Data Structures and Algorithms · Graphs

Minimum spanning trees

The cheapest set of edges that connects every vertex with no cycles.

Also known as: MST, Kruskal's algorithm, Prim's algorithm.

Start a lesson on Minimum spanning trees

Learn first

• Union-find: A structure that tracks which elements belong to the same group and merges groups quickly.
• Heaps and priority queues: A tree-shaped structure that always keeps the smallest, or largest, element quick to find.

Leads to

• Greedy algorithms: Making the locally best choice at every step and trusting it leads to a globally best answer.

Related topics

• Dijkstra's algorithm: Finding the cheapest path from one vertex to all others when no edge weight is negative.
• Greedy algorithms: Making the locally best choice at every step and trusting it leads to a globally best answer.