AVL trees are a special kind of binary search tree (BST) that keep themselves balanced. This helps them search for information quickly and efficiently.
Height Balance Factor: In an AVL tree, for any node (think of a node as a point where data is stored), the heights of the left and right sides can only be different by one level. This rule helps keep the tree balanced and makes it easier to search for information.
Height of AVL Trees: The height (how tall the tree is) of an AVL tree with a certain number of nodes (n) can be figured out using this formula:
This means that an AVL tree stays around the height of (O(\log n)), which is pretty short for the amount of data it holds.
Searching, Adding, and Removing: When you search, add, or take away information in an AVL tree, it only takes about (O(\log n)) time. This is much faster than regular BSTs, which can slow down to (O(n)) in the worst cases.
Rotations: Sometimes, to keep things balanced, an AVL tree might need to perform up to 2 rotations (think of these as little rearrangements) when you add or remove information. These rotations are quick, taking a constant amount of time.
Overall, AVL trees are better at staying balanced compared to regular binary search trees. They offer a steady time for managing data, making them a great choice for lots of different applications.
AVL trees are a special kind of binary search tree (BST) that keep themselves balanced. This helps them search for information quickly and efficiently.
Height Balance Factor: In an AVL tree, for any node (think of a node as a point where data is stored), the heights of the left and right sides can only be different by one level. This rule helps keep the tree balanced and makes it easier to search for information.
Height of AVL Trees: The height (how tall the tree is) of an AVL tree with a certain number of nodes (n) can be figured out using this formula:
This means that an AVL tree stays around the height of (O(\log n)), which is pretty short for the amount of data it holds.
Searching, Adding, and Removing: When you search, add, or take away information in an AVL tree, it only takes about (O(\log n)) time. This is much faster than regular BSTs, which can slow down to (O(n)) in the worst cases.
Rotations: Sometimes, to keep things balanced, an AVL tree might need to perform up to 2 rotations (think of these as little rearrangements) when you add or remove information. These rotations are quick, taking a constant amount of time.
Overall, AVL trees are better at staying balanced compared to regular binary search trees. They offer a steady time for managing data, making them a great choice for lots of different applications.