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This approach utilizes the Union-Find (or Disjoint Set Union, DSU) data structure to manage the connectivity of nodes. The critical idea is to process edge types in a specific order to ensure that both Alice and Bob can fully traverse the graph while maximizing the number of removable edges:
Time Complexity: O(E * α(n)), where E is the number of edges and α(n) is the inverse Ackermann function, effectively constant.
Space Complexity: O(n) for storing the disjoint sets for both Alice and Bob.
1class DSU:
2 def __init__(self, n):
3 self.parent = list(range(n))
4 self
Using Python, the solution constructs a DSU class for the disjoint set operations. The method maxNumEdgesToRemove loops over the edge list and processes each edge list appropriately using the union-find mechanism, giving priority to edges of type 3.
By calculating which edges are genuinely necessary to maintain full connectivity, it retains a count of saved_edges (i.e., the redundant edges). The final graph configurations for Alice and Bob must show each is completely connected for the operation to succeed (i.e., both DSUs must show only one set when checked).