Python Algorithms Course

Free hands-on course with the implementation (in Python) and description of several computational, mathematical and statistical algorithms.

Although it is not intended to have the formal rigor of a book, we tried to be as faithful as possible to the original algorithms and methods, only adding variants, when these were necessary for didactic purposes.

Quick Start

The best way to get the most out of this course is to carefully read each selected problem, try to think of a possible solution (language independent) and then look at the proposed Python code and try to reproduce it in your favorite IDE. If you already have knowledge of the Python language, then you can go directly to programming your solution and then compare it with the one proposed in the course.

If you want to play with these notebooks online without having to install any library or configure hardware, you can use the following service:

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What is an algorithm?

In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation.

Contents

1. Algorithm's Basics

• Greatest Common Divisor
• Fibonacci Serie
• Integer Factorization
• Tower of Hanoi
• Sorting Algorithm
• Convex Hull - Greedy
• Changing Distribution

2. Divide and Conquer

• Binary Search
• Quick Sort
• Merge Sort
• Convex Hull - Recursive

3. Graphs

• Graph or Undirected Simple Graph
• Graph Traversal
• Minimum Spanning Tree
• Eulerian Circuit and Path
• Shortest Path
• All-Pairs Shortest Path
• Graph Coloring

4. Dynamic Programming

• Binomial Coefficient
• World Championship problem
• Coin Change problem
• The Knapsack problem
• Longest Common Subsequence problem
• Sequence Alignment problem

5. Probabilistic Algorithms

• Pseudo-Random Number Generator
• Primality Test
• Monte Carlo Simulation
• Metropolis-Hastings Algorithm
• Las Vegas Algorithm
• Law of Large Numbers

6. Similarity Functions

• Common Similarity functions
• Manual examples
• Sklearn examples

7. Chaotic Systems

• Chaotic Systems intro
• Fractals

8. Cellular Automata

• Linear Cellular Automata (LCA)
• Reversible Linear Cellular Automata (RLCA)

Python Dependencies

  conda install -c anaconda numpy
  conda install -c anaconda pymc
  conda install -c anaconda networkx

Bibliography

• G. Brassard, P. Bratley. (2006). Fundamentals of Algorithmics. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
• R.C.T. Lee, S.S. Tseng, R.C. Chang, Y.T.Tsai. (2005). Introduction to the Design and Analysis of Algorithms. A Strategic Approach. Asia: McGraw-Hill Education.
• K. Rosen. (2012). Discrete Mathematics and Its Applications. NewYork, NY: McGraw-Hill Education; Edición: 7th.

Contributing and Feedback

Any kind of feedback/suggestions would be greatly appreciated (algorithm design, documentation, improvement ideas, spelling mistakes, etc…). If you want to make a contribution to the course you can do it through a PR.

Documentation

Please read the contributing and code of conduct documentation.

Author

• Created by Andrés Segura-Tinoco
• Created on May 17, 2019

License

This project is licensed under the terms of the MIT license.