a. Calculate the theoretical time complexity by counting the number of basic operations. Multiplications and subtractions are considered here as basic operations. What do you think is the Big-Oh for the complexity? b. Use any tool (or by hand) to plot a graph of the theoretical time complexity. c. Implement the code in the language of your choice, and find the running time for several values of n (for instance, for n = 1000, 2000, 3000,...10000) and plot the results. (make sure not to have other applications running in the background. You can use different values for n as you see fit). Submit the full code as an appendix to your assignment. d. Using the two plotted graphs, comment on the growth rate of the theoretical time complexity in comparison with the actual running times.

Python Code

result = 0 for i in range(1, n): result = result * 2 * i for j in range(1, i+1): result = result - j