1579. Remove Max Number of Edges to Keep Graph Fully Traversable || LeetCode POTD || HINDI

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Approach:-
Initialization:
We initialize two DSU instances: one for Alice and one for Bob.
We also sort the edges such that the edges that can be used by both Alice and Bob (type 3) are processed first. This ensures we maximize the shared usage of these edges.
Processing Edges:
We iterate through the edges and use the union operation to connect nodes.
If an edge connects two components (nodes) that are already connected, it can be considered redundant and counted as a removable edge.
We handle type 3 edges first, which both Alice and Bob can use, followed by type 2 (Bob only) and type 1 (Alice only).
Checking Connectivity:
After processing all edges, we check if both Alice and Bob have connected all nodes (i.e., each has used n-1 edges). If either hasn't, it's impossible to connect all nodes, and we return -1.
Time and Space Complexity
Time Complexity:
Sorting the edges takes O(m log m), where m is the number of edges.
Union and find operations in DSU are nearly constant time, O(α(n)), where α is the inverse Ackermann function.
Therefore, the overall time complexity is O(m log m + m α(n)).
Space Complexity:
Storing the DSU structures for Alice and Bob takes O(n) each.
Additional space for storing the edges is O(m).
Hence, the overall space complexity is O(n + m).
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1579. Remove Max Number of Edges to Keep Graph Fully Traversable
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Code link:- leetcode.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable/solutions/5391610/java-solution-explained-in-hindi/