Search⌘ K
Home
Courses
Mastering Algorithms for Problem Solving in Java

Solution: Minimum Spanning Trees

Explore how to update a minimum spanning tree in an undirected weighted graph when an edge's weight is reduced. Understand the algorithm that identifies paths and replaces heavier edges using depth-first search, and implement this efficiently in Java. This lesson enhances your problem-solving skills with graph algorithms and tree optimization techniques.

We'll cover the following...

Let's practice what we've learned so far.

Task

Suppose we are given both an undirected graph GG with weighted edges and a minimum spanning tree TT of GG. Provide code to update the minimum spanning tree when the weight of a single edge ee is decreased. We can follow the algorithm described below.

Logic building

Here’s the algorithm to update the minimum spanning tree TT when the weight of a single edge ee is decreased:

Algorithm

  • Identify the two nodes uu and vv that the edge ee connects.
  • Find the path PP in the minimum spanning tree TT
...