Amazon Online Assessment (OA) 2021 - Storage Optimization
A company is experimenting with a flexible storage system for their warehouses. The storage unit consists of a shelving system
which is one meter deep with removable vertical and horizon separators. When all separators are installed,
each storage space is one cubic meter (1' x 1' x 1').
Determine the volume of the largest space when series of horizontal and vertical separators are removed.
Example 1:
n = 6
m = 6
h = [4]
v = [2]
Consider the diagram below. The left image depicts the initial storage unit with n = 6 horizon and m = 6 Vertical separators,
where the volume of the largest storage space is 1 x 1 x 1.
The right image depicts that unit after the fourth horizon and second vertical separators are removed.
The maximum storage volume for that unit is then 2 x 2 x 1 = 4 cubic meters:
Example 2:
Input:
n = 3
m = 3
h = [2]
v = [2]
Output: 4
Explanation:
There are n = m = 3 separators in the vertical and horizontal directions. Separators to remove are h = [2] and v = [2]. so the unit looks like this:
Return the volume of the biggest space, 4, as the answer.
Example 3:
Input:
n = 3
m = 2
h = [1, 2, 3]
v = [1, 2]
Output: 12
Explanation:
Initially there are n = 3 horizontal and m = 2 vertical separators. Remove separators h = [1, 2, 3] and v = [1,2]. so the unit looks like this:
The volume of the biggest storage space is 12 cubic meters.