Gain insights into algorithms and their implementation for problem-solving in Python. Learn about recursion, dynamic programming, greedy algorithms, and graph algorithms to enhance coding proficiency and problem-solving skills.

As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem-solving in Python.

Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursion, backtracking, dynamic programming, and greedy algorithms. You'll also learn about basic graph algorithms, depth-first search, shortest paths, minimum spanning trees, and all-pairs shortest paths. 

By the end of this course, you'll have acquired a wide range of skills that will significantly enhance your ability to solve problems efficiently in Python. Through this course, not only will you improve your coding skills, but you will also gain confidence in tackling complex problems.

Mastering Algorithms for Problem Solving in Python

# History of graphs            

A **graph** is a collection of pairs—pairs of integers, pairs of people, pairs of cities, pairs of stars, pairs of countries, pairs of scientific papers, pairs of web pages, pairs of game positions, pairs of recursive subproblems, and even pairs of graphs. Mirroring is the most common method for visualizing graphs; the underlying objects being paired are usually called *vertices* or *nodes*, and the pairs themselves are called *edges* or *arcs*, but in fact, the objects and pairs can be anything at all.


One of the earliest examples of graphs is road networks and maps thereof. Roman engineers constructed a network of more than 400,000 km of public roads across Europe, western and central Asia, and northern Africa during the height of the Roman empire. Travelers on the road network would carry itineraries, which were either simple lists or more pictorial representations of the landmarks and distances along various roads. The Tabula Peutingeriana, a 13th-century scroll depicting the entire *Roman cursus publicus*, is widely believed to be a medieval copy of a 5th-century revision of a 1st-century *itinerarium pictum*, commissioned during the reign of Augustus Caesar. The Peutinger Table is not a geographically accurate map—historians debate whether it qualifies as a
“map” at all!—but an abstract representation of the road network, similar to a modern subway map. Cities along each road are indicated by kinks in the curve representing that road; the names of these cities and the lengths of road segments between them are also indicated on the map. Thus, the map contains enough information to find the shortest route between any two cities in the 5th-century Roman empire. See the figure below.












Learn about the history and evolution of graph algorithms.

Getting Started

Introduction to Algorithm

Recursion

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

Introduction and History of Basic Graph Algorithms