Internal bulk loading implementation for sorted items.

Calculate the depth of the tree

Check that branch nodes have correct key-to-children ratio

Check if keys are in ascending order throughout the tree

Check leaf-specific consistency rules

Check that the leaf linked list maintains ordering

Check maximum occupancy constraints

Check minimum occupancy constraints

Check that all leaves are at the same depth

Count total keys in the tree

Delete from a leaf node. Returns True if deleted, False if not found.

Recursively delete a key from the tree. Returns True if the key was found and deleted, False otherwise.

Find the leaf node that contains or would contain the given key

Find the position where key is or would be in the leaf

Helper to find root (simplified - would need parent pointers in real implementation)

Extract all keys from B+ tree by traversing leaves

Handle underflow in a child node by trying redistribution first

Insert a separator and new child into a branch node. Returns None or (new_branch, separator) if split.

Insert into a leaf node. Returns None or (new_leaf, separator) if split.

Recursive insert.

Recursively insert a key-value pair into the tree. Returns None for a simple insertion, or (new_node, separator_key) if a split occur

Optimized insertion for sorted data - avoids repeated tree traversals. Args: key: The key to insert. value: The value

Pre-populate the tree with a specified number of elements to create complex structure

Redistribute keys from left sibling to child

Redistribute keys from right sibling to child

Split node and insert.

Split branch node.

Helper to check if any non-root nodes in tree are underfull

Update the rightmost leaf cache.

Group sessions by day and calculate daily totals.

Group sessions by day and calculate daily totals.

Group sessions by day and calculate daily totals.

Analyze programming patterns.

Benchmark deletions.

Compare with standard dict performance.

Benchmark insertion performance.

Compare performance of single vs two array layouts.

Benchmark full iteration performance.

Benchmark full iteration.

Benchmark lookups on existing tree.

Demonstrate memory efficiency.

Benchmark random insertions.

Benchmark range query performance vs alternatives.

Benchmark range queries.

Benchmark sequential insertions.

Borrow the rightmost key and child from left sibling, returns new separator

Optimized helpers that avoid re-reading parent for IDs/keys

Borrow the leftmost key and child from right sibling, returns new separator

Cache-aligned memory allocation functions */

Calculate programming sessions based on commit gaps. If gap between commits is <= max_gap_minutes, assume continuous work.

Calculate programming sessions based on commit gaps. If gap between commits is <= max_gap_minutes, assume continuous work.

Calculate programming sessions based on commit gaps.

Get the total capacity

Demonstrate the impact of capacity tuning.

Check that arena allocation matches tree structure

Helper function to check tree invariants

Check that all leaf nodes in the tree are reachable via the linked list.

Check that the leaf linked list is properly ordered and complete.

Collapse the root if it's a branch with only one child or no children.

Collect all leaf node IDs from the tree structure.

Recursively collect leaf sizes for debugging.

Compare insertion performance.

Compare lookup performance.

Compare range query performance.

Count nodes at each level of the tree

Recursively count nodes in the tree.

Create a simple ASCII chart of daily programming time.

Create chart showing optimal capacity selection.

Create comparison charts for different operations.

Create comprehensive visualizations.

Create chart showing performance ratios (BPlusTree/BTreeMap).

Standard tree with capacity 4 for integer keys and values

Create visualizations of programming time.

Deallocate and replace with default value

Delete a key, returns the value if found

Demonstrate full API compatibility.

Demonstrate basic range query functionality.