Splay Tree Simulator

What is a Splay Tree?

A Splay Tree is a self-adjusting Binary Search Tree. Every successful insertion or access moves the relevant node to the root using rotations. Frequently accessed values therefore become quick to reach.

Amortized searchO(log n)

Amortized insertO(log n)

Amortized deleteO(log n)

Single-operation worst caseO(n)

Tree operations

Integer value

Animation speed400 ms

Example Splay Tree loaded. Choose an operation.

Nodes0

Height0

Root—

Rotations0

Access path

—

Splay events

No splay event yet.

Splay casesZig:
    node has a parent but no grandparent
    perform one rotation

Zig-Zig:
    node and parent lean the same way
    rotate grandparent, then parent

Zig-Zag:
    node and parent lean opposite ways
    rotate parent, then grandparent

Splay Tree concepts

Successful access

A found node is moved to the root. This improves locality when the same or nearby keys are accessed repeatedly.

Unsuccessful search

This simulator splays the last visited node even when the target is absent, following a common practical Splay Tree convention.

No stored balance data

Unlike AVL or Red-Black Trees, Splay Trees store no height, balance factor, or color metadata.

Amortized guarantee

An individual operation may be linear, but a sequence of operations has logarithmic amortized cost.

Rotation patterns

Pattern	Situation	Rotations
Zig	Parent is the root	One left or right rotation
Zig-Zig	Left-left or right-right	Two rotations in the same direction
Zig-Zag	Left-right or right-left	Two rotations in opposite directions