Advanced Topic 38 of 51 Algorithms
Minimum Spanning Tree
Cheapest set of edges connecting all vertices.
How it works
An MST connects all vertices of a weighted undirected graph with minimum total edge weight and no cycles (V−1 edges). The cut property justifies greedy algorithms.
Where it is used
Designing cable or road networks, clustering.
Common pitfall
Only defined for connected graphs; it is not the same as shortest paths.
Where it fits in the course
Minimum Spanning Tree is topic 38 of 51 in Algorithms, rated Advanced. It follows A* Search. The next topic is Kruskal's Algorithm.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Algorithms quiz.
- Explore the Graph Traversal visualizer: BFS, DFS and Dijkstra on a weighted graph.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Minimum Spanning Tree?
Cheapest set of edges connecting all vertices. It belongs to Algorithms and is an advanced-level topic.
Where do people use Minimum Spanning Tree?
Designing cable or road networks, clustering.
What is the most common mistake with Minimum Spanning Tree?
Only defined for connected graphs; it is not the same as shortest paths.
What should I learn before this topic?
Start with A* Search, the topic just before it in Algorithms.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Algorithms quiz. You can also explore Graph Traversal in the Visual Lab.
Is Minimum Spanning Tree hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn Minimum Spanning Tree?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Minimum Spanning Tree?
A* Search, Kruskal's Algorithm, Floyd-Warshall Algorithm are closely connected. The full list is in the related topics section of this page.
What should I study after Minimum Spanning Tree?
Continue with Kruskal's Algorithm, the next topic in Algorithms.
Related topics
- A* Search (Algorithms)
- Kruskal's Algorithm (Algorithms)
- Floyd-Warshall Algorithm (Algorithms)
- Prim's Algorithm (Algorithms)
- Tree Traversals (Data Structures)