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CSC 263H               Tutorial Outline for Week 11             Winter 2004
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Disjoint Sets
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(a) Trace through at least three different sequences of operations on
    Disjoint Sets implemented using the various data structures described
    in lecture, to make sure you understand each one correctly.

(b) Prove that when using trees with "union-by-weight" to implement
    Disjoint Sets, the maximum height of a tree with n nodes is O(log n).
    (Hint: use induction on the height of the tree to prove a lower bound
    on the number of nodes contained in any tree of height h, and use this
    result to conclude what you need.)