Algorithms - Python

Repository with the implementation (in Python) and description of several computational, mathematical and statistical algorithms.

Algorithms

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.

1. Algorithm's Basics

• Greatest Common Divisor
• Fibonacci Serie
• Integer Factorization
• Tower of Hanoi
• Sorting Algorithm
• Changing Distribution

2. Divide and Conquer

• Binary Search
• Quick Sort
• Merge Sort

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

Contributing and Feedback

Any kind of feedback/criticism would be greatly appreciated (algorithm design, documentation, improvement ideas, spelling mistakes, etc...).

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.

Author

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

License

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