Unit 3: Efficient Sorting – The Power of Divide & Conquer

This is an archived version of this module from Fall 2022.
Click here for the current iteration.

This unit covers

• mergesort and quicksort
• counting sort
• comparions lower bound for sorting
• adaptive sorting
• further divide & conquer algorithms

Learning outcomes

1. Know principles and implementation of mergesort and quicksort.
2. Know properties and performance characteristics of mergesort and quicksort.
3. Know the comparison model and understand the corresponding lower bound.
4. Understand counting sort and how it circumvents the comparison lower bound.
5. Know ways how to exploit presorted inputs.

Material

• slides
• lecture notes

Part I – The Basics

• Video 3-1 (2022-10-12): §3.0 Sorting introduction

• Video 3-2 (2022-10-12): §3.1 Mergesort

• Video 3-3 (2022-10-17): §3.1 Mergesort analysis

• Video 3-4 (2022-10-17): §3.2 Quicksort

• Video 3-5 (2022-10-19): §3.3 Comparison-based lower bound

• Video 3-6 (2022-10-19): §3.4 Integer sorting

Part II – Exploiting presortedness

• Video 3-7 (2022-10-19): §3.5 Adaptive sorting & Peeksort

• Video 3-8 (2022-10-19): §3.6 Python’s list sort & Powersort

Part III – Divide & conquer beyond sorting

• Video 3-9 (2022-10-24): §3.7 Order statistics, quickselect, median of medians

• Video 3-10 (2022-10-24): §3.8 Further divide & conquer algorithms

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Further reading and sources

More elementary sorting methods are described in detail in Algorithms 4th ed.

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

The exposition of adaptive sorting is my own and based on several sources:

• Tim Peters’s description of CPython’s list.sort algorithm
• Munro, Wild: Nearly Optimal Mergesorts, ESA 2018
• Cawley Gelling, Nebel, Smith, Wild: Multiway Powersort, preprint
• Gaurav Sen: Tim sort explained, Part 1, Part 2, Part 3, Part 4.
  Sequence of videos explaining Timsort’s other tricks (prior to adopting powersort’s merge rules).

The presentation of quickselect and the median-of-medians algorithm is inspired by material prepared for the module

• Data Structuring and Data Management, University of Waterloo

The other material of Part III is based on

• Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms 3rd ed (2009), MIT Press

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Unit 2  ⋅  Syllabus  ⋅  Unit 4