Choose container set with minimum total waste

Waste Reduction (Minimum Total Waste Container Set)

A pharmaceutical company prepares liquid medication for multiple patients. Each patient order has a required volume. The company can choose one “container set” to fulfill all orders. A container set contains multiple available container capacities.

Rules for fulfilling an order

For an order with requirement r using a chosen container set:

• You must pick exactly one container from the set.
• The container must be filled completely .
• If a container with capacity exactly r exists, use it (waste = 0).
• Otherwise, use the smallest container capacity c such that c >= r .
• Waste for this order is c - r .
• If a set has no container capacity >= r for any order, that container set is invalid and cannot be chosen.

Task

Given:

• requirements[] : volumes required for each order (patients)
• containerSets : a list where containerSets[i] is an array of container capacities available in set i

Compute the total waste for each valid set (sum of wastes across all orders). Return:

• The 0-based index of the container set with the minimum total waste
• If there is a tie, return the smallest index among those tied
• If no set can fulfill all orders, return -1

Input/Output

• Input: requirements (length m ), and containerSets (length s , each set has one or more capacities)
• Output: integer index of the best set, or -1

Notes / Assumptions

• Container capacities and requirements are positive integers.
• A container set may contain capacities in any order; duplicates may exist.
• Constraints can be large (e.g., up to 2e5 total capacities across all sets), so an efficient approach is expected.