Challenge: Minimum Spanning Trees

Task

Suppose we’re given both an undirected graph $G$ with weighted edges and a minimum spanning tree $T$ of $G$. Provide code to update the minimum spanning tree when the weight of a single edge $e$ is decreased. We can follow the algorithm described below.

Logic building

Here’s the algorithm to update the minimum spanning tree $T$ when the weight of a single edge $e$ is decreased:

Algorithm

• Identify the two nodes $u$ and