Single-direction stock rebalancing on a ring

A company keeps stock in n depots placed around a ring. Depot i is joined to depot (i + 1) % n (the clockwise neighbour) and, through the same link, to depot (i - 1 + n) % n. Depot i starts with products[i] units, and the total is a multiple of n.

Move units between neighbouring depots until every depot holds exactly sum(products) / n units. Moving one unit across one link costs 1.

There is one rule: you must pick a single direction for the whole redistribution. Either every unit travels clockwise (from i toward i + 1), or every unit travels counterclockwise (from i toward i - 1). A unit may cross several links.

Implement:

def min_redistribution_cost(products: list[int]) -> int: ...

Return the minimum total cost over the two allowed directions.

Constraints

• 1 <= n <= 10^5
• 0 <= products[i] <= 10^9
• sum(products) is divisible by n

Example 1

products = [5, 1, 3]        # target 3 each

Clockwise: depot 0 sends 2 units to depot 1. Cost 2. Counterclockwise: depot 0 must send its 2 extra units the long way round (0 -> 2 -> 1), and depot 2 passes them on, cost 4. Answer: 2.

Example 2

products = [6, 0, 0, 2]     # target 2 each

Clockwise: depot 0 sends 4 units to depot 1, which keeps 2 and passes 2 to depot 2. Cost 4 + 2 = 6. Counterclockwise costs 10. Answer: 6.

Reconstructed from the reported question; details may differ from what interviewers ask.