Graph algorithms are the core of many real-world applications of computer science,  such as automotive navigation or routing in computer networks. They’re also a common subject in coding interviews at top-tier tech companies.
 
In this course, we’ll learn about the basic concepts of graph theory and how to represent graphs as data structures in code. We’ll study essential graph algorithms such as depth-first search or Dijkstra's algorithm to traverse graphs and find shortest paths. Finally, we’ll learn to solve more complex optimization problems on graphs, such as matching and network flow problems.

Learn Graph Algorithms in C++

What is the worst-case runtime of Kruskal's algorithm?

What is the worst-case runtime of Kruskal’s algorithm?

There is no other spanning tree $T'$ with $w(T') = w(T)$.

Adding an edge to $T$ would introduce a cycle.

Let $T$ be a minimum spanning tree of a weighted, undirected, connected graph $G = (V, E, w)$. Which of the following statements are true? Select all that apply.

Let <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi></mrow><annotation encoding="application/x-tex">T</annotation></semantics></math>T be a minimum spanning tree of a weighted, undirected, connected graph <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mo stretchy="false">(</mo><mi>V</mi><mo separator="true">,</mo><mi>E</mi><mo separator="true">,</mo><mi>w</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G = (V, E, w)</annotation></semantics></math>G=(V,E,w). Which of the following statements are true? Select all that apply.

Introduction

Graph Representations

Graph Traversal

Shortest Paths

Spanning Trees

Flow Problems

Conclusion

Appendix

Quiz: Spanning Trees