int
bplus_tree_search(struct tree *tree, int key)
{
int i;
struct node *node = tree->root;
struct non_leaf *nln;
struct leaf *ln;
while (node != NULL) {
switch (node->type) {
case BPLUS_TREE_NON_LEAF:
nln = (struct non_leaf *)node;
i = key_binary_search(nln->key, nln->children - 1, key);
if (i >= 0) {
node = nln->sub_ptr[i + 1];
} else {
i = -i - 1;
node = nln->sub_ptr[i];
}
break;
case BPLUS_TREE_LEAF:
ln = (struct leaf *)node;
i = key_binary_search(ln->key, ln->entries, key);
if (i >= 0) {
return ln->data[i];
} else {
return 0;
}
default:
assert(0);
}
}
return 0;
}
void
bplus_tree_delete(struct tree *tree, int key)
{
int i;
struct node *node = tree->root;
struct non_leaf *nln;
struct leaf *ln;
while (node != NULL) {
switch (node->type) {
case BPLUS_TREE_NON_LEAF:
nln = (struct non_leaf *)node;
i = key_binary_search(nln->key, nln->children - 1, key);
if (i >= 0) {
node = nln->sub_ptr[i + 1];
} else {
i = -i - 1;
node = nln->sub_ptr[i];
}
break;
case BPLUS_TREE_LEAF:
ln = (struct leaf *)node;
leaf_remove(tree, ln, key);
return;
default:
break;
}
}
}
static int
bplus_tree_insert(struct bplus_tree *tree, int key, int data)
{
int i;
struct bplus_node *node = tree->root;
struct bplus_non_leaf *nln;
struct bplus_leaf *ln, *root;
while (node != NULL) {
switch (node->type) {
case BPLUS_TREE_NON_LEAF:
nln = (struct bplus_non_leaf *)node;
i = key_binary_search(nln->key, nln->children - 1, key);
if (i >= 0) {
node = nln->sub_ptr[i + 1];
} else {
i = -i - 1;
node = nln->sub_ptr[i];
}
break;
case BPLUS_TREE_LEAF:
ln = (struct bplus_leaf *)node;
return leaf_insert(tree, ln, key, data);
default:
assert(0);
}
}
/* new root */
root = leaf_new();
root->key[0] = key;
root->data[0] = data;
root->entries = 1;
tree->head[0] = (struct bplus_node *)root;
tree->root = (struct bplus_node *)root;
return 0;
}
static void
leaf_remove(struct tree *tree, struct leaf *leaf, int key)
{
int i, j, k;
struct leaf *sibling;
int remove = key_binary_search(leaf->key, leaf->entries, key);
if (remove < 0) {
return;
}
if (leaf->entries <= (ENTRIES + 1) / 2) {
struct non_leaf *parent = leaf->parent;
if (parent != NULL) {
int borrow = 0;
/* find which sibling node with same parent to be borrowed from */
i = key_binary_search(parent->key, parent->children - 1, leaf->key[0]);
if (i >= 0) {
i = i + 1;
if (i == parent->children - 1) {
/* the last node, no right sibling, choose left one */
sibling = (struct leaf *)parent->sub_ptr[i - 1];
borrow = BORROW_FROM_LEFT;
} else {
struct leaf *l_sib = (struct leaf *)parent->sub_ptr[i - 1];
struct leaf *r_sib = (struct leaf *)parent->sub_ptr[i + 1];
/* if both left and right sibling found, choose the one with more entries */
sibling = l_sib->entries >= r_sib->entries ? l_sib : r_sib;
borrow = l_sib->entries >= r_sib->entries ? BORROW_FROM_LEFT : BORROW_FROM_RIGHT;
}
} else {
i = -i - 1;
if (i == 0) {
/* the frist node, no left sibling, choose right one */
sibling = (struct leaf *)parent->sub_ptr[i + 1];
borrow = BORROW_FROM_RIGHT;
} else if (i == parent->children - 1) {
/* the last node, no right sibling, choose left one */
sibling = (struct leaf *)parent->sub_ptr[i - 1];
borrow = BORROW_FROM_LEFT;
} else {
struct leaf *l_sib = (struct leaf *)parent->sub_ptr[i - 1];
struct leaf *r_sib = (struct leaf *)parent->sub_ptr[i + 1];
