LearnViz CompSci
Home / Learn / Algorithms / Kruskal's Algorithm

Advanced Topic 39 of 51 Algorithms

Kruskal's Algorithm

MST built by adding lightest edges avoiding cycles.

How it works

Kruskal's algorithm sorts all edges by weight and adds them one by one to the growing forest, skipping any edge that would create a cycle. A disjoint set union structure checks quickly whether two endpoints are already connected. Time is dominated by sorting, O(E log E), and it stops after V minus 1 edges have been accepted.

Step-by-step walkthrough

  1. Sort all edges by weight.
  2. Take the lightest edge, it joins two components.
  3. Add the next lightest edge if it does not form a cycle.
  4. Skip an edge that would close a cycle, found with union-find.
  5. Stop after V minus 1 edges, the tree is a minimum spanning tree.

Where it is used

Network design, clustering through single-linkage, approximating Steiner trees and building minimum spanning forests on sparse graphs use Kruskal's algorithm. It works naturally on an edge list.

Common pitfall

Forgetting to use union-find, or doing cycle checks with repeated DFS, makes it slow. Sorting by the wrong key or not sorting stably can change which of equal-weight trees is found. On very dense graphs Prim's algorithm can be faster. Make sure vertices are indexed consistently for the DSU.

Where it fits in the course

Kruskal's Algorithm is topic 39 of 51 in Algorithms, rated Advanced. It follows Minimum Spanning Tree. The next topic is Prim's Algorithm.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Kruskal's Algorithm?
MST built by adding lightest edges avoiding cycles. It belongs to Algorithms and is an advanced-level topic.
Where do people use Kruskal's Algorithm?
Network design, clustering through single-linkage, approximating Steiner trees and building minimum spanning forests on sparse graphs use Kruskal's algorithm.
What is the most common mistake with Kruskal's Algorithm?
Forgetting to use union-find, or doing cycle checks with repeated DFS, makes it slow.
What should I learn before this topic?
Start with Minimum Spanning Tree, 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.
Is Kruskal's Algorithm 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 Kruskal's Algorithm?
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 Kruskal's Algorithm?
Minimum Spanning Tree, Prim's Algorithm, A* Search are closely connected. The full list is in the related topics section of this page.
What should I study after Kruskal's Algorithm?
Continue with Prim's Algorithm, the next topic in Algorithms.

Related topics