Weighted quick-union with path compression. Modify weighted quick-union (algorithm 1.5) to implement path compression, as described in exercise 1. 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.
Exercise 1
Quick-union with path compression. Modify quick-union to include path compression, by adding a loop to find() that links every site on the path from p to the root. Give a sequence of input pairs that causes this method to produce a path of length 4. Note : The amortized cost per operation for this algorithm is known to be logarithmic.
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