Question: Implement the following variations of quicksort algorithm: 1- Basic quicksort where the chosen pivot is the first element of an array. 2- Quicksort where the

Implement the following variations of quicksort algorithm:

1- Basic quicksort where the chosen pivot is the first element of an array.

2- Quicksort where the pivot is the median of three elements of an array (first, last, and middle).

3- Quicksort where the pivot is the median of three randomly chosen elements of an array.

* Generate large arrays (of size n=105 ) with different distributions reflecting the algorithms’ best, average, and worst cases.

* Fill in the following table and compare the algorithms’ efficiency theoretically and experimentally. Analyze the results and state your implications.

Best case (???) Average case (???) Worst case (???) Basic Quicksort Theoretical Experimental efficiency

Best case (???) Average case (???) Worst case (???) Basic Quicksort Theoretical Experimental efficiency efficiency (expected # (avg # of of operations operations) several for runs) Quicksort with pivot as median of first, last and middle elements Theoretical efficiency (expected # of operations) Experimental efficiency (avg # of operations for several runs) Quicksort with pivot as median of three randomly chosen elements Theoretical Experimental efficiency efficiency (expected # of operations) (avg # of operations for runs) several Best case (???) Average case (???) Worst case (???) Basic Quicksort Theoretical Experimental efficiency efficiency (expected # (avg # of of operations operations) several for runs) Quicksort with pivot as median of first, last and middle elements Theoretical efficiency (expected # of operations) Experimental efficiency (avg # of operations for several runs) Quicksort with pivot as median of three randomly chosen elements Theoretical Experimental efficiency efficiency (expected # of operations) (avg # of operations for runs) several

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