/python-algorithms

This repository contains Python based examples of many popular algorithms and data structures.

MIT LicenseMIT

python-algorithms

I originally created this as a short to-do list of study topics for my personal use while in campus, but eventually to be used by my community DSC Kabarak University You probably won't have to study as much as I did. Anyway, feel free to contribute to anything you might feel to have been left out.

The items listed here should be a source of inspiration for your venture into deep computer science concepts in algorithms and data structure

Best of luck to you!

What is it?

In preparation for this study plan, I have been using Introduction to Algorithms [CLRS09] by four devilishly handsome fellows. The book is commonly called “CLRS,” after the initials of the authors. Written in pseudocodes, I have been doing the implimentations in python programmming language, this has given me an in depth understanding of the topics covered

This is my multi-month study plan for going from web developer(self taught) to software engineer. It is meant for anyone starting out on algos or those switching from software/web development to software engineering (where computer science knowledge is required).

Motivation

Why use it?

When I started this project, I didn't know a stack from a heap, didn't know Big-O anything, anything about trees, or how to traverse a graph. If I had to code a sorting algorithm, I can tell you it wouldn't have been very good. Every data structure I've ever used was built into the language, and I didn't know how they worked under the hood at all. I've never had to manage memory unless a process I was running would give an "out of memory" error, and then I'd have to find a workaround. I've used a few multidimensional arrays in my life and some of associative arrays, but I've never created data structures from scratch.

It's a long plan. It may take you months. If you are familiar with a lot of this already it will take you a lot less time.

How to use it?

This repository contains Python based examples of many popular algorithms and data structures.

Each algorithm and data structure has its own separate README with related explanations and links for further reading

☝ Note that this project is meant to be used for learning and researching purposes only and it is not meant to be used for production.

Don't feel you aren't smart enough

Algorithms

An algorithm is an unambiguous specification of how to solve a class of problems. It is a set of rules that precisely define a sequence of operations.

Algorithms by Paradigm

An algorithmic paradigm is a generic method or approach which underlies the design of a class of algorithms. It is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program.

Data Structures

A data structure is a particular way of organizing and storing data in a computer so that it can be accessed and modified efficiently. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data.

References

▶ Data Structures and Algorithms on YouTube

Big O Notation

Big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows. On the chart below you may find most common orders of growth of algorithms specified in Big O notation.

Big O graphs

Source: Big O Cheat Sheet.

Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.

Big O Notation Computations for 10 elements Computations for 100 elements Computations for 1000 elements
O(1) 1 1 1
O(log N) 3 6 9
O(N) 10 100 1000
O(N log N) 30 600 9000
O(N^2) 100 10000 1000000
O(2^N) 1024 1.26e+29 1.07e+301
O(N!) 3628800 9.3e+157 4.02e+2567

Data Structure Operations Complexity

Data Structure Access Search Insertion Deletion Comments
Array 1 n n n
Stack n n 1 1
Queue n n 1 1
Linked List n n 1 n
Hash Table - n n n In case of perfect hash function costs would be O(1)
Binary Search Tree n n n n In case of balanced tree costs would be O(log(n))
B-Tree log(n) log(n) log(n) log(n)
Red-Black Tree log(n) log(n) log(n) log(n)
AVL Tree log(n) log(n) log(n) log(n)
Bloom Filter - 1 1 - False positives are possible while searching

Array Sorting Algorithms Complexity

Name Best Average Worst Memory Stable Comments
Bubble sort n n2 n2 1 Yes
Insertion sort n n2 n2 1 Yes
Selection sort n2 n2 n2 1 No
Heap sort n log(n) n log(n) n log(n) 1 No
Merge sort n log(n) n log(n) n log(n) n Yes
Quick sort n log(n) n log(n) n2 log(n) No Quicksort is usually done in-place with O(log(n)) stack space
Shell sort n log(n) depends on gap sequence n (log(n))2 1 No
Counting sort n + r n + r n + r n + r Yes r - biggest number in array
Radix sort n * k n * k n * k n + k Yes k - length of longest key

Overview

Introduction(Week 1 - 5)

  • Growth of functions
  • Divide and Conquer
  • Probabilistic Analysis and Randomized Algorithms

Sorting and Order Statistics(Week 6 - 9)

  • Heapsort
  • Quicksort
  • Sorting in Linear time
  • Medians and order statistics

Data Structures(Week 10 - 14)

  • Elementary Data Structures
  • Hash Tables
  • Binary Search Trees
  • Red-Black Trees
  • Augmenting Data Structures

Advanced Design and Analysis Technique(Week 15- 17)

  • Dynamic Programming
  • Greedy Algorithms
  • Amortized Analysis

Advanced Data Structures(Week 18 - 21)

  • B-Trees
  • Fibonacci Heaps
  • Van Emde Boas Trres
  • Data Structures for Disjoint Sets

Graphs and Algorithms(Week 22 - 26)

  • Elementary Graphs and Algorithms
  • Minimum Spanning Trees
  • Single-Source Shortest Paths
  • All-Pairs Shortest Paths
  • Maximum Flow

Selected Topics(Week 27 - 35)

  • Multithread Algorithms
  • Matrix Operations
  • Linear Programming
  • Polynomial and the FFT
  • Number-Theoretic Algorithms
  • String Matching
  • Computational Geometry
  • Np-Completeness
  • Approximation Algorithms