The retail framing threw me off at first, took a minute to realize it's basically just 'make all array elements distinct with minimum increment cost.' Once I stripped the flavor text it clicked.
Sort the dimensions and use a min-heap to track the next available unique value, ensuring each dimension is incremented to the smallest possible unique value. For each dimension in sorted order, if it's less than the next available, increment it to that value and add the cost (difference times adjustment cost); otherwise, update the next available. This greedy approach minimizes total cost because processing in sorted order and always choosing the smallest feasible increment avoids unnecessary large increments.
Pro tip: Clarify whether the adjustment cost is per unit increment and whether dimensions can be incremented beyond the maximum original value. Also, mention that sorting is safe because the cost depends only on the total increments, not on which specific dimension is incremented.
Restate the problem: given arrays of dimensions and per-unit costs, find the minimum total cost to make all dimensions unique by only incrementing. Ask clarifying questions about cost application and value bounds.
Sort the dimensions in ascending order, keeping track of their associated costs. This allows processing from smallest to largest, which is optimal for greedy assignment.
Initialize a min-heap with the smallest dimension. For each dimension in sorted order, if it's less than the heap's minimum, increment it to that value, add cost, and push the next value. Otherwise, push the dimension itself. This ensures each dimension gets the smallest available unique value.
Accumulate the cost for each increment (difference times per-unit cost) and return the total. Verify with edge cases like all dimensions equal or already unique.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.