Outlines the module's topics progressing from BST fundamentals and imbalance problems through AVL tree properties, balance factors, and performance analysis, serving as a navigational overview for learners and instructors to understand the scope and sequence of the module.
Module Artifacts — 9 items
Covers how binary search trees work, their average and worst-case time complexities for search, insertion, and deletion, and the core limitation that an unbalanced BST can degrade to O(n) performance — serving as prerequisite reading before learners study self-balancing trees.
Explains why plain BSTs degrade on sorted input, then details how AVL trees maintain balance through height tracking, balance factors, and the four rotation cases (left, right, left-right, right-left), giving learners the conceptual foundation to understand and implement self-balancing insertions and deletions.
Analyzes the guaranteed O(log n) performance of AVL trees for search, insertion, and deletion, discusses the constant overhead of rotations, compares AVL trees to other balanced BST variants, and identifies real-world scenarios — such as in-memory sorted dictionaries — where AVL trees are the appropriate choice.
Introduces heap trees by defining the shape property (complete binary tree) and the ordering property (min-heap or max-heap), explains how heaps are efficiently stored in arrays, and connects the structure to its primary application as a priority queue, giving learners a conceptual grounding before studying heap operations.
Details the core heap operations — insert (sift-up), extract-min/max (sift-down), and heapify — analyzes their O(log n) time complexities, discusses trade-offs between min-heaps and max-heaps, and covers practical performance considerations such as heap sort and use in graph algorithms like Dijkstra's.
Describes how tries store strings character by character in a tree of nodes, explains insertion, search, and prefix-matching operations with their O(m) time complexity relative to string length, and highlights use cases such as autocomplete and spell checking where tries outperform hash tables and BSTs.
Compares AVL trees, heaps, and tries side by side across dimensions of time complexity, memory usage, and implementation complexity, and provides guidance on selecting the appropriate structure based on the problem type — ordered lookups, priority access, or string retrieval — helping learners and instructors use it as a decision-making reference.
Compares AVL trees, heaps, and tries side by side across dimensions of time complexity, memory usage, and implementation complexity, and provides guidance on selecting the appropriate structure based on the problem type — ordered lookups, priority access, or string retrieval — helping learners and instructors use it as a decision-making reference.