My first instinct was greedy, just slide each tag toward the highest neighbor.
Clarify the problem constraints and edge cases, then propose a dynamic programming solution that processes cities left to right, tracking the state of the previous city's tag placement. Discuss trade-offs between time and space complexity, and consider greedy alternatives if applicable.
Pro tip: Demonstrate maturity by explicitly stating assumptions (e.g., tags can only move once, or multiple times?) and discussing how the solution scales for large n, showing awareness of Amazon's leadership principles like Customer Obsession and Dive Deep.
Ask questions to resolve ambiguities: Can tags move multiple times? Is movement simultaneous? What happens if multiple tags compete for the same city? Confirm the goal is to maximize sum of populations where tags end up.
Define DP state as dp[i][prev] where i is the current city index and prev indicates whether the previous city has a tag (0 or 1). Consider transitions based on whether the current tag moves left, stays, or moves right.
When two tags want the same city, choose the placement that yields higher revenue. This may require considering both tags' populations and possibly backtracking or using a greedy choice within the DP.
Optimize space to O(1) if possible, and analyze time complexity (likely O(n)). Discuss potential greedy or flow-based alternatives and their trade-offs.
Walk through small examples, edge cases (n=1, all tags 1, no tags 1), and verify the DP recurrence. Mention how to handle large inputs efficiently.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.