/* if both left and right sibling found, choose the one with more entries */
sibling = l_sib->entries >= r_sib->entries ? l_sib : r_sib;
borrow = l_sib->entries >= r_sib->entries ? BORROW_FROM_LEFT : BORROW_FROM_RIGHT;
}
}
/* locate parent node key index */
if (i > 0) {
i = i - 1;
}
if (borrow == BORROW_FROM_LEFT) {
if (sibling->entries > (ENTRIES + 1) / 2) {
/* leaf node right shift */
parent->key[i] = sibling->key[sibling->entries - 1];
for (; remove > 0; remove--) {
leaf->key[remove] = leaf->key[remove - 1];
leaf->data[remove] = leaf->data[remove - 1];
}
leaf->key[0] = sibling->key[sibling->entries - 1];
leaf->data[0] = sibling->data[sibling->entries - 1];
sibling->entries--;
/* adjust parent key */
parent->key[i] = leaf->key[0];
} else {
/* merge leaf and left sibling */
for (j = sibling->entries, k = 0; k < leaf->entries; k++) {
if (k != remove) {
sibling->key[j] = leaf->key[k];
sibling->data[j] = leaf->data[k];
j++;
}
}
sibling->entries = j;
/* delete merged leaf */
sibling->next = leaf->next;
leaf_delete(leaf);
/* trace upwards */
non_leaf_remove(tree, parent, i, 1);
}
} else {
/* remove entry first in case of overflow merging with sibling node */
for (; remove < leaf->entries - 1; remove++) {
leaf->key[remove] = leaf->key[remove + 1];
leaf->data[remove] = leaf->data[remove + 1];
}
leaf->entries--;
if (sibling->entries > (ENTRIES + 1) / 2) {
/* borrow */
leaf->key[leaf->entries] = sibling->key[0];
leaf->data[leaf->entries] = sibling->data[0];
leaf->entries++;
/* right sibling node left shift */
for (j = 0; j < sibling->entries - 1; j++) {
sibling->key[j] = sibling->key[j + 1];
sibling->data[j] = sibling->data[j + 1];
}
sibling->entries--;
/* adjust parent key */
parent->key[i] = sibling->key[0];
} else {
/* merge leaf node */
for (j = leaf->entries, k = 0; k < sibling->entries; j++, k++) {
leaf->key[j] = sibling->key[k];
leaf->data[j] = sibling->data[k];
}
leaf->entries = j;
/* delete merged sibling */
leaf->next = sibling->next;
leaf_delete(sibling);
/* trace upwards */
non_leaf_remove(tree, parent, i, 1);
}
}
/* deletion finishes */
return;
} else {
if (leaf->entries == 1) {
/* delete the only last node */
assert(key == leaf->key[0]);
tree->root = NULL;
tree->head[0] = NULL;
leaf_delete(leaf);
return;
}
}
}
/* simple deletion */
for (; remove < leaf->entries - 1; remove++) {
leaf->key[remove] = leaf->key[remove + 1];
leaf->data[remove] = leaf->data[remove + 1];
}
leaf->entries--;
}
static void
non_leaf_remove(struct tree *tree, struct non_leaf *node, int remove, int level)
{
int i, j, k;
struct non_leaf *sibling;
if (node->children <= (DEGREE + 1) / 2) {
struct non_leaf *parent = node->parent;
if (parent != NULL) {
int borrow = 0;
/* find which sibling node with same parent to be borrowed from */
i = key_binary_search(parent->key, parent->children - 1, node->key[0]);
assert(i < 0);
i = -i - 1;
if (i == 0) {
/* no left sibling, choose right one */
sibling = (struct non_leaf *)parent->sub_ptr[i + 1];
borrow = BORROW_FROM_RIGHT;
} else if (i == parent->children - 1) {
/* no right sibling, choose left one */
sibling = (struct non_leaf *)parent->sub_ptr[i - 1];
borrow = BORROW_FROM_LEFT;
} else {
struct non_leaf *l_sib = (struct non_leaf *)parent->sub_ptr[i - 1];
