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//! Rebalancing operations for B+ Tree
//!
//! This module handles tree rebalancing after deletions, including borrowing
//! from siblings, merging nodes, and collapsing the root.
use super::{
super::structure::{InternalNode, LeafNode},
BTreeIndex,
};
use crate::{page::PageId, StorageError};
impl BTreeIndex {
/// Rebalance a leaf node after deletion
///
/// Tries to borrow from siblings first, then merges if necessary.
pub(super) fn rebalance_leaf(
&mut self,
leaf: LeafNode,
path: Vec<(PageId, usize)>,
) -> Result<(), StorageError> {
if path.is_empty() {
// Leaf is root, no rebalancing needed
return Ok(());
}
let (parent_id, child_idx) = *path.last().unwrap();
let mut parent = self.read_internal_node(parent_id)?;
// Try to borrow from sibling
if self.try_borrow_leaf(&leaf, &mut parent, child_idx)? {
// Successfully borrowed
self.write_internal_node(&parent)?;
return Ok(());
}
// Must merge with sibling
self.merge_leaf(leaf, &mut parent, child_idx)?;
self.write_internal_node(&parent)?;
// Check if parent is now underfull
if parent.children.len() < self.degree / 2 && path.len() > 1 {
// Propagate rebalancing up
self.propagate_rebalance_delete(path)?;
}
Ok(())
}
/// Try to borrow entries from sibling leaf nodes
///
/// Returns true if successfully borrowed, false if no sibling has spare entries.
fn try_borrow_leaf(
&mut self,
leaf: &LeafNode,
parent: &mut InternalNode,
idx: usize,
) -> Result<bool, StorageError> {
// Try left sibling
if idx > 0 {
let mut left_sibling = self.read_leaf_node(parent.children[idx - 1])?;
if left_sibling.entries.len() > self.degree / 2 {
// Borrow last entry from left sibling
let borrowed = left_sibling.entries.pop().unwrap();
let mut updated_leaf = leaf.clone();
updated_leaf.entries.insert(0, borrowed);
// Update parent separator key
parent.keys[idx - 1] = updated_leaf.entries[0].0.clone();
// Write nodes back
self.write_leaf_node(&left_sibling)?;
self.write_leaf_node(&updated_leaf)?;
return Ok(true);
}
}
// Try right sibling
if idx < parent.children.len() - 1 {
let mut right_sibling = self.read_leaf_node(parent.children[idx + 1])?;
if right_sibling.entries.len() > self.degree / 2 {
// Borrow first entry from right sibling
let borrowed = right_sibling.entries.remove(0);
let mut updated_leaf = leaf.clone();
updated_leaf.entries.push(borrowed);
// Update parent separator key
parent.keys[idx] = right_sibling.entries[0].0.clone();
// Write nodes back
self.write_leaf_node(&right_sibling)?;
self.write_leaf_node(&updated_leaf)?;
return Ok(true);
}
}
Ok(false) // No sibling has enough entries to borrow
}
/// Merge underfull leaf with sibling
fn merge_leaf(
&mut self,
leaf: LeafNode,
parent: &mut InternalNode,
idx: usize,
) -> Result<(), StorageError> {
// Prefer merging with left sibling
if idx > 0 {
let mut left_sibling = self.read_leaf_node(parent.children[idx - 1])?;
// Merge leaf into left sibling
left_sibling.entries.extend(leaf.entries);
left_sibling.next_leaf = leaf.next_leaf;
self.write_leaf_node(&left_sibling)?;
// Remove from parent
parent.children.remove(idx);
parent.keys.remove(idx - 1);
// Deallocate merged node
self.page_manager.deallocate_page(leaf.page_id)?;
} else {
// Merge with right sibling
let right_sibling = self.read_leaf_node(parent.children[idx + 1])?;
// Merge right into leaf
let mut updated_leaf = leaf.clone();
updated_leaf.entries.extend(right_sibling.entries);
updated_leaf.next_leaf = right_sibling.next_leaf;
self.write_leaf_node(&updated_leaf)?;
// Remove from parent
parent.children.remove(idx + 1);
parent.keys.remove(idx);
// Deallocate merged node
self.page_manager.deallocate_page(right_sibling.page_id)?;
}
Ok(())
}
/// Propagate rebalancing up the tree after deletion
pub(super) fn propagate_rebalance_delete(
&mut self,
path: Vec<(PageId, usize)>,
) -> Result<(), StorageError> {
