Question

Algorithms and Basic Data Structures

This part involves writing and testing code. You are to make an experiment with 3 sorting algorithms partially given on Blackboard: Insertion sort, Mergesort, Quicksort. First, create a positive integer array of 10000 (ten thousand) elements with random values in it. Then, run the algorithms on this array by recording their running times. That is, take note of the time just before the sorting starts, and just after the sorting finishes, and record the difference. For a complete experiment, do the following:


Perform the experiment on arrays of size 10000, 20000, 40000, 80000, 160000, 320000, where you select the pivot in Quicksort randomly. Record all the running times and plot them using a graph (for example with Excel). Interpret the results in a few sentences. How do you explain the success of Quicksort compared to Mergesort although both of them have the same asymptotic running time?


Again perform the experiment on sorted arrays (from the smallest to the largest) of size 10000, 20000, 40000, 80000, 160000, 320000, where you select the pivot in Quicksort as the first element of the part to be sorted. Record all the running times using a graph. Interpret the results in a few sentences.

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