**Algorithm **

Given three groups of boxes A, B, and C of n boxes each, where the shapes of the boxes are different. The capacity of each box is measured in milliliter (ml). The list of boxes’ capacities in Group A is exactly randomly repeated in Group B and C. This means that for each box in Group A there exist a corresponding box in Group B and C that hold the same capacity, but we do not know which box would match with the other in group A, B and C.

Your mission is to find a smart way to match these boxes.

For example:

Input: capacity in milliliter

Group 1 2 3 4 5 6 7 8

A 140 120 150 100 170 200 90 180

B 170 150 140 90 100 120 180 200

C 120 90 200 150 180 140 100 170

Output:

A[1] with B[3] with C[6]

A[2] with B[6] with C[1]

A[3] with B[2] with C[4]

… and so on

a) Using a brute-force approach, design an algorithm to solve this problem, and analyze its complexity .

b) Design a more efficient algorithm to solve this problem, and analyze its complexity

c) Implement your efficient algorithm using Python .

d) Prepare a brief report comparing the two algorithms .