Do your measurements provide evidence about the time complexity of these operations?

MIST.3050
Homework 9
In this assignment, you will write a program to test the performance of three operations
1. dictionary lookup using key (d[key])
2. list lookup, i.e. finding the index of the first occurrence of a value (lst.index(v))
3. list sort (sorted(lst))
Before writing any code, think about this question:
What is the time complexity of each operation? Assuming Python adopts the most efficient
implementation.
[ Hint: Choose from O(1), O(n), O(n log(n) ), O(n^2) ]
Now, write a program to test the performance of each operation using five problem sizes:
1K, 10K, 100K, 1M, 10M
Use random.sample() to generate unique values in random order. For example.
L=random.sample(range(10), 10)
will assign L a list of size 10 with values 0 to 9, ordered randomly.
For the test dictionaries, you may make each entry’s value the same as the key using a technique
shown in the following example:
d= dict(zip(L,L))
In the example, the dictionary d will have keys and values taken from the two lists passed to the
zip function.
An example output the program is shown in Figure 1. For dictionary lookup: simply test the time
taken for finding d[42] (i.e., retrieving the value for key=42); for list lookup, test the time taken
for finding the index of the first occurrence of 42.
Figure 1. Example output of the program. The ratios are time taken between problem size 10x
and size x; the list sort over list lookup is time ratio between sort and lookup of the same list size.
Note: you may get a divide by 0 error when computing ratios if there are 0’s in measured time.
In your report, make sure that you analyze the results and relate them to your answer to the
question posted earlier. Do your measurements provide evidence about the time complexity of
these operations?