struct non_leaf *r_sib = (struct non_leaf *)parent->sub_ptr[i + 1];
/* if both left and right sibling found, choose the one with more children */
sibling = l_sib->children >= r_sib->children ? l_sib : r_sib;
borrow = l_sib->children >= r_sib->children ? BORROW_FROM_LEFT : BORROW_FROM_RIGHT;
}
/* locate parent node key index */
if (i > 0) {
i = i - 1;
}
if (borrow == BORROW_FROM_LEFT) {
if (sibling->children > (DEGREE + 1) / 2) {
/* node right shift */
for (j = remove; j > 0; j--) {
node->key[j] = node->key[j - 1];
}
for (j = remove + 1; j > 0; j--) {
node->sub_ptr[j] = node->sub_ptr[j - 1];
}
/* right rotate key */
node->key[0] = parent->key[i];
parent->key[i] = sibling->key[sibling->children - 2];
/* move left sibling's last sub-node into node's first location */
node->sub_ptr[0] = sibling->sub_ptr[sibling->children - 1];
sibling->sub_ptr[sibling->children - 1]->parent = node;
sibling->children--;
} else {
/* move parent key down */
sibling->key[sibling->children - 1] = parent->key[i];
/* merge node and left sibling */
for (j = sibling->children, k = 0; k < node->children - 1; k++) {
if (k != remove) {
sibling->key[j] = node->key[k];
j++;
}
}
for (j = sibling->children, k = 0; k < node->children - 1; k++) {
if (k != remove + 1) {
sibling->sub_ptr[j] = node->sub_ptr[k];
node->sub_ptr[k]->parent = sibling;
j++;
}
}
sibling->children = j;
/* delete merged node */
sibling->next = node->next;
non_leaf_delete(node);
/* trace upwards */
non_leaf_remove(tree, parent, i, level + 1);
}
} else {
/* remove key first in case of overflow merging with sibling node */
for (; remove < node->children - 2; remove++) {
node->key[remove] = node->key[remove + 1];
node->sub_ptr[remove + 1] = node->sub_ptr[remove + 2];
}
node->children--;
if (sibling->children > (DEGREE + 1) / 2) {
/* left rotate key */
node->key[node->children - 1] = parent->key[i];
parent->key[i] = sibling->key[0];
node->children++;
/* move right sibling's first sub-node into node's last location */
node->sub_ptr[node->children - 1] = sibling->sub_ptr[0];
sibling->sub_ptr[0]->parent = node;
/* right sibling left shift */
for (j = 0; j < sibling->children - 2; j++) {
sibling->key[j] = sibling->key[j + 1];
}
for (j = 0; j < sibling->children - 1; j++) {
sibling->sub_ptr[j] = sibling->sub_ptr[j + 1];
}
sibling->children--;
} else {
/* move parent key down */
node->key[node->children - 1] = parent->key[i];
node->children++;
/* merge node and right sibling */
for (j = node->children - 1, k = 0; k < sibling->children - 1; j++, k++) {
node->key[j] = sibling->key[k];
}
for (j = node->children - 1, k = 0; k < sibling->children; j++, k++) {
node->sub_ptr[j] = sibling->sub_ptr[k];
sibling->sub_ptr[k]->parent = node;
}
node->children = j;
/* delete merged sibling */
node->next = sibling->next;
non_leaf_delete(sibling);
/* trace upwards */
non_leaf_remove(tree, parent, i, level + 1);
}
}
/* deletion finishes */
return;
} else {
if (node->children == 2) {
/* delete old root node */
assert(remove == 0);
node->sub_ptr[0]->parent = NULL;
tree->root = node->sub_ptr[0];
tree->head[level] = NULL;
non_leaf_delete(node);
return;
}
}
}
/* simple deletion */
assert(node->children > 2);
for (; remove < node->children - 2; remove++) {
node->key[remove] = node->key[remove + 1];
