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Solution: Minimize Max Distance to Gas Station

Explore how to minimize the maximum distance between gas stations by strategically placing new ones. Understand the use of binary search on continuous ranges and develop the ability to efficiently identify the smallest possible maximum gap using precision thresholds.

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 10610^{-6} of the actual answer.

Constraints:

  • 1010 ...