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Mastering Algorithms for Problem Solving in C++

Solution: Minimum Spanning Trees

Explore how to update a minimum spanning tree efficiently when the weight of an edge decreases. This lesson guides you to implement an algorithm in C++ using depth-first search and priority queues to adjust the tree, improving your practical skills in graph algorithms and enhancing your problem-solving abilities.

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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 uu and vv
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