How should I practice Minimum Circular Redistribution Cost?

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Problem · Array

Minimum Circular Redistribution Cost

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Problem statement

A warehouse has n identical containers arranged in a circle. Adjacent containers are one unit apart, and the goal is to make every container hold the same number of products.

Choose either clockwise or counterclockwise movement; all transfers must use that same direction.
Products may be collected from containers with excess units and delivered to containers with deficits.
Moving one product across one edge costs 1.

Return the minimum total transfer cost. It is guaranteed that equal redistribution is possible.

Function

findMinimumCost(products: int[]) → long

Examples

Example 1

products = [3, 4, 6, 6, 6]return = 7

Consider a circular arrangement of containers. The units in each container are products = [3, 4, 6, 6, 6].

Option 1:

Start at the 3^rd position and move clockwise. Collect one product each from the 3^rd, 4^th, and 5^th positions.

Transfer the products from:

the 5^th position to the 1^st position, the cost is 1.
the 4^th position to the 1^st position, the cost is 2.
the 3^rd position to the 2^nd position, the cost is 4.

Now each container has 5 units and the total cost is 1 + 2 + 4 = 7.

Option 2:

Start at the 5^th position moving anti-clockwise. Collect one product each from the 5^th, 4^th, and 3^rd positions.

Transfer the product from:

the 3^rd position to the 1^st position, the cost is 2.
the 4^th position to the 1^st position, the cost is 3.
the 5^th position to the 2^nd position, the cost is 3.

Now each container has 5 units and the total cost is 2 + 3 + 3 = 8. Return 7, the minimum cost achievable.

Example 2

products = [1, 11, 1, 1, 1]return = 20

The final average is 3. One container has 8 extra products. Moving in either fixed direction, send 2 products to each of the other four containers, for total cost 2*1 + 2*2 + 2*3 + 2*4 = 20.

Constraints

1 <= products.length <= 2 * 10^5
0 <= products[i] <= 10^9
The answer may exceed the 32-bit integer range.