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Mastering Algorithms for Problem Solving in C++

Challenge: Minimum Spanning Trees

Explore how to update a minimum spanning tree when an edge weight decreases in a weighted undirected graph. Understand the step-by-step algorithm involving path search, edge comparison, and modification of the tree. Learn to implement this solution in C++ with attention to time complexity and efficient graph operations.

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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
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