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Grokking the Coding Interview Patterns in Go

Solution: Minimize Max Distance to Gas Station

Explore how to minimize the largest distance between gas stations by strategically placing additional stations along a line. Learn to apply a modified binary search over a continuous range to efficiently find the smallest maximum gap, balancing precision and computational efficiency. Understand the algorithm's logic, implementation details, and the reasoning behind stopping criteria in the continuous search space.

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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 10−610^{-6} of the actual answer.

Constraints:

  • 10≤10 \leq stations.length ≤2000\leq 2000

  • 0≤0 \leq stations[i] ≤108\leq 10^8

  • The stations array is sorted in a strictly increasing order.

  • 1≤1 \leq k ≤106\leq 10^{6} ...