Redundant Connection - Solution & Explanation

This approach utilizes the Union-Find (or Disjoint Set Union, DSU) data structure to detect cycles. The key operations in Union-Find are 'find', which determines the representative of a set, and 'union', which merges two sets. When processing each edge, we attempt to unite the vertices. If both vertices are already in the same set, a cycle is detected, and this edge is the redundant one.

This solution implements a Union-Find class with path compression and rank optimization to efficiently find and union nodes. By iteratively applying union operation on each edge, it detects the first edge causing a cycle, which is the redundant edge to be returned.

The DFS approach involves simulating the construction of the graph and utilizing DFS to detect cycles whenever a new edge is being added. If a cycle is detected upon adjacent traversal, that edge is the redundant one.

This solution constructs the graph incrementally while running DFS to check for paths from vertex u to vertex v before adding each edge. If the path exists, addition of the edge creates a cycle, thereby identifying it as redundant.