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Grokking the Coding Interview Patterns in Python

Solution: Minimize Max Distance to Gas Station

Understand how to apply a modified binary search to minimize the maximum distance between gas stations by efficiently placing k additional stations. This lesson guides you through framing the problem as a search over continuous values, implementing a precision-based stopping criterion, and analyzing time and space complexity.

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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} ...