Exercise I For each of the following three code snippets (corresponding Python code is list in the Appendix at the end of this assignment):

1. Calculate the theoretical time complexity by counting the number of subtractions as basic operation. What do you think is the Big-Oh for the complexity? Prove how did you get the big-Oh only for Code Snippet 1.
2. Plot a graph of the theoretical time complexity.
3. 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.
4. Using the two plotted graphs, comment on the growth rate of the theoretical time complexity in comparison with the actual running times.

Code Snippet 1.

NegativeSum = 0;

for (i = 1; i <= n; i++)

NegativeSum = NegativeSum - i;

Part Snippet 2.

Negative3Sum = 0;

for (i = 1; i <= 3*n; i++)

Negative3Sum = Negative3Sum i ;

Part Snippet 3.

NegativeSubSum = 0;

for (i = 1; i <= n; i++)

for (j = 1; j <= i; j++)

NegativeSubSum = NegativeSubSum - j;

Appendix A (Python code for the code snippets in Question I)

1. Code Snippet 1

NegativeSum = 0

for i in range(1, n+1):

NegativeSum = NegativeSum - i

2. Code Snippet 2

Negative3Sum = 0

for i in range(1, (n*3)+1):

Negative3Sum = Negative3Sum - i

3. Code Snippet 3

NegativeSubSum = 0

for i in range(1, n+1):

for j in range(1, i+1):

NegativeSubSum = NegativeSubSum - j