My first instinct was to sort by size and greedily resolve conflicts left to right, but the cost array complicates things because you want to increment the cheaper item, not just the one that comes later.
Sort the sizes while keeping track of their costs, then use a min-heap to efficiently assign each size to the next available unique value, always choosing the cheapest increment. Alternatively, use a greedy approach with a priority queue to process sizes in ascending order and resolve conflicts by incrementing the size with the smallest cost until all are unique.
Pro tip: Clarify whether sizes can only be incremented (not decremented) and whether the cost array corresponds to the original indices; this affects the algorithm choice. Also, discuss time/space complexity trade-offs between sorting and heap-based approaches.
Confirm that sizes can only be increased, costs are per unit increment, and duplicates must be resolved. Ask about input size limits to guide algorithm selection.
Consider sorting sizes with their costs, then using a min-heap to track the cheapest available increments. Alternatively, use a greedy approach with a priority queue to process sizes in order.
Sort the pairs by size, then iterate through, maintaining a min-heap of costs for sizes that need to be incremented. For each duplicate, pop the smallest cost, increment the size, and push the cost back if still conflicting.
Discuss time complexity (O(n log n) due to sorting and heap operations) and space complexity (O(n)). Handle edge cases like all sizes identical, large gaps, and negative costs (if allowed).
Walk through a small example to verify correctness, such as sizes = [2,2,2] and costs = [1,2,3], ensuring the total cost is minimized.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.