// Process from bottom to top (skip the last entry which we already handled)
for i in (0..path.len() - 1).rev() {
let (parent_id, child_idx) = path[i];
let (current_id, _) = path[i + 1];
let mut parent = self.read_internal_node(parent_id)?;
let current = self.read_internal_node(current_id)?;
// Check if current node is underfull
if current.children.len() < self.degree / 2 {
// Try to borrow or merge at internal node level
if !self.try_borrow_internal(¤t, &mut parent, child_idx)? {
self.merge_internal(current, &mut parent, child_idx)?;
}
self.write_internal_node(&parent)?;
} else {
// Parent is OK, stop propagating
self.write_internal_node(&parent)?;
break;
}
}
Ok(())
}
/// Try to borrow entries from sibling internal nodes
fn try_borrow_internal(
&mut self,
node: &InternalNode,
parent: &mut InternalNode,
idx: usize,
) -> Result<bool, StorageError> {
// Try left sibling
if idx > 0 {
let mut left_sibling = self.read_internal_node(parent.children[idx - 1])?;
if left_sibling.children.len() > self.degree / 2 {
// Borrow last child and key from left sibling
let borrowed_child = left_sibling.children.pop().unwrap();
let borrowed_key = left_sibling.keys.pop().unwrap();
let mut updated_node = node.clone();
updated_node.children.insert(0, borrowed_child);
updated_node.keys.insert(0, parent.keys[idx - 1].clone());
// Update parent separator key
parent.keys[idx - 1] = borrowed_key;
// Write nodes back
self.write_internal_node(&left_sibling)?;
self.write_internal_node(&updated_node)?;
return Ok(true);
}
}
// Try right sibling
if idx < parent.children.len() - 1 {
let mut right_sibling = self.read_internal_node(parent.children[idx + 1])?;
if right_sibling.children.len() > self.degree / 2 {
// Borrow first child and key from right sibling
let borrowed_child = right_sibling.children.remove(0);
let borrowed_key = right_sibling.keys.remove(0);
let mut updated_node = node.clone();
updated_node.children.push(borrowed_child);
updated_node.keys.push(parent.keys[idx].clone());
// Update parent separator key
parent.keys[idx] = borrowed_key;
// Write nodes back
self.write_internal_node(&right_sibling)?;
self.write_internal_node(&updated_node)?;
return Ok(true);
}
}
Ok(false) // No sibling has enough entries to borrow
}
/// Merge underfull internal node with sibling
fn merge_internal(
&mut self,
node: InternalNode,
parent: &mut InternalNode,
idx: usize,
) -> Result<(), StorageError> {
// Prefer merging with left sibling
if idx > 0 {
let mut left_sibling = self.read_internal_node(parent.children[idx - 1])?;
// Merge node into left sibling
// Include the parent's separator key
left_sibling.keys.push(parent.keys[idx - 1].clone());
left_sibling.keys.extend(node.keys);
left_sibling.children.extend(node.children);
self.write_internal_node(&left_sibling)?;
// Remove from parent
parent.children.remove(idx);
parent.keys.remove(idx - 1);
// Deallocate merged node
self.page_manager.deallocate_page(node.page_id)?;
} else {
// Merge with right sibling
let right_sibling = self.read_internal_node(parent.children[idx + 1])?;
// Merge right into node
let mut updated_node = node.clone();
updated_node.keys.push(parent.keys[idx].clone());
updated_node.keys.extend(right_sibling.keys);
updated_node.children.extend(right_sibling.children);
self.write_internal_node(&updated_node)?;
// Remove from parent
parent.children.remove(idx + 1);
parent.keys.remove(idx);
// Deallocate merged node
self.page_manager.deallocate_page(right_sibling.page_id)?;
}
Ok(())
}
/// Check if root should be collapsed (height decrease)
pub(super) fn maybe_collapse_root(&mut self) -> Result<(), StorageError> {
if self.height > 1 {
let root = self.read_internal_node(self.root_page_id)?;
if root.children.len() == 1 {
// Collapse root
let old_root_id = self.root_page_id;
self.root_page_id = root.children[0];
self.height -= 1;
self.page_manager.deallocate_page(old_root_id)?;
self.save_metadata()?;
}
}
Ok(())
}
}