Python Data Structures and Algorithms

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

This is the main reference for my YouTube Channel, 2001 Engenharia in PT-BR

▶ Estrutura de Dados e Algoritmos em Python

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

Data Structures

In computer science, a data structure is a data organization, management, and storage format that enables efficient access and modification. 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.

Data structures are the building block for Computer Science and Software Engineering.

B - Beginner, A - Advanced

• B Linked List
• B Doubly Linked List
• B Array
• B Queue
• B Stack
• B Hash Table
• B Priority Queue
• B Dictionaries
• A Trie
• A Tree
  • A Binary Search Tree
  • A AVL Tree
  • A Red-Black Tree
  • A Segment Tree
  • A Fenwick Tree
• A Graph
• A Disjoint Set
• A Bloom Filter

Recursion

In computer science Recursion is a technique for solving problems where the solution to a particular problem depends on the solution to a smaller instance of the same problem.

B - Beginner, A - Advanced

• B Introduction to Recursion
• B Factorial Using Recursion
• B Fibonacci Using Recursion

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. Algorithms are always unambiguous and are used as specifications for performing calculations, data processing, automated reasoning, and other tasks.

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.

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(n2 )	100	10000	1000000
O(2n )	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

References

This project was based on

• JavaScript Algorithms and Data Structures