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Solution: Minimize Max Distance to Gas Station

Explore how to solve the problem of minimizing the maximum distance between gas stations by placing additional stations. Learn to apply a modified binary search on continuous values to find the optimal placement, balance precision, and evaluate solution feasibility efficiently.

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 ...