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Mastering Graph Algorithms

Gain insights into key graph algorithms, including depth-first search, shortest paths, and flow networks. Explore their applications and foundational role in advanced computing disciplines.

4.9

91 Lessons

15h

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LEARNING OBJECTIVES

An understanding of classical graph algorithms
The ability to think and visualize in terms of graph structures
An inside-out understanding of what makes each algorithm work the way it does
Cultivation of a broader perspective that informs other computing disciplines

Learning Roadmap

91 Lessons50 Quizzes

Introduction

Get familiar with the fundamentals and applications of graph algorithms across disciplines.

What Is This Course About?

Review: Asymptotic Notation and Math Prerequisites

Grasp the fundamentals of logarithms, running time, and big-O notation for algorithm analysis.

Getting Started with Logarithms

Food for Thought: Running Time

Running Time as a Function of Input Size

Comparing Running times

Big-O Notation

Ruminating on Constants in Big-O Notation

Some Useful Facts

A Big-O Drill

Leveraging the Proof by Contradiction Technique

Exercise: Order of Growth

Quiz: Big-O Notation

Working with Graphs

9 Lessons

Work your way through understanding and representing graphs, including adjacency matrices, lists, and special graph types.

Depth-First Search and Applications

16 Lessons

Grasp the fundamentals of Depth-First Search and its applications in graph traversal and analysis.

Prelude: Shortest Paths

7 Lessons

Explore shortest-path strategies, BFS for unweighted digraphs, and apply graph traversal concepts.

Single-source Shortest Paths in Weighted Digraphs

12 Lessons

Focus on solving the single-source shortest paths problem using various algorithms in weighted digraphs.

All Pairs Shortest Paths

5 Lessons

Practice using Johnson's and Floyd-Warshall algorithms for efficient all-pairs shortest paths.

Minimum Spanning Tree

12 Lessons

Learn how to use Minimum Spanning Trees via Prim's and Kruskal's algorithms effectively.

Flows

6 Lessons

Walk through network flows, the Ford-Fulkerson algorithm, and practical exercises.

10.

Matchings and Vertex Covers

11 Lessons

Examine matchings, vertex covers, the Ford-Fulkerson algorithm, and the Gale-Shapley algorithm.

11.

Conclusion

Grasp the fundamentals of graph algorithms' applications, utility, and practical significance in various fields.

Final Remarks

Use Simulated Annealing for the Traveling Salesman Problem

Project

Premium

Certificate of Completion

Showcase your accomplishment by sharing your certificate of completion.

Developed by MAANG Engineers

Every Educative lesson is designed by a team of ex-MAANG software engineers and PhD computer science educators, and developed in consultation with developers and data scientists working at Meta, Google, and more. Our mission is to get you hands-on with the necessary skills to stay ahead in a constantly changing industry. No video, no fluff. Just interactive, project-based learning with personalized feedback that adapts to your goals and experience.

ABOUT THIS COURSE

This technology-agnostic course will teach you about many classical graph algorithms essential for a well-rounded software engineer. You will begin with an introduction to the running-time analysis of algorithms and the representation and structure of graphs. You’ll cover the depth-first search algorithm and its many applications, like detecting cycles, topological sorting, and identifying cut-vertices and strongly connected components. You will then cover algorithms for finding shortest paths and minimum spanning trees. You’ll also learn about the Ford-Fulkerson algorithm and its use in finding a maximum flow and minimum cut in networks. Moreover, you will adapt it to find maximum matchings and minimum vertex covers in bipartite graphs. Finally, you will learn about the Gale-Shapley algorithm for finding stable matchings. The material in this course serves as a basis for other advanced algorithms, like parallel and distributed algorithms, and has many diverse applications in other computing disciplines.

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