node->sub_ptr[remove + 1] = node->sub_ptr[remove + 2];
}
node->children--;
}
void
bplus_tree_insert(struct tree *tree, int key, int data)
{
int i, j, level;
struct node *node = tree->root;
struct non_leaf *nln, *rank_nln;
struct leaf *ln;
struct rank_recorder recorder[MAX_LEVEL];
if (node == NULL) {
struct leaf *leaf = leaf_new();
leaf->key[0] = key;
leaf->data[0] = data;
leaf->entries = 1;
tree->head[0] = (struct node *)leaf;
tree->root = (struct node *)leaf;
return;
}
memset(recorder, 0, sizeof(recorder));
level = MAX_LEVEL;
while (--level > 0) {
if (tree->head[level] == node) {
break;
}
}
rank_nln = (struct non_leaf *)tree->head[level];
while (node != NULL) {
switch (node->type) {
case BPLUS_TREE_NON_LEAF:
nln = (struct non_leaf *)node;
/* rank inheritance */
recorder[level].rank = level == MAX_LEVEL - 1 ? 0 : recorder[level + 1].rank;
while (rank_nln != nln) {
for (j = 0; j < rank_nln->children - 2; j++) {
recorder[level].rank += rank_nln->span[j];
}
rank_nln = rank_nln->next;
}
/* search key */
i = key_binary_search(nln->key, nln->children - 1, key);
if (i >= 0) {
node = nln->sub_ptr[i + 1];
if (i < nln->children - 2) {
recorder[level].node = nln;
recorder[level].index = i + 1;
for (j = 0; j < i + 1; j++) {
recorder[level].rank += nln->span[j];
}
} else {
recorder[level].node = nln->next;
recorder[level].index = 0;
for (j = 0; j < nln->children - 1; j++) {
recorder[level].rank += nln->span[j];
}
}
} else {
i = -i - 1;
node = nln->sub_ptr[i];
if (i < nln->children - 1) {
recorder[level].node = nln;
recorder[level].index = i;
for (j = 0; j < i; j++) {
recorder[level].rank += nln->span[j];
}
} else {
recorder[level].node = nln->next;
recorder[level].index = 0;
for (j = 0; j < nln->children - 1; j++) {
recorder[level].rank += nln->span[j];
}
}
}
if (node->type != BPLUS_TREE_LEAF) {
rank_nln = (struct non_leaf *)node;
}
level--;
break;
case BPLUS_TREE_LEAF:
ln = (struct leaf *)node;
leaf_insert(tree, ln, key, data, &recorder[0]);
return;
default:
break;
}
}
}
static void
leaf_insert(struct tree *tree, struct leaf *leaf, int key, int data, struct rank_recorder *recorder)
{
int i, j, split = 0;
struct leaf *sibling;
int insert = key_binary_search(leaf->key, leaf->entries, key);
if (insert >= 0) {
/* Already exists */
return;
}
insert = -insert - 1;
/* node full */
if (leaf->entries == ENTRIES) {
/* split = [m/2] */
split = (ENTRIES + 1) / 2;
/* splited sibling node */
sibling = leaf_new();
sibling->next = leaf->next;
leaf->next = sibling;
leaf->entries = split;
/* sibling leaf replication */
if (insert < split) {
for (i = split - 1, j = 0; i < ENTRIES; i++, j++) {
sibling->key[j] = leaf->key[i];
sibling->data[j] = leaf->data[i];
}
sibling->entries = j;
/* leaf insertion and its entry count stays unchanged(split + 1) */
for (i = leaf->entries; i > insert; i--) {
leaf->key[i] = leaf->key[i - 1];
leaf->data[i] = leaf->data[i - 1];
}
leaf->key[i] = key;
leaf->data[i] = data;
} else {
i = split, j = 0;
while (i < ENTRIES) {
if (j != insert - split) {
sibling->key[j] = leaf->key[i];
sibling->data[j] = leaf->data[i];
i++;
}
j++;
}
/* sibling leaf entries */
if (j > insert - split) {
sibling->entries = j;
} else {
sibling->entries = insert - split + 1;
}
/* insert new key */
j = insert - split;
