Task 1 :Here we're going to write Python code to process historical transaction data to implement the feature.Suppose that we are using a Python list to maintain all products purchased in different transactions:transactions = [[2, 8, 3, 6, 1, 9], [0, 5, 9], [0, 9], [4, 7, 0, 5, 9],
[8, 3], [1, 6, 3, 8], [9, 0, 5], [3, 8], [5, 7, 0, 4], [3, 1, 2, 6, 0]]Elements in each sublist represent product IDs co-purchased in a transaction.Our goal is, for each product in this tiny transaction dataset, recommend products that are most frequently purchased together with the current product.Please complete the following tasks based on the problem description.For each transaction, enumerate all pairs of products that co-occur in the corresponding sublist. For example, processing the sublist [9, 0, 5] should produce three pairs (0, 5), (0, 9), and (5, 9).Pay attention to the order of product IDs in each pair. The same product pair (e.g., product 5 and product 9) can have two different representations (i.e., (5, 9) and (9, 5)). To facilitate the subsequent processing, make sure all pairs each are represented by its ascending representation (e.g., (0, 5) rather than (5, 0)).Moreover, make sure product pairs created from the same sublist are sorted first by the 1st element and then by the 2nd element. E.g., the list of pairs created from the sublist [1, 6, 3, 8] should be presented as [(1, 3), (1, 6), (1, 8), (3, 6), (3, 8), (6, 8)].Produce a Python list, product_pairs, whose values each are a list of such pairs.The expected output of print(product_pairs) is as follows:[[(1, 2), (1, 3), (1, 6), (1, 8), (1, 9), (2, 3), (2, 6), (2, 8), (2, 9), (3, 6), (3, 8),
(3, 9), (6, 8), (6, 9), (8, 9)],
[(0, 5), (0, 9), (5, 9)],
[(0, 9)],
[(0, 4), (0, 5), (0, 7), (0, 9), (4, 5), (4, 7), (4, 9), (5, 7), (5, 9), (7, 9)],
[(3, 8)],
[(1, 3), (1, 6), (1, 8), (3, 6), (3, 8), (6, 8)],
[(0, 5), (0, 9), (5, 9)],
[(3, 8)],
[(0, 4), (0, 5), (0, 7), (4, 5), (4, 7), (5, 7)],
[(0, 1), (0, 2), (0, 3), (0, 6), (1, 2), (1, 3), (1, 6), (2, 3), (2, 6), (3, 6)]]
Full credits will be awarded only if your answer is a comprehension implemention. Loop implementations can only get at most 80% of full marks.Task 2 :Next, we will process product_pairs to create a dictionary cooccurences, whose keys are product pairs and whose values represent the number of their co-occurrences across transactions.The expected output of print(cooccurences) should look like the following (the output formatting can be different):{(0, 1): 1, (0, 2): 1, (0, 3): 1, (0, 4): 2, (0, 5): 4, (0, 6): 1, (0, 7): 2, (0, 9): 4,
(1, 2): 2, (1, 3): 3, (1, 6): 3, (1, 8): 2, (1, 9): 1,
(2, 3): 2, (2, 6): 2, (2, 8): 1, (2, 9): 1,
(3, 6): 3, (3, 8): 4, (3, 9): 1,
(4, 5): 2, (4, 7): 2, (4, 9): 1,
(5, 7): 2, (5, 9): 3,
(6, 8): 2, (6, 9): 1,
(7, 9): 1,
(8, 9): 1}Full credits will be awarded only if the order of keys in your result matches exactly that in the expected output.Task 3 :Process cooccurences to output a new dictionary recommendation whose entries each are a list of recommended products associated with the number of transactions where they were co-purchased.The expected output is as follows:{0: [(5, 4), (9, 4), (4, 2), (7, 2), (1, 1), (2, 1), (3, 1), (6, 1)],
1: [(3, 3), (6, 3), (2, 2), (8, 2), (0, 1), (9, 1)],
2: [(1, 2), (3, 2), (6, 2), (0, 1), (8, 1), (9, 1)],
3: [(8, 4), (1, 3), (6, 3), (2, 2), (0, 1), (9, 1)],
4: [(0, 2), (5, 2), (7, 2), (9, 1)],
5: [(0, 4), (9, 3), (4, 2), (7, 2)],
6: [(1, 3), (3, 3), (2, 2), (8, 2), (0, 1), (9, 1)],
7: [(0, 2), (4, 2), (5, 2), (9, 1)],
9: [(0, 4), (5, 3), (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (7, 1), (8, 1)],
8: [(3, 4), (1, 2), (6, 2), (2, 1), (9, 1)]}It means that, e.g., for product 5 (corresponding to the entry 5: [(0, 4), (9, 3), (4, 2), (7, 2)]), a list of products (i.e., product 0, 9, 4, and 7), each being represented by a tuple with the 1st element being the ID and the 2nd the number of transactions where it has appeared together with product 5, are recommended. The recommended products are also sorted in descending order by the the number of cooccurences with product 5 (i.e., the 2nd element of inner tuples).# starter codetransactions = [[2, 8, 3, 6, 1, 9], [0, 5, 9], [0, 9], [4, 7, 0, 5, 9], [8, 3], [1, 6, 3, 8], [9, 0, 5], [3, 8], [5, 7, 0, 4], [3, 1, 2, 6, 0]]
