Skip to main content

Augmented Binary Trees and Order Statistics Study Guide

This guide explores augmented binary trees, a data structure technique that enhances standard Binary Search Trees (BSTs) by storing additional attributes in nodes. It focuses on how augmenting nodes with information like subtree size allows for efficient computation of order statistics (e.g., finding the k-th smallest element or the rank of an element) and supports sequence operations like insertion, deletion, and retrieval in logarithmic time complexity relative to the tree's height. The guide

Save this study guide to your study set

Sign up free

Your learning path

Augmented Binary Trees and Sequence Implementation

Augmented Binary Trees and Sequences

Implementing sequences using binary trees with augmentations to support efficient operations and subtree size maintenance.

  • Augmented binary trees
  • Binary-tree sequences
  • In-order traversal
  • Subtree size
  • Tree augmentations
  • Sequence operations
  • Maintaining augmentations

Augmented Binary Trees and Order Statistics

Augmented binary trees use subtree size to support order statistics such as OS-Select and OS-Rank through in-order traversal properties.

  • Augmented Binary Trees
  • Subtree Size
  • Order Statistics
  • In-order Traversal
  • OS-Select
  • OS-Rank
  • Binary Search Tree
  • Binary-tree Sequence
  • Rank
  • Complexity O(h)

Augmented Binary Trees and Range Queries

This lecture covers augmenting binary tree data structures with subtree sums, range max, and range min to support efficient range-sum and range-query operations.

  • Augmented Binary Trees
  • Subtree Sums
  • Range-Sum(T,a,b)
  • Suffix-Sum
  • Prefix-Sum
  • Range-Max
  • Range-Min
  • Binary Search Tree augmentation
  • One-sided range queries
  • Two-sided range queries

Augmented Binary Trees and Range Queries

Augmented Binary Trees and Interval Trees

Augment binary search trees to support operations on dynamic sets of intervals using interval trees.

  • Augmented binary search trees
  • Interval trees
  • Closed intervals
  • Interval trichotomy
  • Interval-Insert
  • Interval-Delete
  • Interval-Search
  • Maximum high endpoint augmentation
  • Binary search tree operations

Make it your own.

Keep these readings and topics in a new study set, or add them to one you already use.

Get started freeLog in