Minimize Max Distance to Gas Station
Explore how to minimize the maximum distance between gas stations along a line by strategically adding new stations. Learn to apply modified binary search techniques to efficiently find the smallest possible maximum gap with high precision. This lesson helps you understand the problem constraints and implement a solution that balances placements to reduce travel distances.
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Statement
You are given an integer array, stations, representing the positions of existing gas stations along the x-axis. You are also given an integer k, indicating the number of additional gas stations you must add. These new gas stations can be placed at any position along the x-axis, including non-integer locations.
A penalty is the maximum distance between two adjacent gas stations after placing the k new stations. Your task is to return the smallest possible value of this penalty. An answer is correct if it is within