Model the problem as a dynamic programming or greedy problem where each guard can cover itself or the city to its left, ensuring no overlaps. Process cities from left to right, tracking the optimal coverage using DP states that represent whether the current city is protected and the position of the last guard. Alternatively, use a greedy approach with careful handling of conflicts to maximize population.
Pro tip: Clarify that the problem is equivalent to selecting a set of non-overlapping intervals (each guard covers one city) to maximize total population, and mention that a greedy strategy works if you prioritize higher populations while respecting guard movement constraints.
Restate the problem: each guard can stay or move left, no two guards can occupy the same city, and we want to maximize the sum of populations of protected cities. Identify that guards are initially placed according to the binary string.
Recognize that guards can only move left, so decisions for a city depend on guards to its right. This creates a dependency that can be resolved by processing from right to left or using DP.
Consider dynamic programming where dp[i] represents the maximum population from city i to the end, with states for whether city i is protected. Alternatively, use a greedy approach: process cities from left to right, and for each guard, decide to move left if it increases total population without conflicting with previous guards.
Ensure no two guards share a city. If multiple guards can cover the same city, choose the one that maximizes population. Also handle cases where moving left would displace another guard's coverage.
The DP solution runs in O(n) time and O(n) space. Walk through a small example to verify correctness, and discuss potential optimizations like using constant space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.