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AlgoPlus//structures / avl
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AVL Tree

A self-balancing BST — rotations keep it height-balanced.

Nodes
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Legend
Inserted node
Node
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In a nutshell
An AVL tree is a binary search tree that refuses to get lopsided. After every insert it checks each node's balance factor — the height difference between its two branches — and the moment that gap exceeds one, it performs a rotation: a small, local rearrangement that pivots a few nodes to even the sides out again. Staying height-balanced this way keeps search and insert fast (O(log n)) even when data arrives already sorted, which would turn a plain BST into a slow chain.
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A BST that rebalances itself: after each insert, if a node's two sides differ in height by more than one, a rotation restores balance — keeping operations O(log n).
Key terms
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Code Simulator
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def bst(root, val):
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    # insert / search / traverse
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    if root is None:
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        return Node(val)  # Inserted/Found
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    if val < root.val:
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        root.left = bst(root.left, val)
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    else:
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        root.right = bst(root.right, val)
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    # traversal order
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    visit(root.val)  # Visit
Why Python? · Readable first, fast second

Dynamically typed and interpreted — every comparison and swap is dispatched by the interpreter at run time, so tight loops run roughly 10–100× slower than compiled C/C++. Unbeatable for learning the idea with the least code; not what you reach for when the inner loop is the bottleneck.