Question

774. Minimize Max Distance to Gas Station

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Description

You are given an integer array stations that represents the positions of the gas stations on the x-axis. You are also given an integer k.

You should add k new gas stations. You can add the stations anywhere on the x-axis, and not necessarily on an integer position.

Let penalty() be the maximum distance between adjacent gas stations after adding the k new stations.

Return _the smallest possible value of_ penalty(). Answers within 10-6 of the actual answer will be accepted.

 

Example 1:

Input: stations = [1,2,3,4,5,6,7,8,9,10], k = 9
Output: 0.50000

Example 2:

Input: stations = [23,24,36,39,46,56,57,65,84,98], k = 1
Output: 14.00000

 

Constraints:

• 10 <= stations.length <= 2000
• 0 <= stations[i] <= 108
• stations is sorted in a strictly increasing order.
• 1 <= k <= 106

Solutions

Solution 1

class Solution:
  def minmaxGasDist(self, stations: List[int], k: int) -> float:
    def check(x):
      return sum(int((b - a) / x) for a, b in pairwise(stations)) <= k

    left, right = 0, 1e8
    while right - left > 1e-6:
      mid = (left + right) / 2
      if check(mid):
        right = mid
      else:
        left = mid
    return left

class Solution {
  public double minmaxGasDist(int[] stations, int k) {
    double left = 0, right = 1e8;
    while (right - left > 1e-6) {
      double mid = (left + right) / 2.0;
      if (check(mid, stations, k)) {
        right = mid;
      } else {
        left = mid;
      }
    }
    return left;
  }

  private boolean check(double x, int[] stations, int k) {
    int s = 0;
    for (int i = 0; i < stations.length - 1; ++i) {
      s += (int) ((stations[i + 1] - stations[i]) / x);
    }
    return s <= k;
  }
}

class Solution {
public:
  double minmaxGasDist(vector<int>& stations, int k) {
    double left = 0, right = 1e8;
    auto check = [&](double x) {
      int s = 0;
      for (int i = 0; i < stations.size() - 1; ++i) {
        s += (int) ((stations[i + 1] - stations[i]) / x);
      }
      return s <= k;
    };
    while (right - left > 1e-6) {
      double mid = (left + right) / 2.0;
      if (check(mid)) {
        right = mid;
      } else {
        left = mid;
      }
    }
    return left;
  }
};

func minmaxGasDist(stations []int, k int) float64 {
  check := func(x float64) bool {
    s := 0
    for i, v := range stations[:len(stations)-1] {
      s += int(float64(stations[i+1]-v) / x)
    }
    return s <= k
  }
  var left, right float64 = 0, 1e8
  for right-left > 1e-6 {
    mid := (left + right) / 2.0
    if check(mid) {
      right = mid
    } else {
      left = mid
    }
  }
  return left
}