Minimize Max Distance to Gas Station
Explore how to apply a modified binary search to minimize the largest distance between gas stations by strategically adding new stations. Understand the problem constraints, and learn how to approach this challenge to achieve precise results within defined tolerances. This lesson helps you develop algorithmic thinking for placement optimization problems often encountered in coding interviews.
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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