Union Find 3 - Linked List Running Time Analysis

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In this video we analyze the running time of the Linked List implementation of Union-Find. We also discuss the amortized time of several consecutive union operations.
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4:45 Won't new nodes added at the second last step (n/4 + n/4) be touched only once at the last (n/2 + n/2)? In that case, why we sum from i = 1 to n with the same K_i?

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