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In Algorithms 4th Ed. textbook there is the below question, how can it be solved

ID: 638439 • Letter: I

Question

In Algorithms 4th Ed. textbook there is the below question, how can it be solved also explain the provided answer?

1.5.13 Weighted quick-union with path compression. Modify weighted quick-union (Algorithm 1.5) to implement path compression, as described in Exercise 1.5.12. Give a sequence of input pairs that causes this method to produce a tree of height 4. Note : The amortized cost per operation for this algorithm is known to be bounded by a function known as the inverse Ackermann function and is less than 5 for any conceivable practical value of N.

Explanation / Answer

Union