📚 Algorithms in Python and Java

This repository contains implementations of classic algorithms in both Python and Java, starting with content from Tim Roughgarden’s Algorithms Illuminated and expanding to other sources over time.

It aims to provide clear explanations, step-by-step derivations, and performance analysis of fundamental algorithms.

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📦 Repository Structure

algorithms-in-python-and-java/
├── python/
│   ├── multiplication/
│   │   └── multiplication_algorithms_final.ipynb
│   └── sorting/
│       └── sorting_algorithms_top10.ipynb
├── java/
└── notes/

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📓 Notebooks

• multiplication_algorithms_final.ipynb
  📘 Multiplication Algorithms Comparison:

  • ✏️ Grade-School Multiplication
  • 🔁 Recursive Integer Multiplication (RecIntMult)
  • ⚡ Karatsuba Multiplication
  • 🚀 Toom-Cook 3-Way Multiplication (educational simple version)
  • 🌊 FFT-Based Multiplication (basic polynomial convolution view)

  Includes:

  • 📜 Mathematical derivations and intuition
  • 🧩 Full Python implementations
  • ⏱ Timing experiments with random integers
  • 📈 Log-log performance plots and complexity analysis

• sorting_algorithms_top10.ipynb
  📗 Sorting Algorithms Exploration:

  • 🧹 Simple Sorts (Insertion Sort, Shell Sort)
  • ⚔️ Divide and Conquer Sorts (Merge Sort, Quick Sort)
  • 🛠 Heap-Based Sorts (Heap Sort, IntroSort)
  • 🧮 Non-Comparison-Based Sorts (Counting Sort, Radix Sort, Bucket Sort)

  Includes:

  • 📜 Detailed algorithm descriptions with real-world examples
  • 🧩 Full Python implementations
  • ⏱ Benchmarking experiments from n = 100 to 1000
  • 📈 Log-log performance plots with fitted slopes for empirical complexity analysis

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🧠 Future Work

• Expanding into sorting, searching, graph algorithms, dynamic programming, etc.
• Adding Java implementations alongside Python.
• More educational content focused on learning algorithms deeply.

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🚀 Goal

Build a self-contained educational resource for students, researchers, and anyone interested in mastering algorithms both theoretically and practically.