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/**
* Distributed under the Boost Software License, Version 1.0.
* See accompanying file LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt
*/
#include "bplus_rebalance.h"
#include "bplus_node.h"
#include "bplus_search.h"
#include "bplus_insert.h"
#include "bplus_remove.h"
void bplus_rebalance_propagate(BplusTree const* tree, BplusPath* path)
{
g_return_if_fail(tree != NULL);
g_return_if_fail(path != NULL);
BplusNode* node = path->leaf;
for (size_t i = 1; i < path->length; ++i)
{
size_t const index = path->index[i];
BplusKey const key = bplus_key_first(node);
if (bplus_key_gt(tree, bplus_key_at(node->parent, index), key))
bplus_key_at(node->parent, index) = key;
else
break;
node = node->parent;
}
}
static int64_t bplus_node_get_rebalance_amount(BplusTree const* tree, BplusNode const* node_left, BplusNode const* node_right)
{
g_return_val_if_fail(tree != NULL, 0);
g_return_val_if_fail(node_left != NULL, 0);
g_return_val_if_fail(node_right != NULL, 0);
size_t const total = node_left->length + node_right->length;
/* If the nodes can be merged without overfilling */
if (total <= (BPLUS_TREE_ORDER / 3))
return -node_right->length;
/* If the data can be balanced over the two without overfilling */
else if (total < (BPLUS_TREE_ORDER * 5 / 3))
return node_left->length - (total + 1) / 2;
return 0;
}
static gboolean bplus_node_find_merge_candidate(BplusTree const* tree, size_t const index, BplusNode* node,
BplusNode** node_left, BplusNode** node_right)
{
g_return_val_if_fail(tree != NULL, FALSE);
g_return_val_if_fail(node != NULL, FALSE);
*node_left = node;
*node_right = node;
if ((node->parent == NULL) || (node->parent->length <= 1))
return FALSE;
if (index == 0)
{
*node_right = bplus_node_at(node->parent, index + 1);
if (bplus_node_get_rebalance_amount(tree, node, *node_right) == 0)
*node_right = node;
}
else if (index == node->parent->length - 1)
{
*node_left = bplus_node_at(node->parent, index - 1);
if (bplus_node_get_rebalance_amount(tree, *node_left, node) == 0)
*node_left = node;
}
else
{
*node_left = bplus_node_at(node->parent, index - 1);
*node_right = bplus_node_at(node->parent, index + 1);
int64_t const merge_amount_right = bplus_node_get_rebalance_amount(tree, node, *node_right);
int64_t const merge_amount_left = bplus_node_get_rebalance_amount(tree, *node_left, node);
if (merge_amount_left < 0)
{
/* Merge with left copies data to the left.
* Prefer a merge with right only if it copies less data from the right.
*/
if (merge_amount_right >= 0)
*node_right = node;
else if (merge_amount_right < merge_amount_left)
*node_right = node;
else
*node_left = node;
}
else if (merge_amount_left > 0)
{
/* Merge with left copies data from the left.
* Prefer a merge with right if it copies less data to the right or data from right.
*/
if (merge_amount_right == 0)
*node_right = node;
else if (merge_amount_right > merge_amount_left)
*node_right = node;
else
*node_left = node;
}
else if (merge_amount_right != 0)
{
/* Merge with left is impossible.
* Prefer a merge with right.
