Mastering Graph Algorithms - AI-Powered Learning for Developers

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.

Beginner

91 Lessons

15h

Certificate of Completion

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.

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Explanations

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This course includes

32 Playgrounds

50 Quizzes

This course includes

32 Playgrounds

50 Quizzes

Course Overview

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...Show More

What You'll Learn

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

What You'll Learn

An understanding of classical graph algorithms

Course Content

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

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

Graphs Adjacency Matrix Adjacency List Directed Graphs Weighted Graphs Subgraphs, Paths, Cycles and Components Trees Bipartite Graphs Quiz: Working with Graphs

Depth-First Search and Applications

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

Depth-First Search Edge Classification in Directed Graphs

Exercise: Classify Edges of a Directed Graph Edge Classification in Undirected Graphs Exercise: Classify Edges of an Undirected Graph Identifying Cut-Vertices Exercise: Identify Cut-Vertices Topological Sorting Exercise: Sort the Vertices in Topological Order Thought Exercise: Detecting Cycles in Directed Graphs Characterizing Strongly Connected Components Tarjan’s Algorithm Exercise: Practice Tarjan’s Algorithm The Kosaraju-Sharir Algorithm Exercise: Practice the Kosaraju-Sharir Algorithm Quiz: DFS and Applications

Prelude: Shortest Paths

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

The Shortest-Paths Problem Reflections on Shortest Paths Quiz: Shortest Paths Terminology Breadth-First Search Shortest Paths in Unweighted Digraphs Exercise: Print Shortest Path Quiz: BFS and Shortest Paths

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

1 Lesson

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

Use Simulated Annealing for the Traveling Salesman Problem

Project

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