Project 8: Complete Sorting Algorithm Collection

Implement and compare major sorting algorithms from TAOCP Vol 3.

Quick Reference

Attribute Value
Difficulty Advanced
Time Estimate 2-3 weeks
Language C
Prerequisites Arrays, analysis basics
Key Topics comparisons, stability, complexity

1. Learning Objectives

  1. Implement comparison and distribution sorts.
  2. Measure comparisons, swaps, and runtime.
  3. Compare empirical results to theoretical models.
  4. Understand stability and in-place tradeoffs.

2. Theoretical Foundation

2.1 Core Concepts

  • Comparison-based lower bounds.
  • Stability vs in-place memory usage.
  • Partitioning and merging.

2.2 Why This Matters

Sorting is central to algorithms; TAOCP provides rigorous analysis that you can validate empirically.

2.3 Historical Context / Background

Knuth classified sorting algorithms by their structural properties and cost models.

2.4 Common Misconceptions

  • “Quicksort is always fastest”: Not on all inputs.
  • “Stable and in-place are compatible”: Often not.

3. Project Specification

3.1 What You Will Build

A library with multiple sorting algorithms plus a benchmark harness.

3.2 Functional Requirements

  1. Implement insertion, selection, merge, quick, heap, radix.
  2. Provide comparator interface.
  3. Collect metrics (comparisons, swaps, time).
  4. Report results per input distribution.

3.3 Non-Functional Requirements

  • Correctness: Sorting results validated.
  • Reproducibility: Seeded data generators.
  • Usability: CLI benchmark runner.

3.4 Example Usage / Output

$ ./sortbench --algo quick --n 100000 --dist random
comparisons=1.38 n log n

3.5 Real World Outcome

You can demonstrate which algorithms perform best on different data distributions.

4. Solution Architecture

4.1 High-Level Design

┌──────────────┐     ┌──────────────┐     ┌──────────────┐
│ data gen     │────▶│ sorting impl │────▶│ metrics      │
└──────────────┘     └──────────────┘     └──────────────┘

4.2 Key Components

Component Responsibility Key Decisions
Sort funcs Implement algorithms common interface
Metrics count ops instrumentation
Generator input distributions random/ordered

4.3 Data Structures

typedef struct {
    size_t comparisons;
    size_t swaps;
} SortMetrics;

4.4 Algorithm Overview

Key Algorithm: Quicksort

  1. Partition around pivot.
  2. Recurse on subarrays.

Complexity Analysis:

  • Average O(n log n), worst O(n^2).

5. Implementation Guide

5.1 Development Environment Setup

gcc --version

5.2 Project Structure

project-root/
├── src/sorts.c
├── src/bench.c
├── include/
└── Makefile

5.3 The Core Question You’re Answering

“Which sorting algorithm is best for which kind of input?”

5.4 Concepts You Must Understand First

  • Big-O and lower bounds
  • Stability and in-place constraints
  • Partitioning and merging logic

5.5 Questions to Guide Your Design

  1. How will you measure comparisons consistently?
  2. What distributions should you test?
  3. How will you ensure fairness across algorithms?

5.6 Thinking Exercise

Explain why comparison sorts cannot beat n log n in worst case.

5.7 The Interview Questions They’ll Ask

  1. When is mergesort preferable to quicksort?
  2. What makes radix sort different?
  3. What is stability and why does it matter?

5.8 Hints in Layers

Hint 1: Implement insertion and selection first. Hint 2: Add quick and merge. Hint 3: Add heap and radix.

5.9 Books That Will Help

Topic Book Chapter
Sorting TAOCP Vol 3 Ch. 5

5.10 Implementation Phases

Phase 1: Foundation (1 week)

  • Basic sorts + correctness tests.

Phase 2: Core Functionality (1 week)

  • Add advanced sorts and metrics.

Phase 3: Polish & Edge Cases (3-4 days)

  • Benchmark harness and reports.

5.11 Key Implementation Decisions

Decision Options Recommendation Rationale
Metrics time only vs op counts op counts theory comparison

6. Testing Strategy

6.1 Test Categories

Category Purpose Examples
Correctness sorted output random arrays
Edge cases duplicates repeated values
Stability stable sorts key+index pairs

6.2 Critical Test Cases

  1. Already sorted input.
  2. Reverse sorted input.
  3. Many duplicates.

6.3 Test Data

Random, sorted, reverse, nearly sorted

7. Common Pitfalls & Debugging

7.1 Frequent Mistakes

Pitfall Symptom Solution
Wrong comparator incorrect order standardize compare
Partition bug infinite recursion test small arrays
Overflow in indices crash size_t and bounds checks

7.2 Debugging Strategies

  • Add asserts for partition invariants.
  • Verify after each sort.

7.3 Performance Traps

Poor pivot choice yields worst-case quicksort.

8. Extensions & Challenges

8.1 Beginner Extensions

  • Add shell sort variants.

8.2 Intermediate Extensions

  • Implement introsort.

8.3 Advanced Extensions

  • Implement external sorting.

9. Real-World Connections

  • Databases and systems rely on sorting for joins and indexing.

10. Resources

  • TAOCP Vol 3 Chapter 5.

11. Self-Assessment Checklist

  • I can explain complexity tradeoffs.
  • Benchmarks align with theory.

12. Submission / Completion Criteria

Minimum: Implement 3 sorts with tests. Full: Full collection + benchmarking. Excellence: Introsort or external sort.

This guide was generated from LEARN_TAOCP_DEEP_DIVE.md. For the complete learning path, see the parent directory README.