774. Minimize Max Distance to Gas Station

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

Python Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13

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

Java Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22

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;
    }
}

C++ Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22

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;
    }
};

Go Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19

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
}