0,0 → 1,1003 |
/* |
* 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. |
*/ |
|
/** @addtogroup genericadt |
* @{ |
*/ |
|
/** |
* @file |
* @brief B+tree implementation. |
* |
* This file implements B+tree type and operations. |
* |
* The B+tree has the following properties: |
* @li it is a ballanced 3-4-5 tree (i.e. BTREE_M = 5) |
* @li values (i.e. pointers to values) are stored only in leaves |
* @li leaves are linked in a list |
* |
* 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_destroy_subtree(btree_node_t *root); |
static void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node); |
static void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node); |
static void node_initialize(btree_node_t *node); |
static void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree); |
static void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree); |
static void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key); |
static void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key); |
static btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *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, btree_key_t key, void *value, btree_node_t *rsubtree); |
static bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t 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))]); |
|
static slab_cache_t *btree_node_slab; |
|
/** Initialize B-trees. */ |
void btree_init(void) |
{ |
btree_node_slab = slab_cache_create("btree_node_slab", sizeof(btree_node_t), 0, NULL, NULL, SLAB_CACHE_MAGDEFERRED); |
} |
|
/** Create empty B-tree. |
* |
* @param t B-tree. |
*/ |
void btree_create(btree_t *t) |
{ |
list_initialize(&t->leaf_head); |
t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0); |
node_initialize(t->root); |
list_append(&t->root->leaf_link, &t->leaf_head); |
} |
|
/** Destroy empty B-tree. */ |
void btree_destroy(btree_t *t) |
{ |
btree_destroy_subtree(t->root); |
} |
|
/** 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, btree_key_t 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); |
} |
|
/** Destroy subtree rooted in a node. |
* |
* @param root Root of the subtree. |
*/ |
void btree_destroy_subtree(btree_node_t *root) |
{ |
int i; |
|
if (root->keys) { |
for (i = 0; i < root->keys + 1; i++) { |
if (root->subtree[i]) |
btree_destroy_subtree(root->subtree[i]); |
} |
} |
slab_free(btree_node_slab, root); |
} |
|
/** 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, btree_key_t 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; |
btree_key_t 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 *) slab_alloc(btree_node_slab, 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 t 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, btree_key_t 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 t 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, btree_key_t 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; |
slab_free(btree_node_slab, node); |
} 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); |
slab_free(btree_node_slab, rnode); |
_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, btree_key_t 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; |
} |
|
/** Return pointer to B-tree leaf node's left neighbour. |
* |
* @param t B-tree. |
* @param node Node whose left neighbour will be returned. |
* |
* @return Left neighbour of the node or NULL if the node does not have the left neighbour. |
*/ |
btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node) |
{ |
ASSERT(LEAF_NODE(node)); |
if (node->leaf_link.prev != &t->leaf_head) |
return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link); |
else |
return NULL; |
} |
|
/** Return pointer to B-tree leaf node's right neighbour. |
* |
* @param t B-tree. |
* @param node Node whose right neighbour will be returned. |
* |
* @return Right neighbour of the node or NULL if the node does not have the right neighbour. |
*/ |
btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node) |
{ |
ASSERT(LEAF_NODE(node)); |
if (node->leaf_link.next != &t->leaf_head) |
return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link); |
else |
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, btree_key_t 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, btree_key_t 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, btree_key_t 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, btree_key_t 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, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *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 *) slab_alloc(btree_node_slab, 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) |
{ |
btree_key_t 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) |
{ |
btree_key_t 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, btree_key_t 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, btree_key_t 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 lnode 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; |
|
printf("Printing B-tree:\n"); |
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) { |
printf("\n"); |
depth = node->depth; |
} |
|
printf("("); |
for (i = 0; i < node->keys; i++) { |
printf("%lld%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(")"); |
} |
printf("\n"); |
|
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); |
|
printf("("); |
for (i = 0; i < node->keys; i++) |
printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : ""); |
printf(")"); |
} |
printf("\n"); |
} |
|
/** @} |
*/ |
|