Given a disjoint-set forest with N elements, what is the maximum height of the trees in the forest after M union operations if union by rank and path compression techniques are used?
(A)
O(M)
(B)
O(logM)
(C)
O(N)
(D)
O(N + M)
Answer: (B)
Explanation:
Using union by rank and path compression, the maximum height of the trees in the forest after M union operations is logarithmic with respect to M, resulting in a time complexity of O(log M).
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