Unit 3: Fundamental Data Structures

This is an archived version of this module from Winter 2024-25.

This unit covers fundamental data structures:

• stacks, queues, and resizable arrays
• priority queues and binary heaps
• binary search trees
• hash tables

Learning outcomes

1. Understand and demonstrate the difference between abstract data type (ADT) and its implementation
2. Be able to define the ADTs stack, queue, priority queue and dictionary/symbol table
3. Understand array-based implementations of stack and queue
4. Understand linked lists and the corresponding implementations of stack and queue
5. Know binary heaps and their performance characteristics
6. Understand binary search trees and their performance characteristics
7. Know high-level idea of basic hashing strategies and their performance characteristics

About this unit

This unit is a recap of topics that you will have previously seen in a first algorithms and data structures module, to bring you all on the same page.

In case you have never seen the material before, the brief summary I give in the context of this module will not suffice to replace such a module. You are highly encouraged to learn more in depth about these gems of computer science. The material below for further reading and sources will help you get started.

Material

• slides

• lecture notes

• Video 3-0 (2024-10-28): §3.0 word-RAM vs Python & Java

• Video 3-1 (2024-10-28): §3.1 ADTs, Stacks and Queues

• Video 3-2 (2024-10-28): §3.2 Resizable arrays

• Video 3-3 (2024-10-28): §3.3 Priority queues & binary heaps

• Video 3-4 (2024-10-28): §3.4 Operations on binary heaps

• Video 3-5 (2024-10-29): §3.5 Symbol tables

• Video 3-6 (2024-10-29): §3.6 Binary search trees

• Video 3-7 (2024-10-29): §3.7 Ordered symbol tables

• Video 3-8 (2024-10-29): §3.8 Balanced binary search trees

• Video 3-9 (2024-11-04): §3.9 Hashing recap

Further reading and sources

The sections on stacks, queues, and symbol tables follow the book

• Sedgewick, Wayne: Algorithms 4th ed (2011), Pearson
• Algorithms 4th ed booksite

The presentation of resizable arrays (including deamortized and optimal-space versions), priority queues and heaps is my own. The amortized analysis of the resizable arrays is spelled out in detail in my blog post:

• Amortized analysis of resizing-array stacks

The hashing summary follows our book, which (like Sedgewick and Wayne) has complete Java implementations of the discussed data structures.

• Nebel, Wild: Entwurf und Analyse von Algorithmen (2018), Springer Vieweg

For a lovely illustration of how memory management and pointers can be implemented conceptually, I recommend this:

• TREPL

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