Spent the first few minutes just re-reading the constraints because I kept second-guessing whether units could move right too.
Model the problem as an optimization over cities with safety units, where each unit can cover itself or the city to its left. Use dynamic programming to decide for each unit whether to move left or stay, maximizing the sum of populations of covered cities. Consider edge cases such as multiple units covering the same city and cities with no units.
Pro tip: Clarify that each unit can move at most once and only left, and that a city is protected if at least one unit ends there. Then, discuss how to handle overlapping coverage efficiently, perhaps by precomputing prefix sums or using a greedy approach after sorting units.
Restate the problem: n cities in a row, each with a population and possibly a safety unit. Each unit can stay or move one step left, at most once. Goal: maximize total population of cities that end with at least one unit.
For each city with a unit, decide whether to keep the unit there or move it left. This decision affects coverage of the current city and the left neighbor.
Define DP state based on the current city index and whether the previous city is already covered by a unit from the right. This captures the dependency between adjacent cities.
At each city, if there is a unit, consider moving it left (covering current and left) or staying (covering current only). If no unit, coverage depends on whether a unit from the right moved left. Maximize population sum.
The DP runs in O(n) time and O(1) or O(n) space. Discuss potential greedy simplifications or edge cases like consecutive units.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.