B-Trees Overview

Beginner Algorithms and Data Structures English

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Created by Best · 16.08.2026 at 09:13 UTC

B-trees store multiple keys per node and keep leaves at the same depth. They are designed for block-oriented storage (hard drive, SSD pages).

Compared to AVL trees: fewer rotations along the path, wider nodes, typically found in databases and file systems.

high branching, balanced height.

Structure	Height idea	Typical storage
BST	can degenerate to a chain	RAM, nodes
AVL		balance
B-tree	high fan-out, leaves level	blocks / pages
## Where used

Database and file system indexes (InnoDB, NTFS/HFS ideas), because high branching factors align with the block sizes of SSDs/HDDs. Less random I/O per search than with binary nodes.

Depth

A B-tree stores multiple sorted keys per node and accordingly has multiple children. All leaves are at the same level. The high branching reduces the number of nodes visited on a search path.

This structure is suitable for block-oriented storage. A node is sized to read many keys with a single page access. The relevant cost metric is therefore often the number of memory accesses rather than individual comparisons.

When inserting, a full node is split and a separating key is promoted to the parent node. Deletion may require borrowing or merging to maintain minimum occupancy.

Difficulty levels

Assign key ranges to the children of a node.
Track a node split and the promotion.
Justify high branching with external storage blocks.

Pitfalls

A B-tree is not a binary tree. The allowable number of keys depends on the ordering definition used, which is often noted differently in textbooks.

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Tasks

Question 1

Why are B-trees suitable for secondary storage?

Because they do not store keys.

Because large nodes amortize side accesses.

Because they only use stacks.

Because equals is forbidden.

Question 2

Why do B-trees typically have a high branching factor?

So that each key receives its own process.

So that a memory block covers many keys and paths.

So that leaves have different depths.

So that comparisons are completely eliminated.

Question 3

Check if the key number is within the allowed limits.

Hint

Area checks can be combined with &&. The method expects a boolean expression as a return value.

public class BTreeRules {
  public static boolean isValidBTreeNode(
      int keyCount, int minKeys, int maxKeys) {
    // TODO
    return false;
  }
}

Starter code is prefilled; replace TODO blocks with your solution.

Runtime output (stdout/stderr)

1 test case will be used for grading

Run checks runtime behavior only. Final correctness is evaluated when you submit.

Card Info

Topic: Algorithms and Data Structures
Difficulty: Beginner
Completed: 0 users

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