Consider the computer algorithm for percolation described in Section 16.5, but suppose that upon the addition of an edge between two clusters we relabel not the smaller of the two clusters but one or the other chosen at random. Show by an argument analogous to the one in Section 16.5 that the worst-case running time of this algorithm is O(n^2), which is substantially worse than the O(n logn) of the algorithm that always relabels the smaller cluster. | Numerade
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