Overview
A B-Tree keeps many keys per node and maintains all leaves at the same depth, reducing expensive storage reads.
CoreSource checked
B-Tree
Stores sorted keys in wide balanced nodes for efficient disk or page access.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Data Structures
- Difficulty
- Advanced
- Family
- Balanced Search Tree
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 2
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
stored invarianttree balancingsorted search spacebalanced search treeinvariant maintenancequery operationupdate operation
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(log n)
Average
O(log n)
Worst
O(log n)
Space
O(n)
When to Use
- Use B-Tree when you need to keep keys sorted inside wide nodes.
- Use it when the input assumptions match the method's model.
- Use it when the operation mix matches the structure's strengths.
- Use it when the method's tradeoffs fit the workload.
When Not to Use
- Avoid it when the input cannot be kept sorted cheaply.
- Avoid it when simpler arrays or maps meet the performance and clarity needs.
- Avoid it when the required output is not balanced search tree.
What It Does
- Keeps keys sorted inside wide nodes
- Splits and merges nodes to stay balanced
Use Cases
- Database indexes
- File systems
- On-disk sorted maps
Inputs
- Keys and values
- Node capacity
Outputs
- Balanced search tree
Pseudocode
- 1.Search within the current node's sorted keys
- 2.Follow the child range that can contain the key
- 3.Insert into a leaf
- 4.Split full nodes on the way back up
- 5.Keep all leaves at the same depth
Canonical Example
- Input
- operations = insert 5, insert 2, query 5
- Output
- query result = found
- Explanation
- B-Tree: The structure stores data so later operations can answer efficiently.
Implementation Notes
- Keep the input contract explicit: Keys and values; Node capacity.
- Write operation-level tests that check both returned values and internal invariants.
- Test updates and queries as sequences, not only one operation at a time.
Common Pitfalls
- B-Trees are designed around block or page access rather than single pointer hops.
- Forgetting to maintain invariants after insert, delete, merge, or update operations.
- Handle empty, invalid, and boundary inputs before trusting balanced search tree.
- Incorrect updates can leave stale pointers, counts, balance metadata, or cached summaries.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow multi-key nodes splitting while tree height stays small.
Step 1 of 5: Search within the current node's sorted keys
wide-balanced-treeNotes
B-Tree operates in O(log n) time and O(n) space within the Balanced Search Tree family. Often compared with Red-Black Tree and Binary Search Tree.
Sources (2)
What each reference supports for this entry.
B-Trees
PaperOriginal B-tree paper supporting balanced multiway search trees for external storage.
Open sourceIntroduction to Algorithms (CLRS)
BookAlgorithms textbook support for B-Tree's invariant, correctness argument, and asymptotic analysis.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toRed-Black Tree
B-trees optimize block-oriented ordered search, while red-black trees optimize pointer-based memory search.
Related Algorithms
Tags
Data StructureBalanced TreeSorted Data