Doubling test for Erdos-Renyi model. Develop a performance-testing client that takes an int value T from the command line and performs T trials of the following experiment: Use your client from exercise 1 to generate random connections, using UF to determine connectivity as in our development client, looping until all sites are connected. For each N, print the value of N, the average number of connections processed, and the ratio of the running time to the previous. Use your program to validate the hypotheses in the text that the running times for quick-find and quick-union are quadratic and weighted quick-union is near-linear.
Exercise 1
Random connections. Develop a UF client ErdosRenyi that takes an integer value N from the command line, generates random pairs of integers between 0 and N-1, calling connected() to determine if they are connected and then um'on() if not (as in our development client), looping until all sites are connected, and printing the number of connections generated. Package your program as a static method count() that takes N as argument and returns the number of connections and a main() that takes N from the command line, calls count(), and prints the returned value.
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