L3 Binary Search Tree as Sequences

What is a binary search tree (BST)?

It is a data structure that maintains sorted data in a way that allows for efficient insertion, deletion and lookup operations.

What is the select operation in a binary search tree?

The select operation identifies the element of a particular rank within the tree, where rank k corresponds to the k-th element in an in order traversal.

How is the rank of an element determined in BST?

The rank of an element is determined by counting how many elements are smaller than it, which can be done by traversing from the element to the root and using subtree sizes.

What is the time complexity of the select operation in balanced BST?

The select operation runs in O(log n) time in a balanced binary search tree.

What additional information is typically stored in each node of an augmented BST?

Each node is augmented with the size of its subtree, which helps in efficiently performing select and rank operations.

What is the difference between value-based access and rank-based access in a BST?

Value-based access uses the find function to locate elements by their value, while rank-based access uses the select function to locate elements by their rank.

How can a binary search tree be used to represent a sequence?

A BST can represent a sequence by storing elements such that the in order traversal of the tree reflects the order of the success.

What operations can be performed on a BST used as a sequence?

Operation include selecting an element at a specific rank, inserting an element at a specific rank, and deleting an element at a specific rank.

What is an order statistic tree?

An order statistic tree is a type of binary search tree that supports efficient rank-based operations, allowing for the retrieval of the k-th smallest element.

What is the role of the left subtree in determining the rank of the root in a BST?

The size of the left subtree indicates how many elements precede the root in an inorder traversal, which helps determine the rank of the root.

What happens to the rank when recursing to the right subtree during the select operation?

When recursing to the right subtree, the rank must be adjusted by subtracting the size of the left subtree and the root itself from the original rank.

What are predecessor and successor operations in a BST?

The predecessor operation finds the element that comes before a given element that comes before a given element in a sequence, while the successor operation finds the element that comes after it.

How can the min and max operations be performed in a BST?

The min operation can be performed by traversing to the leftmost node, while the max operation is done by traversing to the rightmost node.

What is the significance of the in order traversal in a BST?

The in order traversal of a BST produces a sorted sequence of the elements stored in the tree.

How does a BST handle inserts and deletes?

Inserts and deletes in a BST are performed by maintain the binary search tree property, ensuring that the left child is less than the parent and the right child is greater.