Minimum Circular Redistribution Cost

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.