deals three sorting algorithms: Insertion-Sort, Quick -Sort and Merge-Sort. comparison with real time cpu usage

The assignment aims to develop your insight into the performance of algorithms. You shall look at both the actual running time of algorithms (in milliseconds of CPU usage) and the complexity of algorithms (in terms of the number of operations performed). The main emphasis is not so much on coding but is on understanding the performance of the algorithms and why they perform well and poorly on different inputs. The assignment deals three sorting algorithms: Insertion-Sort, Quick -Sort and Merge-Sort. Part 1 . Computing Running Time in Milli Seconds Perform timing analysis on the three sorting algorithms on the various types of lists above (random, ascending, descending and few items). You should run each sorting algorithm on the various types of lists of increasing lengths. The actual lengths of the lists for realistic timing in milliseconds depend (of course) on the speed of your processor. A maximum length of 5,000 or 10,000 may be appropriate, but on slower processors this may be too large. Plot the count of the number of operations against the length of the lists. Part 2. Counting the Number of Operations This task measures the performance of algorithms by counting how many operations are executed during processing. This is the time complexity of an algorithm. Count the order operation by which we compare elements. Modify your sorting algorithms to count the number of comparison operations performed. Run the modified algorithms on the same lists as for the timing analysis and plot the count of the number of operations against the length of the lists. How does it compare to the timing analysis? Part 3: Interpretation of Results Interpret the plots of results in Part 2. You will need to explain the shape of the graphs. Looking at the timing graphs for random lists, clearly some algorithms grow slower than others as the size of the input increases. For example: are they linear - a straight line, quadratic - grow as n2, cubic n3, or linear-logarithmic nlog(n), etc., where n is the size. Why is this? Also consider the behavior on the special forms of lists. Explain each of these and compare them to the behavior on the random lists.