Suggest an edit

Improve this article

Refine the answer for “What is tree balancing?”. Your changes go to moderation before they’re published.

Approval required

Content

What you’re changing

Title (EN)

Short answer (EN)

Shown above the full answer for quick recall.

Answer (EN)

**Tree balancing** is the process of restructuring a tree so that its **height stays minimal** and its elements are **distributed evenly**.

## Why it's needed

In an unbalanced tree (for example, when all elements are inserted in increasing order), the structure becomes **similar to a list**,
and search, insertion, and deletion slow down from **O(log n)** to **O(n)**.

## Goal of balancing

Make sure that for every node,
the difference between the heights of its left and right subtree is **small** (usually ≤ 1).
Then the tree stays "dense", and search works quickly again.

## Example

Unbalanced tree (all to the right):

```javascript
1
 \
  2
   \
    3
     \
      4
```

After balancing:

```javascript
     3
    / \
   2   4
  /
 1
```

## Types of balanced trees

- **AVL tree** - strict height balance (difference ≤ 1).
- **Red-black tree** - a more flexible balance based on node-coloring rules.
- **B-tree, B+ tree** - balancing for storing data on disk (for example, in databases).

## Summary

**Tree balancing** means keeping the tree in a shape where search, insertion, and deletion run **as fast as possible (≈ O(log n))**, regardless of the order elements were added in.

Markdown · drag & drop images · ⌘B / ⌘I shortcuts196 words

For the reviewer

Note to the moderator (optional)

Visible only to the moderator. Helps review go faster.