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Solution: Minimize Max Distance to Gas Station

Explore how to minimize the maximum distance between adjacent gas stations by strategically placing new stations. Learn to apply binary search over a continuous range to find the smallest possible maximum gap within a precise margin, enhancing your problem-solving skills for complex coding interviews.

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 ...