[idx];
if (lnode->keys > FILL_FACTOR) {
rotate_from_left(lnode, rnode, idx);
return true;
}
return false;
}
/** Rotate in a key from the right sibling or from the index node, if this operation can be done.
*
* @param rnode Node into which to add key from its right sibling or from the index node.
*
* @return True if the rotation was performed, false otherwise.
*/
bool try_rotation_from_right(btree_node_t *lnode)
{
index_t idx;
btree_node_t *rnode;
/*
* If this is root node, the rotation can not be done.
*/
if (ROOT_NODE(lnode))
return false;
idx = find_key_by_subtree(lnode->parent, lnode, false);
if (idx == lnode->parent->keys) {
/*
* If this node is the rightmost subtree of its parent,
* the rotation can not be done.
*/
return false;
}
rnode = lnode->parent->subtree[idx + 1];
if (rnode->keys > FILL_FACTOR) {
rotate_from_right(lnode, rnode, idx);
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, *cur;
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++) {
printf("%d%s", node
->key
[i
], i
< node
->keys
- 1 ? "," : ""); 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);
}
}
printf("Printing list of leaves:\n"); for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) {
btree_node_t *node;
node = list_get_instance(cur, btree_node_t, leaf_link);
ASSERT(node);
for (i = 0; i < node->keys; i++)
printf("%d%s", node
->key
[i
], i
< node
->keys
- 1 ? "," : ""); }
}