*/
*node_left = node;
}
else
{
*node_left = node;
*node_right = node;
}
}
return *node_left != *node_right;
} /* bplus_node_find_merge_candidate */
static size_t bplus_rebalance_data(BplusTree const* tree, BplusNode* node_left, BplusNode* node_right)
{
g_return_val_if_fail(tree != NULL, 0);
g_return_val_if_fail(node_left != NULL, 0);
g_return_val_if_fail(node_right != NULL, 0);
int64_t const amount = bplus_node_get_rebalance_amount(tree, node_left, node_right);
g_return_val_if_fail(amount <= 0 || amount < node_left->length, 0);
g_return_val_if_fail(amount >= 0 || -amount <= node_right->length, 0);
if (amount > 0)
{
size_t const index = node_left->length - amount;
BplusItem const* items = node_left->items + index;
bplus_node_insert_at(tree, node_right, 0, amount, items);
bplus_node_remove_at(tree, node_left, index, amount);
}
else if (amount < 0)
{
size_t const index = node_left->length;
BplusItem const* items = node_right->items;
bplus_node_insert_at(tree, node_left, index, -amount, items);
bplus_node_remove_at(tree, node_right, 0, -amount);
}
return 0;
} /* bplus_rebalance_data */
static void bplus_rebalance_split_node(BplusTree* tree, BplusNode* node_left, size_t const index)
{
g_return_if_fail(tree != NULL);
g_return_if_fail(node_left != NULL);
BplusNode* const node_right = bplus_node_new_right(tree, node_left);
bplus_rebalance_data(tree, node_left, node_right);
BplusItem const item = { .key = bplus_key_first(node_right), .value = node_right };
bplus_node_insert_at(tree, node_left->parent, index + 1, 1, &item);
}
static void bplus_rebalance_new_root(BplusTree* tree)
{
g_return_if_fail(tree != NULL);
BplusNode* const node = tree->root;
BplusNode* const root = bplus_node_new(tree);
bplus_key_first(root) = bplus_key_first(node);
bplus_value_first(root) = node;
root->length = 1;
node->parent = root;
tree->root = root;
tree->height++;
}
static int bplus_rebalance_try_merge(BplusTree* tree, BplusNode* node, size_t const index)
{
g_return_val_if_fail(tree != NULL, 0);
g_return_val_if_fail(node != NULL, 0);
BplusNode* node_left;
BplusNode* node_right;
if (!bplus_node_find_merge_candidate(tree, index, node, &node_left, &node_right))
return 0;
size_t const index_right = (node == node_left) ? index + 1 : index;
bplus_rebalance_data(tree, node_left, node_right);
if (node_right->length == 0)
{
bplus_node_remove_at(tree, node->parent, index_right, 1);
bplus_node_destroy(tree, node_right);
}
else
{
bplus_key_at(node->parent, index_right) = bplus_key_first(node_right);
}
return 1;
}
void bplus_rebalance_overfilled(BplusTree* tree, BplusPath const* path)
{
g_return_if_fail(tree != NULL);
g_return_if_fail(path != NULL);
BplusNode* node = (BplusNode*) path->leaf;
for (size_t i = 1; i < path->length; ++i)
{
if (!bplus_node_overfilled(node))
break;
size_t const index = path->index[i];
if (!bplus_rebalance_try_merge(tree, node, index))
bplus_rebalance_split_node(tree, node, index);
node = node->parent;
}
if (bplus_node_overfilled(node))
{
bplus_rebalance_new_root(tree);
bplus_rebalance_split_node(tree, node, 0);
}
}
static void bplus_rebalance_shrink_tree(BplusTree* tree)
{
g_return_if_fail(tree != NULL);
g_return_if_fail(tree->root != NULL);
size_t i = 0;
for (; i < tree->height; ++i)
{
if (tree->root->length != 1)
break;
if (tree->root->is_leaf)
break;
BplusNode* node = tree->root;
tree->root = bplus_node_first(tree->root);
tree->root->parent = NULL;
node->length = 0;
bplus_node_destroy(tree, node);
}
tree->height -= i;
}
void bplus_rebalance_underfilled(BplusTree* tree, BplusPath const* path)
{
g_return_if_fail(tree != NULL);
g_return_if_fail(path != NULL);
BplusNode* node = (BplusNode*) path->leaf;
for (size_t i = 1; i < path->length; ++i)
{
if (!bplus_node_underfilled(node))
break;
size_t const index = path->index[i];
if (!bplus_rebalance_try_merge(tree, node, index) && (node->length == 0))
{
bplus_node_remove_at(tree, node->parent, index, 1);
bplus_node_destroy(tree, node);
}
node = node->parent;
}
bplus_rebalance_shrink_tree(tree);
}
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