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 .
