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FDS Data Structures Fundamentals Lecture Notes

Translation status

This is an English companion version generated for the bilingual site. It summarizes and translates the structure of the Chinese source while keeping key mathematical and technical notation intact. A full line-by-line translation can be generated later with scripts/translate.py after an API key is configured.

Source

What This Note Covers

Lecture notes for data structures, covering algorithm analysis, lists, stacks and queues, trees, heaps, union-find, segment trees, graphs, and topological sorting.

Study Outline

  • Algorithm Analysis: Asymptotic notation, common complexity classes, and the source of time and space costs.
  • Abstract Data Types and Lists: Interface design, linear lists, linked lists, cursor implementation, and polynomial examples.
  • Stacks and Queues: LIFO/FIFO structures, expression conversion, recursion stacks, and circular queues.
  • Trees and Binary Trees: Tree terminology, traversal, expression trees, threaded trees, and recursive structure.
  • Search Trees and Heaps: Binary search trees, priority queues, binary heaps, and heap applications.
  • Union-Find and Segment Trees: Dynamic equivalence, path compression, interval query, point update, range update, and lazy propagation.
  • Graphs: Graph definitions, storage methods, AOV networks, and topological sorting.

Preserved Notation Examples

The Chinese source contains mathematical notation and technical symbols. Examples preserved for cross-language lookup:

  • \(O(N\log N)\)
  • \(O(N)\)
  • \(O(1)\)
  • \(O(\log N)\)
  • \(N\)
  • \(O(N^2)\)
  • \(N/2\)
  • \(T(N)=O(f(N))\)
  • \(T\)
  • \(f\)

How to Use This Page

Use this English page as a quick map before reading the Chinese lecture note. The Chinese page contains the complete detailed content, formulas, examples, tables, and course structure. This companion page makes the topic discoverable to English visitors and gives Biying enough English context to explain what the note is about.