sibling->key[j] = key;
sibling->data[j] = data;
}
} else {
/* simple insertion */
for (i = leaf->entries; i > insert; i--) {
leaf->key[i] = leaf->key[i - 1];
leaf->data[i] = leaf->data[i - 1];
}
leaf->key[i] = key;
leaf->data[i] = data;
leaf->entries++;
}
if (split) {
struct non_leaf *parent = leaf->parent;
if (parent == NULL) {
parent = non_leaf_new();
parent->key[0] = sibling->key[0];
parent->sub_ptr[0] = (struct node *)leaf;
parent->sub_ptr[1] = (struct node *)sibling;
parent->children = 2;
/* new root */
tree->root = (struct node *)parent;
tree->head[1] = (struct node *)parent;
leaf->parent = parent;
sibling->parent = parent;
} else {
/* trace upwards */
sibling->parent = parent;
non_leaf_insert(tree, parent, (struct node *)sibling, sibling->key[0], 1, recorder);
}
}
}
static void
non_leaf_insert(struct tree *tree, struct non_leaf *node, struct node *sub_node, int key, int level, struct rank_recorder *recorder)
{
int i, j, split_key;
int split = 0;
struct non_leaf *sibling;
int insert = key_binary_search(node->key, node->children - 1, key);
assert(insert < 0);
insert = -insert - 1;
/* node full */
if (node->children == DEGREE) {
/* split key index */
split = (DEGREE + 1) / 2;
/* splited sibling node */
sibling = non_leaf_new();
sibling->next = node->next;
node->next = sibling;
node->children = split + 1;
/* sibling node replication */
if (insert < split) {
i = split - 1, j = 0;
split_key = node->key[i];
sibling->sub_ptr[j] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
for (; i < DEGREE - 1; i++, j++) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
}
sibling->children = j + 1;
/* node insertion and its children count stays unchanged(split + 1) */
for (i = node->children - 1; i > insert; i--) {
node->key[i] = node->key[i - 1];
node->sub_ptr[i + 1] = node->sub_ptr[i];
}
node->key[i] = key;
node->sub_ptr[i + 1] = sub_node;
} else if (insert == split) {
i = split, j = 0;
split_key = key;
sibling->sub_ptr[j] = sub_node;
sub_node->parent = sibling;
i++;
for (; i < DEGREE - 1; i++, j++) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
}
sibling->children = j + 1;
} else {
i = split, j = 0;
split_key = node->key[i];
sibling->sub_ptr[j] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
while (i < DEGREE - 1) {
if (j != insert - split) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
}
j++;
}
/* sibling node children count */
if (j > insert - split) {
sibling->children = j + 1;
} else {
sibling->children = insert - split + 1;
}
/* insert new key */
j = insert - split - 1;
sibling->key[j] = key;
sibling->sub_ptr[j + 1] = sub_node;
sub_node->parent = sibling;
}
} else {
/* simple insertion */
for (i = node->children - 1; i > insert; i--) {
node->key[i] = node->key[i - 1];
node->sub_ptr[i + 1] = node->sub_ptr[i];
}
node->key[i] = key;
node->sub_ptr[i + 1] = sub_node;
node->children++;
}
if (split) {
struct non_leaf *parent = node->parent;
if (parent == NULL) {
/* new parent */
parent = non_leaf_new();
parent->key[0] = split_key;
parent->sub_ptr[0] = (struct node *)node;
parent->sub_ptr[1] = (struct node *)sibling;
parent->children = 2;
/* new root */
tree->root = (struct node *)parent;
if (++level >= MAX_LEVEL) {
fprintf(stderr, "!!Panic: Level exceeded, please expand the non-leaf degree or leaf capacity of the tree!\n");
