minimun-spanning-trees

What problem does it solve?

Facilitates solving, proving, implementing, or reviewing minimum spanning-tree problems by emphasizing safe edges, cut properties, light edges, and MST update reasoning. It follows formal proof style and data-structure contracts as used in standard textbooks.

Core Features & Use Cases

• Kruskal's algorithm, Prim's algorithm, and Boruvka-style contractions for constructing MSTs.
• Use of union-find for maintaining forest components and supporting fast connectivity checks.
• Dynamic MST updates, second-best MST computation, and bottleneck analysis for practical problem solving.
• Guidance on modeling graphs to ensure connectivity and correct handling of multi-edges and ties.

Quick Start

Run Kruskal or Prim on a connected weighted graph to construct an MST and verify the cut and cycle certificates.