AVL Trees and Balance Criteria Quiz

A binary search tree where the difference in height between the left and right subtrees of every node is at most 1. This ensures that the tree remains relatively balanced, preventing worst-case scenarios where the depth of the tree becomes equal to the number of nodes.

A binary search tree where the difference in the number of inner nodes between the left and right subtrees of every node is at most 1.

A type of binary tree where every node satisfies the heap property, meaning that the value of a node is greater than or equal to the values of its children (for a max-heap) or less than or equal to the values of its children (for a min-heap).

A self-balancing binary search tree where the difference in height between the left and right subtrees of every node is at most 1. It maintains balance by performing rotations whenever an insertion or deletion disrupts the balance.

A specialized self-balancing search tree designed for disk-based data storage. It consists of a multi-way tree with a fixed order, typically with a branching factor (the number of children per node) greater than or equal to 2.

A balanced tree where no leaf is significantly farther from the root than any other leaf. Different balancing schemes define 'much farther' differently, requiring different amounts of work to maintain balance.

A heap-based data structure where the parent node is always greater than or equal to its children.

A heap-based data structure where the parent node is always less than or equal to its children.

A procedure to restore the heap property after a deletion or insertion. It ensures that the parent node remains greater than or equal to its children in a max-heap (or less than or equal in a min-heap).

An operation that removes and returns the maximum element from a max-heap.

The difference in height between the left and right subtrees of a node in an AVL tree.

This operation deletes the root node of a heap and maintains the heap property.

A binary tree that automatically maintains a balanced height by adjusting the structure after insertions and deletions.

A tree rotation operation that involves moving a node to the left to rebalance a tree. This operation is performed when the left subtree of the node is taller than the right subtree, creating an imbalance.

A tree rotation operation that involves moving a node to the right to rebalance a tree. This operation is performed when the right subtree of the node is taller than the left subtree, creating an imbalance.

The process of making adjustments to an AVL tree after an insertion or deletion operation to maintain the height-balanced property. This involves rotations and other operations to ensure optimal performance.

A binary search tree where the left and right subtrees of every node are the same height. Difficult to achieve in practice, but provides the theoretical basis for balanced trees.

An operation performed in an AVL tree to ensure it remains balanced after an insertion. It involves rotating nodes to maintain the height difference condition for efficient searching.

A tree structure where, at every level, there are twice as many nodes as at the previous level, achieving a height of O(log N). This is rarely achievable in real-world scenarios but serves as a theoretical ideal.

The process of checking every node in a tree to determine whether it's height-balanced, by evaluating the height difference between its left and right subtrees.

An AVL tree is a self-balancing binary search tree that ensures efficient search, insertion, and deletion operations by maintaining a height difference of at most 1 between its subtrees, providing a practical alternative to the ideal perfectly balanced tree.

A generalization of a binary search tree that allows multiple values to be stored in each node, creating a tree with a fixed maximum degree (M) for the number of values per node and subtrees.

A tree where a single left rotation is not enough to balance it. This occurs when the right subtree has a negative balance, meaning it's left-heavy.

A technique to balance an unbalanced tree by performing a right rotation on the right subtree.

The process of performing a series of rotations to restore balance in a tree. These rotations adjust the tree's structure to maintain the height difference between subtrees within a defined limit.

The state where the right subtree of a node is heavier than the left subtree. This can lead to an unbalanced tree.

The state where the left subtree of a node is heavier than the right subtree. This can lead to an unbalanced tree.

A rotation that restructures the tree to move a node up one level and its parent down one level. This is a fundamental operation in tree balancing techniques.