assert(0);
}
tree->head[level] = (struct node *)parent;
node->parent = parent;
sibling->parent = parent;
} else {
/* Trace upwards */
sibling->parent = parent;
non_leaf_insert(tree, parent, (struct node *)sibling, split_key, level + 1, recorder);
}
}
}
static int
non_leaf_insert(struct bplus_tree *tree, struct bplus_non_leaf *node, struct bplus_node *sub_node, int key, int level)
{
int i, j, split_key;
int split = 0;
struct bplus_non_leaf *sibling;
int insert = key_binary_search(node->key, node->children - 1, key);
assert(insert < 0);
insert = -insert - 1;
/* node full */
if (node->children == tree->order) {
/* split key index */
split = (tree->order + 1) / 2;
/* splited sibling node */
sibling = non_leaf_new();
sibling->next = node->next;
node->next = sibling;
node->children = split + 1;
/* sibling node replication */
if (insert < split) {
i = split - 1, j = 0;
split_key = node->key[i];
sibling->sub_ptr[j] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
for (; i < tree->order - 1; i++, j++) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
}
sibling->children = j + 1;
/* node insertion and its children count stays unchanged(split + 1) */
for (i = node->children - 1; i > insert; i--) {
node->key[i] = node->key[i - 1];
node->sub_ptr[i + 1] = node->sub_ptr[i];
}
node->key[i] = key;
node->sub_ptr[i + 1] = sub_node;
} else if (insert == split) {
i = split, j = 0;
split_key = key;
sibling->sub_ptr[j] = sub_node;
sub_node->parent = sibling;
i++;
for (; i < tree->order - 1; i++, j++) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
}
sibling->children = j + 1;
} else {
i = split, j = 0;
split_key = node->key[i];
sibling->sub_ptr[j] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
while (i < tree->order - 1) {
if (j != insert - split) {
sibling->key[j] = node->key[i];
sibling->sub_ptr[j + 1] = node->sub_ptr[i + 1];
node->sub_ptr[i + 1]->parent = sibling;
i++;
}
j++;
}
/* sibling node children count */
if (j > insert - split) {
sibling->children = j + 1;
} else {
sibling->children = insert - split + 1;
}
/* insert new key */
j = insert - split - 1;
sibling->key[j] = key;
sibling->sub_ptr[j + 1] = sub_node;
sub_node->parent = sibling;
}
} else {
/* simple insertion */
for (i = node->children - 1; i > insert; i--) {
node->key[i] = node->key[i - 1];
node->sub_ptr[i + 1] = node->sub_ptr[i];
}
node->key[i] = key;
node->sub_ptr[i + 1] = sub_node;
node->children++;
}
if (split) {
struct bplus_non_leaf *parent = node->parent;
if (parent == NULL) {
if (++level >= tree->level) {
fprintf(stderr, "!!Panic: Level exceeded, please expand the tree level, non-leaf order or leaf entries for element capacity!\n");
node->next = sibling->next;
non_leaf_delete(sibling);
return -1;
}
/* new parent */
parent = non_leaf_new();
parent->key[0] = split_key;
parent->sub_ptr[0] = (struct bplus_node *)node;
parent->sub_ptr[1] = (struct bplus_node *)sibling;
parent->children = 2;
/* new root */
tree->root = (struct bplus_node *)parent;
tree->head[level] = (struct bplus_node *)parent;
node->parent = parent;
sibling->parent = parent;
} else {
/* Trace upwards */
sibling->parent = parent;
return non_leaf_insert(tree, parent, (struct bplus_node *)sibling, split_key, level + 1);
}
}
return 0;
}
