Performance of W-Union / PC-Find

• The time complexity of PC-Find is O(log n).

• An up tree formed by W-Union of height h has at least 2h nodes. Inductive Proof.

h+1

h

Weight(T2) > 2h (ind. hyp.)

Weight(T1) > Weight(T2)

> 2h

Weight(T) > 2h +2h =2h+1

T1

T2

T

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